TSTP Solution File: COM005-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM005-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 18:05:43 EDT 2022
% Result : Unsatisfiable 0.62s 0.66s
% Output : Proof 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : COM005-1 : TPTP v8.1.0. Released v2.7.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 13:34:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.62/0.66 % SZS status Unsatisfiable
% 0.62/0.66 % SZS output start Proof
% 0.62/0.66 tff(r_type, type, (
% 0.62/0.66 r: $i > $o)).
% 0.62/0.66 tff(s_type, type, (
% 0.62/0.66 s: $i > $i)).
% 0.62/0.66 tff(a_type, type, (
% 0.62/0.66 a: $i)).
% 0.62/0.66 tff(rr_type, type, (
% 0.62/0.66 rr: $i > $o)).
% 0.62/0.66 tff(q_type, type, (
% 0.62/0.66 q: $i > $o)).
% 0.62/0.66 tff(pp_type, type, (
% 0.62/0.66 pp: $i > $o)).
% 0.62/0.66 tff(qq_type, type, (
% 0.62/0.66 qq: $i > $o)).
% 0.62/0.66 tff(qrp3_type, type, (
% 0.62/0.66 qrp3: $i > $o)).
% 0.62/0.66 tff(p_type, type, (
% 0.62/0.66 p: $i > $o)).
% 0.62/0.66 tff(ap_type, type, (
% 0.62/0.66 ap: $i > $o)).
% 0.62/0.66 tff(aq_type, type, (
% 0.62/0.66 aq: $i > $o)).
% 0.62/0.66 tff(rq_type, type, (
% 0.62/0.66 rq: $i > $o)).
% 0.62/0.66 tff(qp_type, type, (
% 0.62/0.66 qp: $i > $o)).
% 0.62/0.66 tff(ar_type, type, (
% 0.62/0.66 ar: $i > $o)).
% 0.62/0.66 tff(pqr1_type, type, (
% 0.62/0.66 pqr1: $i > $o)).
% 0.62/0.66 tff(pqr4_type, type, (
% 0.62/0.66 pqr4: $i > $o)).
% 0.62/0.66 tff(pr_type, type, (
% 0.62/0.66 pr: $i > $o)).
% 0.62/0.66 tff(pqr3_type, type, (
% 0.62/0.66 pqr3: $i > $o)).
% 0.62/0.66 tff(pqr2_type, type, (
% 0.62/0.66 pqr2: $i > $o)).
% 0.62/0.66 tff(qrp1_type, type, (
% 0.62/0.66 qrp1: $i > $o)).
% 0.62/0.66 tff(qrp2_type, type, (
% 0.62/0.66 qrp2: $i > $o)).
% 0.62/0.66 tff(qrp4_type, type, (
% 0.62/0.66 qrp4: $i > $o)).
% 0.62/0.66 tff(rpq4_type, type, (
% 0.62/0.66 rpq4: $i > $o)).
% 0.62/0.66 tff(rpq3_type, type, (
% 0.62/0.66 rpq3: $i > $o)).
% 0.62/0.66 tff(rpq1_type, type, (
% 0.62/0.66 rpq1: $i > $o)).
% 0.62/0.66 tff(rpq2_type, type, (
% 0.62/0.66 rpq2: $i > $o)).
% 0.62/0.66 tff(1,assumption,(~q(s(s(a)))), introduced(assumption)).
% 0.62/0.66 tff(2,assumption,(~r(s(s(a)))), introduced(assumption)).
% 0.62/0.66 tff(3,assumption,(~r(s(s(s(a))))), introduced(assumption)).
% 0.62/0.66 tff(4,assumption,(~p(s(a))), introduced(assumption)).
% 0.62/0.66 tff(5,plain,
% 0.62/0.66 (^[X: $i] : refl(((~ap(X)) | aq(s(X))) <=> ((~ap(X)) | aq(s(X))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(6,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | aq(s(X))) <=> ![X: $i] : ((~ap(X)) | aq(s(X)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[5])).
% 0.62/0.66 tff(7,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | aq(s(X))) <=> ![X: $i] : ((~ap(X)) | aq(s(X)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(8,axiom,(![X: $i] : ((~ap(X)) | aq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c092')).
% 0.62/0.66 tff(9,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | aq(s(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.62/0.66 tff(10,plain,(
% 0.62/0.66 ![X: $i] : ((~ap(X)) | aq(s(X)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[9])).
% 0.62/0.66 tff(11,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | aq(s(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.62/0.66 tff(12,plain,
% 0.62/0.66 (ap(a) <=> ap(a)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(13,axiom,(ap(a)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c001')).
% 0.62/0.66 tff(14,plain,
% 0.62/0.66 (ap(a)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.62/0.66 tff(15,plain,
% 0.62/0.66 (((~![X: $i] : ((~ap(X)) | aq(s(X)))) | ((~ap(a)) | aq(s(a)))) <=> ((~![X: $i] : ((~ap(X)) | aq(s(X)))) | (~ap(a)) | aq(s(a)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(16,plain,
% 0.62/0.66 ((~![X: $i] : ((~ap(X)) | aq(s(X)))) | ((~ap(a)) | aq(s(a)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(17,plain,
% 0.62/0.66 ((~![X: $i] : ((~ap(X)) | aq(s(X)))) | (~ap(a)) | aq(s(a))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.62/0.66 tff(18,plain,
% 0.62/0.66 (aq(s(a))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[17, 14, 11])).
% 0.62/0.66 tff(19,plain,
% 0.62/0.66 (^[X: $i] : refl(((~ap(X)) | (~aq(X))) <=> ((~ap(X)) | (~aq(X))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(20,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | (~aq(X))) <=> ![X: $i] : ((~ap(X)) | (~aq(X)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[19])).
% 0.62/0.66 tff(21,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | (~aq(X))) <=> ![X: $i] : ((~ap(X)) | (~aq(X)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(22,axiom,(![X: $i] : ((~ap(X)) | (~aq(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c002')).
% 0.62/0.66 tff(23,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | (~aq(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.62/0.66 tff(24,plain,(
% 0.62/0.66 ![X: $i] : ((~ap(X)) | (~aq(X)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[23])).
% 0.62/0.66 tff(25,plain,
% 0.62/0.66 (![X: $i] : ((~ap(X)) | (~aq(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.62/0.66 tff(26,plain,
% 0.62/0.66 (((~![X: $i] : ((~ap(X)) | (~aq(X)))) | ((~ap(s(a))) | (~aq(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | (~aq(X)))) | (~ap(s(a))) | (~aq(s(a))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(27,plain,
% 0.62/0.66 ((~![X: $i] : ((~ap(X)) | (~aq(X)))) | ((~ap(s(a))) | (~aq(s(a))))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(28,plain,
% 0.62/0.66 ((~![X: $i] : ((~ap(X)) | (~aq(X)))) | (~ap(s(a))) | (~aq(s(a)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.62/0.66 tff(29,plain,
% 0.62/0.66 (~ap(s(a))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 0.62/0.66 tff(30,plain,
% 0.62/0.66 (^[X: $i] : refl((ap(X) | p(X) | (~p(s(X)))) <=> (ap(X) | p(X) | (~p(s(X)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(31,plain,
% 0.62/0.66 (![X: $i] : (ap(X) | p(X) | (~p(s(X)))) <=> ![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[30])).
% 0.62/0.66 tff(32,plain,
% 0.62/0.66 (![X: $i] : (ap(X) | p(X) | (~p(s(X)))) <=> ![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(33,plain,
% 0.62/0.66 (^[X: $i] : rewrite(((ap(X) | p(X)) | (~p(s(X)))) <=> (ap(X) | p(X) | (~p(s(X)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(34,plain,
% 0.62/0.66 (![X: $i] : ((ap(X) | p(X)) | (~p(s(X)))) <=> ![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[33])).
% 0.62/0.66 tff(35,axiom,(![X: $i] : ((ap(X) | p(X)) | (~p(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c263')).
% 0.62/0.66 tff(36,plain,
% 0.62/0.66 (![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.62/0.66 tff(37,plain,
% 0.62/0.66 (![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.62/0.66 tff(38,plain,(
% 0.62/0.66 ![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(skolemize,[status(sab)],[37])).
% 0.62/0.66 tff(39,plain,
% 0.62/0.66 (![X: $i] : (ap(X) | p(X) | (~p(s(X))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[38, 31])).
% 0.62/0.66 tff(40,plain,
% 0.62/0.66 (((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | (ap(s(a)) | p(s(a)) | (~p(s(s(a)))))) <=> ((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | ap(s(a)) | p(s(a)) | (~p(s(s(a)))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(41,plain,
% 0.62/0.66 ((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | (ap(s(a)) | p(s(a)) | (~p(s(s(a)))))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(42,plain,
% 0.62/0.66 ((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | ap(s(a)) | p(s(a)) | (~p(s(s(a))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.62/0.66 tff(43,plain,
% 0.62/0.66 (p(s(a)) | (~p(s(s(a))))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[42, 39, 29])).
% 0.62/0.66 tff(44,plain,
% 0.62/0.66 (~p(s(s(a)))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[43, 4])).
% 0.62/0.66 tff(45,assumption,(~r(s(a))), introduced(assumption)).
% 0.62/0.66 tff(46,plain,
% 0.62/0.66 (^[X: $i] : refl(((~aq(X)) | p(X) | r(X) | q(X) | q(s(X))) <=> ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(47,plain,
% 0.62/0.66 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[46])).
% 0.62/0.66 tff(48,plain,
% 0.62/0.66 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(49,plain,
% 0.62/0.66 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~aq(X)) | p(X)) <=> ((~aq(X)) | p(X))), ((((~aq(X)) | p(X)) | q(X)) <=> (((~aq(X)) | p(X)) | q(X)))), rewrite((((~aq(X)) | p(X)) | q(X)) <=> ((~aq(X)) | p(X) | q(X))), ((((~aq(X)) | p(X)) | q(X)) <=> ((~aq(X)) | p(X) | q(X)))), (((((~aq(X)) | p(X)) | q(X)) | r(X)) <=> (((~aq(X)) | p(X) | q(X)) | r(X)))), rewrite((((~aq(X)) | p(X) | q(X)) | r(X)) <=> ((~aq(X)) | p(X) | r(X) | q(X))), (((((~aq(X)) | p(X)) | q(X)) | r(X)) <=> ((~aq(X)) | p(X) | r(X) | q(X)))), ((((((~aq(X)) | p(X)) | q(X)) | r(X)) | q(s(X))) <=> (((~aq(X)) | p(X) | r(X) | q(X)) | q(s(X))))), rewrite((((~aq(X)) | p(X) | r(X) | q(X)) | q(s(X))) <=> ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))), ((((((~aq(X)) | p(X)) | q(X)) | r(X)) | q(s(X))) <=> ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(50,plain,
% 0.62/0.66 (![X: $i] : (((((~aq(X)) | p(X)) | q(X)) | r(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[49])).
% 0.62/0.66 tff(51,axiom,(![X: $i] : (((((~aq(X)) | p(X)) | q(X)) | r(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c095')).
% 0.62/0.66 tff(52,plain,
% 0.62/0.66 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.62/0.66 tff(53,plain,
% 0.62/0.66 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.62/0.66 tff(54,plain,(
% 0.62/0.66 ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[53])).
% 0.62/0.66 tff(55,plain,
% 0.62/0.66 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.62/0.66 tff(56,plain,
% 0.62/0.66 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | (p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(57,plain,
% 0.62/0.66 (((~aq(s(a))) | p(s(a)) | r(s(a)) | q(s(a)) | q(s(s(a)))) <=> (p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(58,plain,
% 0.62/0.66 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | q(s(a)) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | (p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a)))))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[57])).
% 0.62/0.66 tff(59,plain,
% 0.62/0.66 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | q(s(a)) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a))))),
% 0.62/0.66 inference(transitivity,[status(thm)],[58, 56])).
% 0.62/0.66 tff(60,plain,
% 0.62/0.66 ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | q(s(a)) | q(s(s(a))))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(61,plain,
% 0.62/0.66 ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | q(s(X)))) | p(s(a)) | (~aq(s(a))) | q(s(a)) | r(s(a)) | q(s(s(a)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.62/0.66 tff(62,plain,
% 0.62/0.66 (p(s(a)) | q(s(a)) | r(s(a)) | q(s(s(a)))),
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% 0.62/0.66 tff(69,axiom,(![X: $i] : (((((~aq(X)) | p(X)) | (~q(X))) | r(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c097')).
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% 0.62/0.66 tff(87,axiom,(![X: $i] : ((~aq(X)) | (~ar(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c004')).
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% 0.62/0.66 tff(100,axiom,(![X: $i] : ((ar(X) | (~r(X))) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c206')).
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% 0.62/0.66 tff(126,axiom,(![X: $i] : (((((~ar(X)) | q(X)) | (~r(X))) | p(X)) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c155')).
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% 0.62/0.66 inference(rewrite,[status(thm)],[])).
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% 0.62/0.66 inference(monotonicity,[status(thm)],[132])).
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% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.66 inference(modus_ponens,[status(thm)],[135, 134])).
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% 0.62/0.66 inference(unit_resolution,[status(thm)],[136, 130, 120])).
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% 0.62/0.66 inference(quant_intro,[status(thm)],[139])).
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% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(142,axiom,(![X: $i] : ((~ar(X)) | ap(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c094')).
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% 0.62/0.66 inference(skolemize,[status(sab)],[143])).
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% 0.62/0.66 inference(modus_ponens,[status(thm)],[144, 140])).
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% 0.62/0.67 inference(rewrite,[status(thm)],[])).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[147, 146])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[148, 145, 120])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[150])).
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% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(153,axiom,(![X: $i] : ((~ap(X)) | (~ar(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c003')).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[153, 152])).
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% 0.62/0.67 inference(skolemize,[status(sab)],[154])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[155, 151])).
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% 0.62/0.67 inference(rewrite,[status(thm)],[])).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[158, 157])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[159, 156, 149])).
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% 0.62/0.67 inference(rewrite,[status(thm)],[])).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[162, 161])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[163, 104, 160])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[164, 138])).
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% 0.62/0.67 inference(rewrite,[status(thm)],[])).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[167, 166])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[168, 156, 120])).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[171, 170])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[172, 39, 169])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[173, 44])).
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% 0.62/0.67 tff(176,assumption,(~qq(s(s(a)))), introduced(assumption)).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[181])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[184])).
% 0.62/0.67 tff(186,axiom,(![X: $i] : ((aq(X) | qq(X)) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c149')).
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% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.67 inference(unit_resolution,[status(thm)],[193, 190, 180])).
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% 0.62/0.67 tff(213,assumption,(~p(s(s(s(a))))), introduced(assumption)).
% 0.62/0.67 tff(214,assumption,(r(s(s(s(a))))), introduced(assumption)).
% 0.62/0.67 tff(215,assumption,(~q(s(s(s(a))))), introduced(assumption)).
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% 0.62/0.67 inference(bind,[status(th)],[])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[219])).
% 0.62/0.67 tff(221,axiom,(![X: $i] : (((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c238')).
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% 0.62/0.67 inference(skolemize,[status(sab)],[223])).
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% 0.62/0.67 tff(239,axiom,(![X: $i] : (((((((~ap(X)) | (~r(X))) | p(X)) | pp(X)) | q(X)) | qq(X)) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c228')).
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% 0.62/0.67 inference(bind,[status(th)],[])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[254])).
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% 0.62/0.67 inference(bind,[status(th)],[])).
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% 0.62/0.67 inference(quant_intro,[status(thm)],[257])).
% 0.62/0.67 tff(259,axiom,(![X: $i] : ((((((((~ap(X)) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c255')).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[259, 258])).
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% 0.62/0.67 inference(modus_ponens,[status(thm)],[260, 256])).
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% 0.62/0.67 inference(skolemize,[status(sab)],[261])).
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% 0.62/0.68 (r(a) | (~r(s(a)))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[308, 305, 295])).
% 0.62/0.68 tff(310,plain,
% 0.62/0.68 (r(a)),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[309, 83])).
% 0.62/0.68 tff(311,plain,
% 0.62/0.68 (qq(s(s(a)))),
% 0.62/0.68 inference(unit_resolution,[status(thm)],[194, 253])).
% 0.62/0.68 tff(312,assumption,(qq(s(s(a)))), introduced(assumption)).
% 0.62/0.68 tff(313,assumption,(~q(s(a))), introduced(assumption)).
% 0.62/0.68 tff(314,assumption,(pp(s(a))), introduced(assumption)).
% 0.62/0.68 tff(315,plain,
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% 0.62/0.68 inference(bind,[status(th)],[])).
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% 0.62/0.68 inference(quant_intro,[status(thm)],[315])).
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% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(319,plain,
% 0.62/0.68 (![X: $i] : (((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~r(X))) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[318])).
% 0.62/0.68 tff(320,axiom,(![X: $i] : (((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~r(X))) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c106')).
% 0.62/0.68 tff(321,plain,
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% 0.62/0.68 inference(modus_ponens,[status(thm)],[320, 319])).
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% 0.62/0.68 inference(modus_ponens,[status(thm)],[321, 317])).
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% 0.62/0.68 ![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.62/0.68 inference(skolemize,[status(sab)],[322])).
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% 0.62/0.68 inference(modus_ponens,[status(thm)],[323, 316])).
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% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(326,plain,
% 0.62/0.68 (((~aq(s(a))) | p(s(a)) | q(s(a)) | (~qq(s(a))) | (~r(s(a))) | (~pp(s(a))) | (~qq(s(s(a))))) <=> (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(327,plain,
% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | q(s(a)) | (~qq(s(a))) | (~r(s(a))) | (~pp(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a)))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[326])).
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% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | q(s(a)) | (~qq(s(a))) | (~r(s(a))) | (~pp(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.62/0.68 inference(transitivity,[status(thm)],[327, 325])).
% 0.62/0.68 tff(329,plain,
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% 0.62/0.68 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.68 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.62/0.68 tff(331,plain,
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% 0.62/0.68 inference(unit_resolution,[status(thm)],[330, 324, 18])).
% 0.62/0.68 tff(332,plain,
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% 0.62/0.68 tff(333,plain,
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% 0.62/0.68 inference(bind,[status(th)],[])).
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% 0.62/0.68 inference(quant_intro,[status(thm)],[333])).
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% 0.62/0.68 inference(bind,[status(th)],[])).
% 0.62/0.68 tff(337,plain,
% 0.62/0.68 (![X: $i] : ((((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))),
% 0.62/0.68 inference(quant_intro,[status(thm)],[336])).
% 0.62/0.68 tff(338,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c135')).
% 0.62/0.68 tff(339,plain,
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% 0.62/0.68 inference(modus_ponens,[status(thm)],[338, 337])).
% 0.62/0.68 tff(340,plain,
% 0.62/0.68 (![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[339, 335])).
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% 0.62/0.68 ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))),
% 0.62/0.68 inference(skolemize,[status(sab)],[340])).
% 0.62/0.68 tff(342,plain,
% 0.62/0.68 (![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))),
% 0.62/0.68 inference(modus_ponens,[status(thm)],[341, 334])).
% 0.62/0.68 tff(343,plain,
% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | q(s(s(a))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(344,plain,
% 0.62/0.68 (((~aq(s(a))) | p(s(a)) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | (~pp(s(a))) | q(s(s(a)))) <=> (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | q(s(s(a))))),
% 0.62/0.68 inference(rewrite,[status(thm)],[])).
% 0.62/0.68 tff(345,plain,
% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | (~pp(s(a))) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | (p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | q(s(s(a)))))),
% 0.62/0.68 inference(monotonicity,[status(thm)],[344])).
% 0.62/0.68 tff(346,plain,
% 0.62/0.68 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | (~pp(s(a))) | q(s(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | p(s(a)) | (~pp(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | q(s(s(a))))),
% 0.62/0.68 inference(transitivity,[status(thm)],[345, 343])).
% 0.62/0.68 tff(347,plain,
% 0.62/0.68 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(a))) | p(s(a)) | q(s(a)) | qq(s(a)) | rr(s(a)) | (~r(s(a))) | (~pp(s(a))) | q(s(s(a))))),
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.62/0.69 tff(458,plain,
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.62/0.69 tff(459,plain,(
% 0.62/0.69 ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))),
% 0.62/0.69 inference(skolemize,[status(sab)],[458])).
% 0.62/0.69 tff(460,plain,
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.62/0.69 tff(461,plain,
% 0.62/0.69 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(462,plain,
% 0.62/0.69 (((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))) <=> (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(463,plain,
% 0.62/0.69 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))))),
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% 0.62/0.69 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
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% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[467, 446, 445, 444, 443, 442, 441])).
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% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[471, 116, 450])).
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% 0.62/0.69 inference(quant_inst,[status(thm)],[])).
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.62/0.69 tff(476,plain,
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[475, 90, 472])).
% 0.62/0.69 tff(477,plain,
% 0.62/0.69 (^[X: $i] : refl((aq(X) | (~qq(X)) | qq(s(X))) <=> (aq(X) | (~qq(X)) | qq(s(X))))),
% 0.62/0.69 inference(bind,[status(th)],[])).
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% 0.62/0.69 inference(quant_intro,[status(thm)],[477])).
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% 0.62/0.69 inference(rewrite,[status(thm)],[])).
% 0.62/0.69 tff(480,plain,
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% 0.62/0.69 inference(bind,[status(th)],[])).
% 0.62/0.69 tff(481,plain,
% 0.62/0.69 (![X: $i] : ((aq(X) | (~qq(X))) | qq(s(X))) <=> ![X: $i] : (aq(X) | (~qq(X)) | qq(s(X)))),
% 0.62/0.69 inference(quant_intro,[status(thm)],[480])).
% 0.62/0.69 tff(482,axiom,(![X: $i] : ((aq(X) | (~qq(X))) | qq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c150')).
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% 0.62/0.69 tff(484,plain,
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.62/0.69 tff(485,plain,(
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% 0.62/0.69 inference(skolemize,[status(sab)],[484])).
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[485, 478])).
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[489, 486, 476])).
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[490, 468])).
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% 0.62/0.69 inference(modus_ponens,[status(thm)],[521, 517])).
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% 0.62/0.69 inference(unit_resolution,[status(thm)],[525, 522, 504])).
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% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(782,plain,
% 0.68/0.72 (![X: $i] : ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | rr(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | rr(s(X)))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[781])).
% 0.68/0.72 tff(783,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c200')).
% 0.68/0.72 tff(784,plain,
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% 0.68/0.72 tff(785,plain,
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% 0.68/0.72 tff(786,plain,(
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% 0.68/0.72 tff(787,plain,
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% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(789,plain,
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% 0.68/0.72 inference(rewrite,[status(thm)],[])).
% 0.68/0.72 tff(790,plain,
% 0.68/0.72 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | rr(s(X)))) | ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.68/0.72 inference(monotonicity,[status(thm)],[789])).
% 0.68/0.72 tff(791,plain,
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% 0.68/0.72 inference(transitivity,[status(thm)],[790, 788])).
% 0.68/0.72 tff(792,plain,
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% 0.68/0.72 inference(quant_inst,[status(thm)],[])).
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% 0.68/0.72 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.68/0.72 tff(794,plain,
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% 0.68/0.72 inference(unit_resolution,[status(thm)],[793, 787, 695])).
% 0.68/0.72 tff(795,plain,
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% 0.68/0.72 inference(unit_resolution,[status(thm)],[794, 758, 748, 777, 772, 721, 691])).
% 0.68/0.72 tff(796,plain,
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% 0.68/0.72 inference(bind,[status(th)],[])).
% 0.68/0.72 tff(797,plain,
% 0.68/0.72 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X)))) <=> ![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))),
% 0.68/0.72 inference(quant_intro,[status(thm)],[796])).
% 0.68/0.72 tff(798,plain,
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% 0.68/0.72 inference(rewrite,[status(thm)],[])).
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% 0.68/0.72 inference(bind,[status(th)],[])).
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% 0.68/0.72 tff(801,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | (~r(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c199')).
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% 0.68/0.72 inference(modus_ponens,[status(thm)],[804, 797])).
% 0.68/0.72 tff(806,plain,
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% 0.68/0.73 inference(monotonicity,[status(thm)],[807])).
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% 0.68/0.73 inference(quant_inst,[status(thm)],[])).
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% 0.68/0.73 inference(modus_ponens,[status(thm)],[810, 809])).
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% 0.68/0.73 inference(unit_resolution,[status(thm)],[812, 758, 748, 777, 772, 721, 691])).
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% 0.68/0.73 inference(unit_resolution,[status(thm)],[816, 145, 695])).
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% 0.68/0.73 inference(bind,[status(th)],[])).
% 0.68/0.73 tff(819,plain,
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% 0.68/0.73 inference(monotonicity,[status(thm)],[829])).
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% 0.68/0.76 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((pqr1(X) | pqr2(X)) | pqr3(X)) <=> (pqr1(X) | pqr2(X) | pqr3(X))), ((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) <=> ((pqr1(X) | pqr2(X) | pqr3(X)) | pqr4(X)))), rewrite(((pqr1(X) | pqr2(X) | pqr3(X)) | pqr4(X)) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X))), ((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X)))), (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) <=> ((pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X)) | (~pr(X))))), rewrite(((pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X)) | (~pr(X))) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)))), (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X))))), ((((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) | pr(s(X))) <=> ((pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X))) | pr(s(X))))), rewrite(((pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X))) | pr(s(X))) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))), ((((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) | pr(s(X))) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))))),
% 0.68/0.76 inference(bind,[status(th)],[])).
% 0.68/0.76 tff(1164,plain,
% 0.68/0.76 (![X: $i] : (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) | pr(s(X))) <=> ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))),
% 0.68/0.76 inference(quant_intro,[status(thm)],[1163])).
% 0.68/0.76 tff(1165,axiom,(![X: $i] : (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | (~pr(X))) | pr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c151')).
% 0.68/0.76 tff(1166,plain,
% 0.68/0.76 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1165, 1164])).
% 0.68/0.76 tff(1167,plain,
% 0.68/0.76 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1166, 1162])).
% 0.68/0.76 tff(1168,plain,(
% 0.68/0.76 ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))),
% 0.68/0.76 inference(skolemize,[status(sab)],[1167])).
% 0.68/0.76 tff(1169,plain,
% 0.68/0.76 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1168, 1161])).
% 0.68/0.76 tff(1170,plain,
% 0.68/0.76 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr3(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr3(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1171,plain,
% 0.68/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr3(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(1172,plain,
% 0.68/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr3(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1171, 1170])).
% 0.68/0.76 tff(1173,plain,
% 0.68/0.76 (pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1172, 1169, 1159, 1158, 1152, 1138, 1134])).
% 0.68/0.76 tff(1174,assumption,(~pqr4(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1175,assumption,(~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1176,assumption,(~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1177,assumption,(~pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1178,assumption,(pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1179,assumption,(~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 0.68/0.76 tff(1180,plain,
% 0.68/0.76 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.68/0.76 inference(rewrite,[status(thm)],[])).
% 0.68/0.76 tff(1181,plain,
% 0.68/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.68/0.76 inference(quant_inst,[status(thm)],[])).
% 0.68/0.76 tff(1182,plain,
% 0.68/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.68/0.76 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 0.68/0.76 tff(1183,plain,
% 0.68/0.76 ($false),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1182, 1169, 1179, 1178, 1177, 1176, 1175, 1174])).
% 0.68/0.76 tff(1184,plain,(pr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.68/0.76 tff(1185,plain,
% 0.68/0.76 (pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.68/0.76 inference(unit_resolution,[status(thm)],[1184, 1173, 1130, 1116, 1102, 1088])).
% 0.68/0.76 tff(1186,plain,
% 0.68/0.76 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1187,plain,
% 0.74/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.76 inference(quant_inst,[status(thm)],[])).
% 0.74/0.76 tff(1188,plain,
% 0.74/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.74/0.76 tff(1189,plain,
% 0.74/0.76 (pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[1188, 1169, 1185, 1075, 1064, 1053, 1049])).
% 0.74/0.76 tff(1190,plain,
% 0.74/0.76 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1191,plain,
% 0.74/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.76 inference(quant_inst,[status(thm)],[])).
% 0.74/0.76 tff(1192,plain,
% 0.74/0.76 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1191, 1190])).
% 0.74/0.76 tff(1193,plain,
% 0.74/0.76 (pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.76 inference(unit_resolution,[status(thm)],[1192, 1169, 1189, 1045, 1034, 1005, 904])).
% 0.74/0.76 tff(1194,plain,
% 0.74/0.76 (^[X: $i] : refl(((~qrp1(X)) | (~rr(X))) <=> ((~qrp1(X)) | (~rr(X))))),
% 0.74/0.76 inference(bind,[status(th)],[])).
% 0.74/0.76 tff(1195,plain,
% 0.74/0.76 (![X: $i] : ((~qrp1(X)) | (~rr(X))) <=> ![X: $i] : ((~qrp1(X)) | (~rr(X)))),
% 0.74/0.76 inference(quant_intro,[status(thm)],[1194])).
% 0.74/0.76 tff(1196,plain,
% 0.74/0.76 (![X: $i] : ((~qrp1(X)) | (~rr(X))) <=> ![X: $i] : ((~qrp1(X)) | (~rr(X)))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1197,axiom,(![X: $i] : ((~qrp1(X)) | (~rr(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c037')).
% 0.74/0.76 tff(1198,plain,
% 0.74/0.76 (![X: $i] : ((~qrp1(X)) | (~rr(X)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1197, 1196])).
% 0.74/0.76 tff(1199,plain,(
% 0.74/0.76 ![X: $i] : ((~qrp1(X)) | (~rr(X)))),
% 0.74/0.76 inference(skolemize,[status(sab)],[1198])).
% 0.74/0.76 tff(1200,plain,
% 0.74/0.76 (![X: $i] : ((~qrp1(X)) | (~rr(X)))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.74/0.76 tff(1201,plain,
% 0.74/0.76 (((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.76 inference(rewrite,[status(thm)],[])).
% 0.74/0.76 tff(1202,plain,
% 0.74/0.76 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.76 inference(quant_inst,[status(thm)],[])).
% 0.74/0.76 tff(1203,plain,
% 0.74/0.76 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.76 inference(modus_ponens,[status(thm)],[1202, 1201])).
% 0.74/0.76 tff(1204,plain,
% 0.74/0.76 (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
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% 0.74/0.77 inference(quant_intro,[status(thm)],[1347])).
% 0.74/0.77 tff(1349,axiom,(![X: $i] : ((~qrp4(X)) | ar(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c061')).
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% 0.74/0.77 inference(modus_ponens,[status(thm)],[1352, 1345])).
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% 0.74/0.77 tff(1361,plain,
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% 0.74/0.77 inference(unit_resolution,[status(thm)],[1360, 1200, 938])).
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% 0.74/0.77 inference(quant_intro,[status(thm)],[1362])).
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% 0.74/0.77 inference(quant_intro,[status(thm)],[1365])).
% 0.74/0.77 tff(1367,axiom,(![X: $i] : ((~qrp2(X)) | r(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c043')).
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% 0.74/0.77 inference(modus_ponens,[status(thm)],[1368, 1364])).
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% 0.74/0.77 inference(modus_ponens,[status(thm)],[1370, 1363])).
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% 0.74/0.77 inference(quant_intro,[status(thm)],[1383])).
% 0.74/0.77 tff(1385,axiom,(![X: $i] : ((~qrp4(X)) | r(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c057')).
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% 0.74/0.77 inference(modus_ponens,[status(thm)],[1391, 1390])).
% 0.74/0.77 tff(1393,plain,
% 0.74/0.77 (~qrp4(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.77 inference(unit_resolution,[status(thm)],[1392, 1389, 923])).
% 0.74/0.77 tff(1394,assumption,(qp(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
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% 0.74/0.77 inference(bind,[status(th)],[])).
% 0.74/0.77 tff(1399,plain,
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% 0.74/0.77 tff(1400,axiom,(![X: $i] : (((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | (~qp(X))) | qp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c209')).
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% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1438,plain,
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% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1439,plain,
% 0.74/0.78 ((~![X: $i] : (aq(X) | (~q(X)) | q(s(X)))) | aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1438, 1437])).
% 0.74/0.78 tff(1440,plain,
% 0.74/0.78 (q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1439, 544, 973, 1432])).
% 0.74/0.78 tff(1441,plain,
% 0.74/0.78 (((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (ap(X) | p(X) | (~p(s(X))))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1442,plain,
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% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
% 0.74/0.78 tff(1443,plain,
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% 0.74/0.78 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 0.74/0.78 tff(1444,plain,
% 0.74/0.78 (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.74/0.78 inference(unit_resolution,[status(thm)],[1443, 39, 918, 1424])).
% 0.74/0.78 tff(1445,plain,
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% 0.74/0.78 inference(bind,[status(th)],[])).
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% 0.74/0.78 inference(quant_intro,[status(thm)],[1445])).
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% 0.74/0.78 inference(quant_intro,[status(thm)],[1448])).
% 0.74/0.78 tff(1450,axiom,(![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | rq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c253')).
% 0.74/0.78 tff(1451,plain,
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% 0.74/0.78 inference(modus_ponens,[status(thm)],[1450, 1449])).
% 0.74/0.78 tff(1452,plain,
% 0.74/0.78 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1451, 1447])).
% 0.74/0.78 tff(1453,plain,(
% 0.74/0.78 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))),
% 0.74/0.78 inference(skolemize,[status(sab)],[1452])).
% 0.74/0.78 tff(1454,plain,
% 0.74/0.78 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1453, 1446])).
% 0.74/0.78 tff(1455,plain,
% 0.74/0.78 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1456,plain,
% 0.74/0.78 ((pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> (r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.78 inference(rewrite,[status(thm)],[])).
% 0.74/0.78 tff(1457,plain,
% 0.74/0.78 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))))),
% 0.74/0.78 inference(monotonicity,[status(thm)],[1456])).
% 0.74/0.78 tff(1458,plain,
% 0.74/0.78 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.78 inference(transitivity,[status(thm)],[1457, 1455])).
% 0.74/0.78 tff(1459,plain,
% 0.74/0.78 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 0.74/0.78 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.78 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 0.74/0.78 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.74/0.78 tff(1461,plain,
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% 0.74/0.78 tff(1462,plain,
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% 0.74/0.78 inference(unit_resolution,[status(thm)],[1461, 1444, 1440, 1436, 1428])).
% 0.74/0.78 tff(1463,plain,
% 0.74/0.78 (^[X: $i] : refl(((~pr(X)) | (~rq(X)) | (~qp(X))) <=> ((~pr(X)) | (~rq(X)) | (~qp(X))))),
% 0.74/0.78 inference(bind,[status(th)],[])).
% 0.74/0.78 tff(1464,plain,
% 0.74/0.78 (![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X))) <=> ![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))),
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% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1530,plain,
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% 0.74/0.79 inference(modus_ponens,[status(thm)],[1529, 1528])).
% 0.74/0.79 tff(1531,plain,
% 0.74/0.79 (pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1530, 1169])).
% 0.74/0.79 tff(1532,plain,
% 0.74/0.79 ((~pr(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1531, 1527, 1513, 1509, 1495])).
% 0.74/0.79 tff(1533,plain,
% 0.74/0.79 (~pr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1532, 1481])).
% 0.74/0.79 tff(1534,plain,
% 0.74/0.79 (^[X: $i] : refl(((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X))) <=> ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X))))),
% 0.74/0.79 inference(bind,[status(th)],[])).
% 0.74/0.79 tff(1535,plain,
% 0.74/0.79 (![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))),
% 0.74/0.79 inference(quant_intro,[status(thm)],[1534])).
% 0.74/0.79 tff(1536,plain,
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% 0.74/0.79 inference(rewrite,[status(thm)],[])).
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% 0.74/0.79 inference(bind,[status(th)],[])).
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% 0.74/0.79 (![X: $i] : ((((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | pr(s(X))) <=> ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))),
% 0.74/0.79 inference(quant_intro,[status(thm)],[1537])).
% 0.74/0.79 tff(1539,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | pr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c137')).
% 0.74/0.79 tff(1540,plain,
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% 0.74/0.79 inference(modus_ponens,[status(thm)],[1539, 1538])).
% 0.74/0.79 tff(1541,plain,
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% 0.74/0.79 inference(modus_ponens,[status(thm)],[1540, 1536])).
% 0.74/0.79 tff(1542,plain,(
% 0.74/0.79 ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))),
% 0.74/0.79 inference(skolemize,[status(sab)],[1541])).
% 0.74/0.79 tff(1543,plain,
% 0.74/0.79 (![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))),
% 0.74/0.79 inference(modus_ponens,[status(thm)],[1542, 1535])).
% 0.74/0.79 tff(1544,plain,
% 0.74/0.79 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))),
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% 0.74/0.79 tff(1545,plain,
% 0.74/0.79 (((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | pr(s(s(s(s(s(a))))))) <=> (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))),
% 0.74/0.79 inference(rewrite,[status(thm)],[])).
% 0.74/0.79 tff(1546,plain,
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% 0.74/0.79 inference(monotonicity,[status(thm)],[1545])).
% 0.74/0.79 tff(1547,plain,
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% 0.74/0.79 inference(transitivity,[status(thm)],[1546, 1544])).
% 0.74/0.79 tff(1548,plain,
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% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1549,plain,
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% 0.74/0.79 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 0.74/0.79 tff(1550,plain,
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% 0.74/0.79 inference(unit_resolution,[status(thm)],[1549, 1543, 450])).
% 0.74/0.79 tff(1551,plain,
% 0.74/0.79 (pr(s(s(s(s(s(a))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1550, 446, 445, 444, 443, 442, 441])).
% 0.74/0.79 tff(1552,plain,
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% 0.74/0.79 tff(1554,plain,
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% 0.74/0.79 tff(1555,plain,
% 0.74/0.79 (~pqr1(s(s(s(s(s(a))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1554, 1491, 476])).
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% 0.74/0.79 tff(1559,plain,
% 0.74/0.79 (~pqr4(s(s(s(s(s(a))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1558, 1505, 476])).
% 0.74/0.79 tff(1560,plain,
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% 0.74/0.79 inference(rewrite,[status(thm)],[])).
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% 0.74/0.79 inference(quant_inst,[status(thm)],[])).
% 0.74/0.79 tff(1562,plain,
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% 0.74/0.79 inference(modus_ponens,[status(thm)],[1561, 1560])).
% 0.74/0.79 tff(1563,plain,
% 0.74/0.79 (~pqr3(s(s(s(s(s(a))))))),
% 0.74/0.79 inference(unit_resolution,[status(thm)],[1562, 900, 476])).
% 0.74/0.79 tff(1564,plain,
% 0.74/0.79 (((~![X: $i] : (aq(X) | (~pqr2(X)))) | (aq(s(s(s(s(s(a)))))) | (~pqr2(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (aq(X) | (~pqr2(X)))) | aq(s(s(s(s(s(a)))))) | (~pqr2(s(s(s(s(s(a))))))))),
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% 0.74/0.79 tff(1567,plain,
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% 0.74/0.79 inference(unit_resolution,[status(thm)],[1566, 1523, 476])).
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% 0.74/0.79 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | (pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | (~pr(X)) | pr(s(X)))) | pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))))),
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% 0.74/0.80 tff(1666,plain,
% 0.74/0.80 (![X: $i] : ((ap(X) | (~p(X))) | p(s(X))) <=> ![X: $i] : (ap(X) | (~p(X)) | p(s(X)))),
% 0.74/0.80 inference(quant_intro,[status(thm)],[1665])).
% 0.74/0.80 tff(1667,axiom,(![X: $i] : ((ap(X) | (~p(X))) | p(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c264')).
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1667, 1666])).
% 0.74/0.80 tff(1669,plain,
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1668, 1664])).
% 0.74/0.80 tff(1670,plain,(
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% 0.74/0.80 inference(skolemize,[status(sab)],[1669])).
% 0.74/0.80 tff(1671,plain,
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1670, 1663])).
% 0.74/0.80 tff(1672,plain,
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1673, 1672])).
% 0.74/0.80 tff(1675,plain,
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% 0.74/0.80 inference(unit_resolution,[status(thm)],[1674, 1671, 29])).
% 0.74/0.80 tff(1676,plain,
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% 0.74/0.80 inference(unit_resolution,[status(thm)],[1675, 1661])).
% 0.74/0.80 tff(1677,assumption,(p(s(s(a)))), introduced(assumption)).
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% 0.74/0.80 inference(quant_intro,[status(thm)],[1678])).
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% 0.74/0.80 inference(bind,[status(th)],[])).
% 0.74/0.80 tff(1682,plain,
% 0.74/0.80 (![X: $i] : (((((((~ar(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | (~p(X))) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | rr(s(X)))),
% 0.74/0.80 inference(quant_intro,[status(thm)],[1681])).
% 0.74/0.80 tff(1683,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | (~p(X))) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c184')).
% 0.74/0.80 tff(1684,plain,
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1683, 1682])).
% 0.74/0.80 tff(1685,plain,
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% 0.74/0.80 tff(1686,plain,(
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% 0.74/0.80 inference(skolemize,[status(sab)],[1685])).
% 0.74/0.80 tff(1687,plain,
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% 0.74/0.80 inference(modus_ponens,[status(thm)],[1686, 1679])).
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% 0.74/0.80 tff(1695,plain,
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% 0.74/0.80 tff(1696,plain,
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% 0.74/0.81 tff(1701,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | qq(X)) | r(X)) | rr(X)) | (~p(X))) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c162')).
% 0.74/0.81 tff(1702,plain,
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% 0.74/0.81 tff(1703,plain,
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% 0.74/0.81 inference(skolemize,[status(sab)],[1703])).
% 0.74/0.81 tff(1705,plain,
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% 0.74/0.81 tff(1707,plain,
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% 0.74/0.82 inference(monotonicity,[status(thm)],[1874])).
% 0.74/0.82 tff(1876,plain,
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% 0.74/0.82 inference(transitivity,[status(thm)],[1875, 1873])).
% 0.74/0.82 tff(1877,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | rr(X) | (~r(X)) | rr(s(X)))) | (pp(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | rr(s(s(s(a)))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1878,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | rr(X) | (~r(X)) | rr(s(X)))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | rr(s(s(s(a))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1877, 1876])).
% 0.74/0.82 tff(1879,plain,
% 0.74/0.82 (q(s(s(a))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | rr(s(s(s(a))))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1878, 1872, 120])).
% 0.74/0.82 tff(1880,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1879, 1862, 1844, 1, 1677, 1843, 175])).
% 0.74/0.82 tff(1881,plain,(pp(s(s(a))) | q(s(s(a))) | (~p(s(s(a)))) | (~r(s(s(a)))) | rr(s(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1882,plain,
% 0.74/0.82 (pp(s(s(a)))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1881, 1841, 1, 1842, 175])).
% 0.74/0.82 tff(1883,plain,
% 0.74/0.82 (pp(s(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[290, 1882])).
% 0.74/0.82 tff(1884,plain,
% 0.74/0.82 (^[X: $i] : refl(((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1885,plain,
% 0.74/0.82 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1884])).
% 0.74/0.82 tff(1886,plain,
% 0.74/0.82 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1887,plain,
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% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1888,plain,
% 0.74/0.82 (![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1887])).
% 0.74/0.82 tff(1889,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c203')).
% 0.74/0.82 tff(1890,plain,
% 0.74/0.82 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1889, 1888])).
% 0.74/0.82 tff(1891,plain,
% 0.74/0.82 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1890, 1886])).
% 0.74/0.82 tff(1892,plain,(
% 0.74/0.82 ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(skolemize,[status(sab)],[1891])).
% 0.74/0.82 tff(1893,plain,
% 0.74/0.82 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1892, 1885])).
% 0.74/0.82 tff(1894,plain,
% 0.74/0.82 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | (qq(s(s(a))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | qq(s(s(a))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1895,plain,
% 0.74/0.82 (((~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | qq(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a))))) <=> (qq(s(s(a))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1896,plain,
% 0.74/0.82 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | qq(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | (qq(s(s(a))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a))))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1895])).
% 0.74/0.82 tff(1897,plain,
% 0.74/0.82 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | qq(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | qq(s(s(a))) | q(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1896, 1894])).
% 0.74/0.82 tff(1898,plain,
% 0.74/0.82 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | qq(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1899,plain,
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% 0.74/0.82 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 0.74/0.82 tff(1900,plain,
% 0.74/0.82 (qq(s(s(a))) | q(s(s(a))) | (~p(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | rr(s(s(s(a))))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1899, 1893, 120])).
% 0.74/0.82 tff(1901,plain,
% 0.74/0.82 (rr(s(s(a)))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1900, 1882, 175, 1, 176, 1841, 1842])).
% 0.74/0.82 tff(1902,plain,
% 0.74/0.82 (((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(s(a)) | rr(s(a)) | (~rr(s(s(a)))))) <=> ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(s(a)) | rr(s(a)) | (~rr(s(s(a)))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1903,plain,
% 0.74/0.82 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(s(a)) | rr(s(a)) | (~rr(s(s(a)))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1904,plain,
% 0.74/0.82 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(s(a)) | rr(s(a)) | (~rr(s(s(a))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1903, 1902])).
% 0.74/0.82 tff(1905,plain,
% 0.74/0.82 (rr(s(a)) | (~rr(s(s(a))))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1904, 430, 94])).
% 0.74/0.82 tff(1906,plain,
% 0.74/0.82 (rr(s(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1905, 1901])).
% 0.74/0.82 tff(1907,plain,
% 0.74/0.82 (((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(a) | rr(a) | (~rr(s(a))))) <=> ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(a) | rr(a) | (~rr(s(a))))),
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% 0.74/0.82 tff(1908,plain,
% 0.74/0.82 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(a) | rr(a) | (~rr(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1909,plain,
% 0.74/0.82 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(a) | rr(a) | (~rr(s(a)))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1908, 1907])).
% 0.74/0.82 tff(1910,plain,
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% 0.74/0.82 inference(unit_resolution,[status(thm)],[1909, 430, 295])).
% 0.74/0.82 tff(1911,plain,
% 0.74/0.82 (rr(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1910, 1906])).
% 0.74/0.82 tff(1912,plain,
% 0.74/0.82 (((~![X: $i] : (aq(X) | (~q(X)) | q(s(X)))) | (aq(a) | (~q(a)) | q(s(a)))) <=> ((~![X: $i] : (aq(X) | (~q(X)) | q(s(X)))) | aq(a) | (~q(a)) | q(s(a)))),
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% 0.74/0.82 tff(1913,plain,
% 0.74/0.82 ((~![X: $i] : (aq(X) | (~q(X)) | q(s(X)))) | (aq(a) | (~q(a)) | q(s(a)))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1914,plain,
% 0.74/0.82 ((~![X: $i] : (aq(X) | (~q(X)) | q(s(X)))) | aq(a) | (~q(a)) | q(s(a))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 0.74/0.82 tff(1915,plain,
% 0.74/0.82 ((~q(a)) | q(s(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1914, 544, 374])).
% 0.74/0.82 tff(1916,plain,
% 0.74/0.82 (~q(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1915, 313])).
% 0.74/0.82 tff(1917,plain,
% 0.74/0.82 (r(s(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1719, 1842])).
% 0.74/0.82 tff(1918,plain,
% 0.74/0.82 (r(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[309, 1917])).
% 0.74/0.82 tff(1919,assumption,(rr(a)), introduced(assumption)).
% 0.74/0.82 tff(1920,assumption,(~q(a)), introduced(assumption)).
% 0.74/0.82 tff(1921,assumption,(r(a)), introduced(assumption)).
% 0.74/0.82 tff(1922,assumption,(p(s(a))), introduced(assumption)).
% 0.74/0.82 tff(1923,assumption,(~qq(a)), introduced(assumption)).
% 0.74/0.82 tff(1924,assumption,(~p(a)), introduced(assumption)).
% 0.74/0.82 tff(1925,plain,
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% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1926,plain,
% 0.74/0.82 (((~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~pp(a)) | (~p(s(a)))) <=> ((~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)) | (~pp(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1927,plain,
% 0.74/0.82 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~pp(a)) | (~p(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)) | (~pp(a))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1926])).
% 0.74/0.82 tff(1928,plain,
% 0.74/0.82 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~pp(a)) | (~p(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)) | (~pp(a)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1927, 1925])).
% 0.74/0.82 tff(1929,plain,
% 0.74/0.82 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~pp(a)) | (~p(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1930,plain,
% 0.74/0.82 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)) | (~pp(a))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1929, 1928])).
% 0.74/0.82 tff(1931,plain,
% 0.74/0.82 (p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)) | (~pp(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1930, 14, 1633])).
% 0.74/0.82 tff(1932,plain,
% 0.74/0.82 (~pp(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1931, 1924, 1922, 1920, 1921, 1923])).
% 0.74/0.82 tff(1933,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1934,plain,
% 0.74/0.82 ((pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~p(s(a)))) <=> (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1935,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~p(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1934])).
% 0.74/0.82 tff(1936,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~p(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1935, 1933])).
% 0.74/0.82 tff(1937,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~r(a)) | (~p(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1938,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1937, 1936])).
% 0.74/0.82 tff(1939,plain,
% 0.74/0.82 (pp(a) | p(a) | q(a) | qq(a) | (~p(s(a))) | (~r(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1938, 14, 1651])).
% 0.74/0.82 tff(1940,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1939, 1932, 1924, 1922, 1920, 1921, 1923])).
% 0.74/0.82 tff(1941,plain,(p(a) | (~p(s(a))) | q(a) | (~r(a)) | qq(a)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1942,plain,
% 0.74/0.82 (p(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1941, 1923, 1920, 1921, 1922])).
% 0.74/0.82 tff(1943,plain,
% 0.74/0.82 (^[X: $i] : refl((pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X)))) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X)))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1944,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1943])).
% 0.74/0.82 tff(1945,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1946,plain,
% 0.74/0.82 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ap(X)) | (~r(X))) | (~rr(X))) <=> ((~ap(X)) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> (((~ap(X)) | (~rr(X)) | (~r(X))) | (~p(X))))), rewrite((((~ap(X)) | (~rr(X)) | (~r(X))) | (~p(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) <=> (((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | pp(X)))), rewrite((((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | pp(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) <=> ((pp(X) | (~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | q(X)))), rewrite(((pp(X) | (~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | q(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) <=> ((pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))) | qq(X)))), rewrite(((pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))) | qq(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X))))), (((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | (~p(s(X)))) <=> ((pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X))) | (~p(s(X)))))), rewrite(((pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X))) | (~p(s(X)))) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))), (((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | (~p(s(X)))) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1947,plain,
% 0.74/0.82 (![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | (~p(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1946])).
% 0.74/0.82 tff(1948,axiom,(![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | (~p(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c257')).
% 0.74/0.82 tff(1949,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1948, 1947])).
% 0.74/0.82 tff(1950,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1949, 1945])).
% 0.74/0.82 tff(1951,plain,(
% 0.74/0.82 ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(skolemize,[status(sab)],[1950])).
% 0.74/0.82 tff(1952,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1951, 1944])).
% 0.74/0.82 tff(1953,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1954,plain,
% 0.74/0.82 ((pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~rr(a)) | (~r(a)) | (~p(s(a)))) <=> (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1955,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~rr(a)) | (~r(a)) | (~p(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1954])).
% 0.74/0.82 tff(1956,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~rr(a)) | (~r(a)) | (~p(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1955, 1953])).
% 0.74/0.82 tff(1957,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~rr(a)) | (~r(a)) | (~p(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1958,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | pp(a) | (~ap(a)) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1957, 1956])).
% 0.74/0.82 tff(1959,plain,
% 0.74/0.82 (pp(a) | (~p(a)) | q(a) | qq(a) | (~p(s(a))) | (~rr(a)) | (~r(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1958, 14, 1952])).
% 0.74/0.82 tff(1960,plain,
% 0.74/0.82 (pp(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1959, 1942, 1923, 1920, 1921, 1919, 1922])).
% 0.74/0.82 tff(1961,plain,
% 0.74/0.82 (^[X: $i] : refl(((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1962,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1961])).
% 0.74/0.82 tff(1963,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1964,plain,
% 0.74/0.82 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ap(X)) | (~r(X))) | (~rr(X))) <=> ((~ap(X)) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> (((~ap(X)) | (~rr(X)) | (~r(X))) | (~p(X))))), rewrite((((~ap(X)) | (~rr(X)) | (~r(X))) | (~p(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) <=> (((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | (~pp(X))))), rewrite((((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X))) | (~pp(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)) | (~pp(X)))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) <=> ((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)) | (~pp(X))))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) <=> (((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)) | (~pp(X))) | q(X)))), rewrite((((~ap(X)) | (~p(X)) | (~rr(X)) | (~r(X)) | (~pp(X))) | q(X)) <=> ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) <=> ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) | (~pp(s(X)))) <=> (((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))) | (~pp(s(X)))))), rewrite((((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))) | (~pp(s(X)))) <=> ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) | (~pp(s(X)))) <=> ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1965,plain,
% 0.74/0.82 (![X: $i] : (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1964])).
% 0.74/0.82 tff(1966,axiom,(![X: $i] : (((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | q(X)) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c226')).
% 0.74/0.82 tff(1967,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1966, 1965])).
% 0.74/0.82 tff(1968,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1967, 1963])).
% 0.74/0.82 tff(1969,plain,(
% 0.74/0.82 ![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(skolemize,[status(sab)],[1968])).
% 0.74/0.82 tff(1970,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1969, 1962])).
% 0.74/0.82 tff(1971,plain,
% 0.74/0.82 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1972,plain,
% 0.74/0.82 (((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(a)) | (~pp(s(a)))) <=> ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1973,plain,
% 0.74/0.82 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(a)) | (~pp(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a))))),
% 0.74/0.82 inference(monotonicity,[status(thm)],[1972])).
% 0.74/0.82 tff(1974,plain,
% 0.74/0.82 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(a)) | (~pp(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.74/0.82 inference(transitivity,[status(thm)],[1973, 1971])).
% 0.74/0.82 tff(1975,plain,
% 0.74/0.82 ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(a)) | (~pp(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1976,plain,
% 0.74/0.82 ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | (~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1975, 1974])).
% 0.74/0.82 tff(1977,plain,
% 0.74/0.82 ((~p(a)) | q(a) | (~rr(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1976, 14, 1970])).
% 0.74/0.82 tff(1978,plain,
% 0.74/0.82 ($false),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1977, 1960, 1942, 1921, 1920, 1919, 314])).
% 0.74/0.82 tff(1979,plain,(qq(a) | (~r(a)) | q(a) | (~rr(a)) | (~pp(s(a))) | (~p(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.82 tff(1980,plain,
% 0.74/0.82 (qq(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1979, 1918, 1916, 1911, 1883, 1840])).
% 0.74/0.82 tff(1981,assumption,(qq(a)), introduced(assumption)).
% 0.74/0.82 tff(1982,plain,
% 0.74/0.82 (^[X: $i] : refl((pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X)))) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X)))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1983,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1982])).
% 0.74/0.82 tff(1984,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1985,plain,
% 0.74/0.82 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ap(X)) | (~r(X))) | (~rr(X))) <=> ((~ap(X)) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) <=> (((~ap(X)) | (~rr(X)) | (~r(X))) | p(X)))), rewrite((((~ap(X)) | (~rr(X)) | (~r(X))) | p(X)) <=> ((~ap(X)) | p(X) | (~rr(X)) | (~r(X)))), (((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) <=> ((~ap(X)) | p(X) | (~rr(X)) | (~r(X))))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) <=> (((~ap(X)) | p(X) | (~rr(X)) | (~r(X))) | pp(X)))), rewrite((((~ap(X)) | p(X) | (~rr(X)) | (~r(X))) | pp(X)) <=> (pp(X) | (~ap(X)) | p(X) | (~rr(X)) | (~r(X)))), ((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) <=> (pp(X) | (~ap(X)) | p(X) | (~rr(X)) | (~r(X))))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) <=> ((pp(X) | (~ap(X)) | p(X) | (~rr(X)) | (~r(X))) | q(X)))), rewrite(((pp(X) | (~ap(X)) | p(X) | (~rr(X)) | (~r(X))) | q(X)) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~rr(X)) | (~r(X)))), (((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~rr(X)) | (~r(X))))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) <=> ((pp(X) | (~ap(X)) | p(X) | q(X) | (~rr(X)) | (~r(X))) | (~qq(X))))), rewrite(((pp(X) | (~ap(X)) | p(X) | q(X) | (~rr(X)) | (~r(X))) | (~qq(X))) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)))), ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X))))), (((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> ((pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X))) | (~pp(s(X)))))), rewrite(((pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X))) | (~pp(s(X)))) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))), (((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1986,plain,
% 0.74/0.82 (![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1985])).
% 0.74/0.82 tff(1987,axiom,(![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c246')).
% 0.74/0.82 tff(1988,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1987, 1986])).
% 0.74/0.82 tff(1989,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1988, 1984])).
% 0.74/0.82 tff(1990,plain,(
% 0.74/0.82 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(skolemize,[status(sab)],[1989])).
% 0.74/0.82 tff(1991,plain,
% 0.74/0.82 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1990, 1983])).
% 0.74/0.82 tff(1992,plain,
% 0.74/0.82 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | (~qq(a)) | (~rr(a)) | (~r(a)) | (~pp(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | p(a) | q(a) | (~qq(a)) | (~rr(a)) | (~r(a)) | (~pp(s(a))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(1993,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | p(a) | q(a) | (~qq(a)) | (~rr(a)) | (~r(a)) | (~pp(s(a))))),
% 0.74/0.82 inference(quant_inst,[status(thm)],[])).
% 0.74/0.82 tff(1994,plain,
% 0.74/0.82 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | p(a) | q(a) | (~qq(a)) | (~rr(a)) | (~r(a)) | (~pp(s(a)))),
% 0.74/0.82 inference(modus_ponens,[status(thm)],[1993, 1992])).
% 0.74/0.82 tff(1995,plain,
% 0.74/0.82 (pp(a) | p(a) | q(a) | (~qq(a)) | (~rr(a)) | (~r(a)) | (~pp(s(a)))),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1994, 14, 1991])).
% 0.74/0.82 tff(1996,plain,
% 0.74/0.82 (pp(a)),
% 0.74/0.82 inference(unit_resolution,[status(thm)],[1995, 1924, 1921, 1920, 1981, 1919, 314])).
% 0.74/0.82 tff(1997,plain,
% 0.74/0.82 (^[X: $i] : refl(((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(1998,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[1997])).
% 0.74/0.82 tff(1999,plain,
% 0.74/0.82 (![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(rewrite,[status(thm)],[])).
% 0.74/0.82 tff(2000,plain,
% 0.74/0.82 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ap(X)) | (~r(X))) | p(X)) <=> ((~ap(X)) | p(X) | (~r(X)))), (((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) <=> (((~ap(X)) | p(X) | (~r(X))) | (~pp(X))))), rewrite((((~ap(X)) | p(X) | (~r(X))) | (~pp(X))) <=> ((~ap(X)) | p(X) | (~r(X)) | (~pp(X)))), (((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) <=> ((~ap(X)) | p(X) | (~r(X)) | (~pp(X))))), ((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) <=> (((~ap(X)) | p(X) | (~r(X)) | (~pp(X))) | q(X)))), rewrite((((~ap(X)) | p(X) | (~r(X)) | (~pp(X))) | q(X)) <=> ((~ap(X)) | p(X) | q(X) | (~r(X)) | (~pp(X)))), ((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) <=> ((~ap(X)) | p(X) | q(X) | (~r(X)) | (~pp(X))))), (((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) <=> (((~ap(X)) | p(X) | q(X) | (~r(X)) | (~pp(X))) | (~qq(X))))), rewrite((((~ap(X)) | p(X) | q(X) | (~r(X)) | (~pp(X))) | (~qq(X))) <=> ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)))), (((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) <=> ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X))))), ((((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> (((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X))) | (~pp(s(X)))))), rewrite((((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X))) | (~pp(s(X)))) <=> ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))), ((((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))))),
% 0.74/0.82 inference(bind,[status(th)],[])).
% 0.74/0.82 tff(2001,plain,
% 0.74/0.82 (![X: $i] : (((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.82 inference(quant_intro,[status(thm)],[2000])).
% 0.74/0.82 tff(2002,axiom,(![X: $i] : (((((((~ap(X)) | (~r(X))) | p(X)) | (~pp(X))) | q(X)) | (~qq(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c230')).
% 0.74/0.83 tff(2003,plain,
% 0.74/0.83 (![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2002, 2001])).
% 0.74/0.83 tff(2004,plain,
% 0.74/0.83 (![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2003, 1999])).
% 0.74/0.83 tff(2005,plain,(
% 0.74/0.83 ![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.83 inference(skolemize,[status(sab)],[2004])).
% 0.74/0.83 tff(2006,plain,
% 0.74/0.83 (![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2005, 1998])).
% 0.74/0.83 tff(2007,plain,
% 0.74/0.83 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | q(a) | (~qq(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | p(a) | q(a) | (~qq(a)) | (~r(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2008,plain,
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% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2009,plain,
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% 0.74/0.83 tff(2013,plain,
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% 0.74/0.83 tff(2014,plain,
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% 0.74/0.83 tff(2015,plain,(p(a) | (~r(a)) | q(a) | (~qq(a)) | (~pp(s(a))) | (~rr(a))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.83 tff(2016,plain,
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% 0.74/0.83 tff(2018,plain,
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% 0.74/0.83 tff(2019,plain,
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% 0.74/0.83 tff(2021,plain,
% 0.74/0.83 (![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))),
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% 0.74/0.83 tff(2022,axiom,(![X: $i] : ((((((((~ap(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | q(X)) | (~qq(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c244')).
% 0.74/0.83 tff(2023,plain,
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% 0.74/0.83 tff(2024,plain,
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% 0.74/0.83 inference(modus_ponens,[status(thm)],[2023, 2019])).
% 0.74/0.83 tff(2025,plain,(
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% 0.74/0.83 inference(skolemize,[status(sab)],[2024])).
% 0.74/0.83 tff(2026,plain,
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% 0.74/0.83 tff(2027,plain,
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% 0.74/0.83 tff(2028,plain,
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% 0.74/0.83 tff(2029,plain,
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% 0.74/0.83 tff(2030,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[2029, 14, 2026])).
% 0.74/0.83 tff(2031,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[2030, 2016, 1980, 1916, 1918, 1911, 1883])).
% 0.74/0.83 tff(2032,plain,
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% 0.74/0.83 tff(2033,plain,(q(s(a)) | rr(s(s(s(a)))) | q(s(s(a))) | qq(s(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.83 tff(2034,plain,
% 0.74/0.83 (q(s(a))),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[2033, 176, 1, 175])).
% 0.74/0.83 tff(2035,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[378, 2034])).
% 0.74/0.83 tff(2036,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[1881, 1676, 1, 1715, 175])).
% 0.74/0.83 tff(2037,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[290, 2036])).
% 0.74/0.83 tff(2038,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[393, 2037, 2035, 1721])).
% 0.74/0.83 tff(2039,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[408, 2038, 2037, 2035, 1721])).
% 0.74/0.83 tff(2040,plain,(qq(s(s(a))) | q(s(s(a))) | rr(s(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.83 tff(2041,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[2040, 175, 1])).
% 0.74/0.83 tff(2042,plain,
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% 0.74/0.83 tff(2043,plain,
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% 0.74/0.83 tff(2044,plain,
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% 0.74/0.83 tff(2045,plain,
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% 0.74/0.83 inference(unit_resolution,[status(thm)],[2044, 486, 180])).
% 0.74/0.83 tff(2046,plain,
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% 0.74/0.83 tff(2054,plain,
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% 0.74/0.83 inference(bind,[status(th)],[])).
% 0.74/0.83 tff(2056,plain,
% 0.74/0.83 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(quant_intro,[status(thm)],[2055])).
% 0.74/0.83 tff(2057,plain,
% 0.74/0.83 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
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% 0.74/0.83 inference(bind,[status(th)],[])).
% 0.74/0.83 tff(2059,plain,
% 0.74/0.83 (![X: $i] : ((((((((~ap(X)) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(quant_intro,[status(thm)],[2058])).
% 0.74/0.83 tff(2060,axiom,(![X: $i] : ((((((((~ap(X)) | (~r(X))) | rr(X)) | p(X)) | pp(X)) | q(X)) | (~qq(X))) | p(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c254')).
% 0.74/0.83 tff(2061,plain,
% 0.74/0.83 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2060, 2059])).
% 0.74/0.83 tff(2062,plain,
% 0.74/0.83 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2061, 2057])).
% 0.74/0.83 tff(2063,plain,(
% 0.74/0.83 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(skolemize,[status(sab)],[2062])).
% 0.74/0.83 tff(2064,plain,
% 0.74/0.83 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2063, 2056])).
% 0.74/0.83 tff(2065,plain,
% 0.74/0.83 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2066,plain,
% 0.74/0.83 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | p(s(s(s(s(a)))))) <=> (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2067,plain,
% 0.74/0.83 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a)))))))),
% 0.74/0.83 inference(monotonicity,[status(thm)],[2066])).
% 0.74/0.83 tff(2068,plain,
% 0.74/0.83 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 0.74/0.83 inference(transitivity,[status(thm)],[2067, 2065])).
% 0.74/0.83 tff(2069,plain,
% 0.74/0.83 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 0.74/0.83 inference(quant_inst,[status(thm)],[])).
% 0.74/0.83 tff(2070,plain,
% 0.74/0.83 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a)))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2069, 2068])).
% 0.74/0.83 tff(2071,plain,
% 0.74/0.83 (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | p(s(s(s(s(a)))))),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[2070, 2064, 149])).
% 0.74/0.83 tff(2072,plain,
% 0.74/0.83 (p(s(s(s(s(a)))))),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[2071, 2054, 211, 175, 2046, 174, 138])).
% 0.74/0.83 tff(2073,assumption,(p(s(s(s(s(a)))))), introduced(assumption)).
% 0.74/0.83 tff(2074,assumption,(qq(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.74/0.83 tff(2075,plain,
% 0.74/0.83 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X)))) <=> ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X)))))),
% 0.74/0.83 inference(bind,[status(th)],[])).
% 0.74/0.83 tff(2076,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(quant_intro,[status(thm)],[2075])).
% 0.74/0.83 tff(2077,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2078,plain,
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% 0.74/0.83 inference(bind,[status(th)],[])).
% 0.74/0.83 tff(2079,plain,
% 0.74/0.83 (![X: $i] : (((((~aq(X)) | (~p(X))) | q(X)) | (~r(X))) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(quant_intro,[status(thm)],[2078])).
% 0.74/0.83 tff(2080,axiom,(![X: $i] : (((((~aq(X)) | (~p(X))) | q(X)) | (~r(X))) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c102')).
% 0.74/0.83 tff(2081,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2080, 2079])).
% 0.74/0.83 tff(2082,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2081, 2077])).
% 0.74/0.83 tff(2083,plain,(
% 0.74/0.83 ![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(skolemize,[status(sab)],[2082])).
% 0.74/0.83 tff(2084,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2083, 2076])).
% 0.74/0.83 tff(2085,plain,
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% 0.74/0.83 inference(rewrite,[status(thm)],[])).
% 0.74/0.83 tff(2086,plain,
% 0.74/0.83 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))) <=> ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 0.74/0.83 inference(rewrite,[status(thm)],[])).
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% 0.74/0.83 inference(monotonicity,[status(thm)],[2086])).
% 0.74/0.83 tff(2088,plain,
% 0.74/0.83 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 0.74/0.83 inference(transitivity,[status(thm)],[2087, 2085])).
% 0.74/0.83 tff(2089,plain,
% 0.74/0.83 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 0.74/0.83 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.83 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))),
% 0.74/0.83 inference(modus_ponens,[status(thm)],[2089, 2088])).
% 0.74/0.83 tff(2091,plain,
% 0.74/0.83 ((~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[2090, 2084, 450])).
% 0.74/0.83 tff(2092,plain,
% 0.74/0.83 (q(s(s(s(s(a)))))),
% 0.74/0.83 inference(unit_resolution,[status(thm)],[2091, 442, 2074, 2073])).
% 0.74/0.83 tff(2093,plain,
% 0.74/0.83 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X)))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X)))))),
% 0.74/0.83 inference(bind,[status(th)],[])).
% 0.74/0.83 tff(2094,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))),
% 0.74/0.83 inference(quant_intro,[status(thm)],[2093])).
% 0.74/0.83 tff(2095,plain,
% 0.74/0.83 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))),
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% 0.74/0.84 inference(bind,[status(th)],[])).
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% 0.74/0.84 (![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | (~qp(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2138])).
% 0.74/0.84 tff(2140,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | (~qp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c204')).
% 0.74/0.84 tff(2141,plain,
% 0.74/0.84 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2140, 2139])).
% 0.74/0.84 tff(2142,plain,
% 0.74/0.84 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2141, 2137])).
% 0.74/0.84 tff(2143,plain,(
% 0.74/0.84 ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))),
% 0.74/0.84 inference(skolemize,[status(sab)],[2142])).
% 0.74/0.84 tff(2144,plain,
% 0.74/0.84 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2143, 2136])).
% 0.74/0.84 tff(2145,plain,
% 0.74/0.84 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2146,plain,
% 0.74/0.84 (((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | q(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a))))))))) <=> (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2147,plain,
% 0.74/0.84 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | q(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(monotonicity,[status(thm)],[2146])).
% 0.74/0.84 tff(2148,plain,
% 0.74/0.84 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | q(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(transitivity,[status(thm)],[2147, 2145])).
% 0.74/0.84 tff(2149,plain,
% 0.74/0.84 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | q(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2150,plain,
% 0.74/0.84 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2149, 2148])).
% 0.74/0.84 tff(2151,plain,
% 0.74/0.84 (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2150, 2144, 472])).
% 0.74/0.84 tff(2152,plain,
% 0.74/0.84 (~qp(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2151, 2134, 2116, 2115, 2114, 1778, 2109])).
% 0.74/0.84 tff(2153,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp1(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp1(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp1(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp1(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2154,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp1(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp1(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2155,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp1(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp1(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2154, 2153])).
% 0.74/0.84 tff(2156,plain,
% 0.74/0.84 (~qrp1(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2155, 1311, 614])).
% 0.74/0.84 tff(2157,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp4(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp4(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp4(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp4(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2158,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp4(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp4(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2159,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp4(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp4(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2158, 2157])).
% 0.74/0.84 tff(2160,plain,
% 0.74/0.84 (~qrp4(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2159, 1353, 614])).
% 0.74/0.84 tff(2161,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp3(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp3(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp3(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp3(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2162,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp3(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp3(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2163,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp3(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp3(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 0.74/0.84 tff(2164,plain,
% 0.74/0.84 (~qrp3(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2163, 1339, 614])).
% 0.74/0.84 tff(2165,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp2(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp2(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp2(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp2(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2166,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp2(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~qrp2(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2167,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp2(X)))) | ar(s(s(s(s(s(s(a))))))) | (~qrp2(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2166, 2165])).
% 0.74/0.84 tff(2168,plain,
% 0.74/0.84 (~qrp2(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2167, 1325, 614])).
% 0.74/0.84 tff(2169,plain,
% 0.74/0.84 (^[X: $i] : refl((qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X)))) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X)))))),
% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2170,plain,
% 0.74/0.84 (![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X)))) <=> ![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2169])).
% 0.74/0.84 tff(2171,plain,
% 0.74/0.84 (![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X)))) <=> ![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2172,plain,
% 0.74/0.84 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((qrp1(X) | qrp2(X)) | qrp3(X)) <=> (qrp1(X) | qrp2(X) | qrp3(X))), ((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) <=> ((qrp1(X) | qrp2(X) | qrp3(X)) | qrp4(X)))), rewrite(((qrp1(X) | qrp2(X) | qrp3(X)) | qrp4(X)) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X))), ((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X)))), (((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) <=> ((qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X)) | qp(X)))), rewrite(((qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X)) | qp(X)) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X))), (((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X)))), ((((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) | (~qp(s(X)))) <=> ((qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X)) | (~qp(s(X)))))), rewrite(((qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X)) | (~qp(s(X)))) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))), ((((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) | (~qp(s(X)))) <=> (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))))),
% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2173,plain,
% 0.74/0.84 (![X: $i] : (((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) | (~qp(s(X)))) <=> ![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2172])).
% 0.74/0.84 tff(2174,axiom,(![X: $i] : (((((qrp1(X) | qrp2(X)) | qrp3(X)) | qrp4(X)) | qp(X)) | (~qp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c210')).
% 0.74/0.84 tff(2175,plain,
% 0.74/0.84 (![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2174, 2173])).
% 0.74/0.84 tff(2176,plain,
% 0.74/0.84 (![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2175, 2171])).
% 0.74/0.84 tff(2177,plain,(
% 0.74/0.84 ![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(skolemize,[status(sab)],[2176])).
% 0.74/0.84 tff(2178,plain,
% 0.74/0.84 (![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2177, 2170])).
% 0.74/0.84 tff(2179,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2180,plain,
% 0.74/0.84 ((qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | qp(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a)))))))))) <=> (qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2181,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | qp(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.84 inference(monotonicity,[status(thm)],[2180])).
% 0.74/0.84 tff(2182,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | qp(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(transitivity,[status(thm)],[2181, 2179])).
% 0.74/0.84 tff(2183,plain,
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% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2184,plain,
% 0.74/0.84 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2183, 2182])).
% 0.74/0.84 tff(2185,plain,
% 0.74/0.84 (qp(s(s(s(s(s(s(a))))))) | qrp1(s(s(s(s(s(s(a))))))) | qrp2(s(s(s(s(s(s(a))))))) | qrp3(s(s(s(s(s(s(a))))))) | qrp4(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2184, 2178])).
% 0.74/0.84 tff(2186,plain,
% 0.74/0.84 (qp(s(s(s(s(s(s(a))))))) | (~qp(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2185, 2168, 2164, 2160, 2156])).
% 0.74/0.84 tff(2187,plain,
% 0.74/0.84 (~qp(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2186, 2152])).
% 0.74/0.84 tff(2188,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp1(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp1(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp1(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp1(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2189,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp1(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp1(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2190,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp1(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp1(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2189, 2188])).
% 0.74/0.84 tff(2191,plain,
% 0.74/0.84 (~qrp1(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2190, 1311, 767])).
% 0.74/0.84 tff(2192,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp2(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp2(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp2(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp2(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2193,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp2(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp2(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2194,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp2(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp2(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2193, 2192])).
% 0.74/0.84 tff(2195,plain,
% 0.74/0.84 (~qrp2(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2194, 1325, 767])).
% 0.74/0.84 tff(2196,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp3(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp3(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp3(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp3(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2197,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp3(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp3(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2198,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp3(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp3(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2197, 2196])).
% 0.74/0.84 tff(2199,plain,
% 0.74/0.84 (~qrp3(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2198, 1339, 767])).
% 0.74/0.84 tff(2200,plain,
% 0.74/0.84 (((~![X: $i] : (ar(X) | (~qrp4(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp4(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (ar(X) | (~qrp4(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp4(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2201,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp4(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~qrp4(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2202,plain,
% 0.74/0.84 ((~![X: $i] : (ar(X) | (~qrp4(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~qrp4(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2201, 2200])).
% 0.74/0.84 tff(2203,plain,
% 0.74/0.84 (~qrp4(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2202, 1353, 767])).
% 0.74/0.84 tff(2204,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2205,plain,
% 0.74/0.84 ((qrp1(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a))))))))))) <=> (qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2206,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.74/0.84 inference(monotonicity,[status(thm)],[2205])).
% 0.74/0.84 tff(2207,plain,
% 0.74/0.84 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.84 inference(transitivity,[status(thm)],[2206, 2204])).
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% 0.74/0.84 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.84 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(s(s(s(a)))))))) | qrp4(s(s(s(s(s(s(s(a)))))))) | qrp3(s(s(s(s(s(s(s(a)))))))) | qrp2(s(s(s(s(s(s(s(a)))))))) | qrp1(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2208, 2207])).
% 0.74/0.84 tff(2210,plain,
% 0.74/0.84 (qp(s(s(s(s(s(s(s(a)))))))) | (~qp(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2209, 2178, 2203, 2199, 2195, 2191])).
% 0.74/0.84 tff(2211,plain,
% 0.74/0.84 (~qp(s(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2210, 2187])).
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% 0.74/0.84 ((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | (ap(s(s(s(s(s(a)))))) | (~p(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(a))))))))),
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% 0.74/0.84 ((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | ap(s(s(s(s(s(a)))))) | (~p(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 0.74/0.84 tff(2215,plain,
% 0.74/0.84 ((~p(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2214, 1671, 646])).
% 0.74/0.84 tff(2216,plain,
% 0.74/0.84 (p(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2215, 2114])).
% 0.74/0.84 tff(2217,plain,
% 0.74/0.84 (^[X: $i] : refl(((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X)))) <=> ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X)))))),
% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2218,plain,
% 0.74/0.84 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X))))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2217])).
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% 0.74/0.84 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2220,plain,
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% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2221,plain,
% 0.74/0.84 (![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X))))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2220])).
% 0.74/0.84 tff(2222,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | qq(X)) | (~r(X))) | rr(X)) | (~p(X))) | (~pp(X))) | (~r(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c202')).
% 0.74/0.84 tff(2223,plain,
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% 0.74/0.84 tff(2224,plain,
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% 0.74/0.84 inference(modus_ponens,[status(thm)],[2223, 2219])).
% 0.74/0.84 tff(2225,plain,(
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% 0.74/0.84 inference(skolemize,[status(sab)],[2224])).
% 0.74/0.84 tff(2226,plain,
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% 0.74/0.84 inference(modus_ponens,[status(thm)],[2225, 2218])).
% 0.74/0.84 tff(2227,plain,
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% 0.74/0.84 tff(2228,plain,
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% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2229,plain,
% 0.74/0.84 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | q(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~r(s(X))))) | (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))))),
% 0.74/0.84 inference(monotonicity,[status(thm)],[2228])).
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% 0.74/0.84 inference(transitivity,[status(thm)],[2229, 2227])).
% 0.74/0.84 tff(2231,plain,
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% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2232,plain,
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% 0.74/0.84 inference(modus_ponens,[status(thm)],[2231, 2230])).
% 0.74/0.84 tff(2233,plain,
% 0.74/0.84 (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2232, 2226, 472])).
% 0.74/0.84 tff(2234,plain,
% 0.74/0.84 (~r(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2233, 2134, 2116, 2115, 2114, 1778, 2109])).
% 0.74/0.84 tff(2235,plain,
% 0.74/0.84 (((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2236,plain,
% 0.74/0.84 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2237,plain,
% 0.74/0.84 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2236, 2235])).
% 0.74/0.84 tff(2238,plain,
% 0.74/0.84 (q(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2237, 206, 476])).
% 0.74/0.84 tff(2239,plain,
% 0.74/0.84 (~q(s(s(s(s(s(s(a)))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2238, 2134])).
% 0.74/0.84 tff(2240,plain,
% 0.74/0.84 (^[X: $i] : refl(((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X))) <=> ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X))))),
% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2241,plain,
% 0.74/0.84 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2240])).
% 0.74/0.84 tff(2242,plain,
% 0.74/0.84 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
% 0.74/0.84 tff(2243,plain,
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% 0.74/0.84 inference(bind,[status(th)],[])).
% 0.74/0.84 tff(2244,plain,
% 0.74/0.84 (![X: $i] : (((((~ap(X)) | r(X)) | (~p(X))) | q(X)) | p(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(quant_intro,[status(thm)],[2243])).
% 0.74/0.84 tff(2245,axiom,(![X: $i] : (((((~ap(X)) | r(X)) | (~p(X))) | q(X)) | p(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c213')).
% 0.74/0.84 tff(2246,plain,
% 0.74/0.84 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2245, 2244])).
% 0.74/0.84 tff(2247,plain,
% 0.74/0.84 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2246, 2242])).
% 0.74/0.84 tff(2248,plain,(
% 0.74/0.84 ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(skolemize,[status(sab)],[2247])).
% 0.74/0.84 tff(2249,plain,
% 0.74/0.84 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))),
% 0.74/0.84 inference(modus_ponens,[status(thm)],[2248, 2241])).
% 0.74/0.84 tff(2250,plain,
% 0.74/0.84 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
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% 0.74/0.84 (((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a))))))))) <=> (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(rewrite,[status(thm)],[])).
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% 0.74/0.84 inference(monotonicity,[status(thm)],[2251])).
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% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.84 inference(modus_ponens,[status(thm)],[2254, 2253])).
% 0.74/0.84 tff(2256,plain,
% 0.74/0.84 (r(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2255, 2249, 495])).
% 0.74/0.84 tff(2257,plain,
% 0.74/0.84 (p(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2256, 2239, 2234, 2216])).
% 0.74/0.84 tff(2258,plain,
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% 0.74/0.84 inference(quant_inst,[status(thm)],[])).
% 0.74/0.84 tff(2260,plain,
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% 0.74/0.84 inference(modus_ponens,[status(thm)],[2259, 2258])).
% 0.74/0.84 tff(2261,plain,
% 0.74/0.84 (r(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2260, 305, 614])).
% 0.74/0.84 tff(2262,plain,
% 0.74/0.84 (~r(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.84 inference(unit_resolution,[status(thm)],[2261, 2234])).
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% 0.74/0.85 inference(rewrite,[status(thm)],[])).
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% 0.74/0.85 inference(monotonicity,[status(thm)],[2264])).
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% 0.74/0.85 inference(transitivity,[status(thm)],[2265, 2263])).
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% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.85 inference(modus_ponens,[status(thm)],[2267, 2266])).
% 0.74/0.85 tff(2269,plain,
% 0.74/0.85 (qq(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a)))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2268, 1893, 472])).
% 0.74/0.85 tff(2270,plain,
% 0.74/0.85 (rr(s(s(s(s(s(s(a)))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2269, 2134, 2116, 2115, 2114, 1778, 2109])).
% 0.74/0.85 tff(2271,plain,
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% 0.74/0.85 inference(rewrite,[status(thm)],[])).
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% 0.74/0.85 ((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | (ar(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.85 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 0.74/0.85 tff(2274,plain,
% 0.74/0.85 ((~rr(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2273, 948, 614])).
% 0.74/0.85 tff(2275,plain,
% 0.74/0.85 (rr(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2274, 2270])).
% 0.74/0.85 tff(2276,plain,
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% 0.74/0.85 inference(rewrite,[status(thm)],[])).
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% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
% 0.74/0.85 tff(2278,plain,
% 0.74/0.85 ((~![X: $i] : (aq(X) | qq(X) | (~qq(s(X))))) | aq(s(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 0.74/0.85 tff(2279,plain,
% 0.74/0.85 (qq(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2278, 190, 476])).
% 0.74/0.85 tff(2280,plain,
% 0.74/0.85 (~qq(s(s(s(s(s(s(a)))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2279, 2109])).
% 0.74/0.85 tff(2281,plain,
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% 0.74/0.85 inference(rewrite,[status(thm)],[])).
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% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.85 inference(modus_ponens,[status(thm)],[2282, 2281])).
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% 0.74/0.85 inference(unit_resolution,[status(thm)],[2283, 190, 499])).
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% 0.74/0.85 inference(unit_resolution,[status(thm)],[2284, 2280])).
% 0.74/0.85 tff(2286,plain,
% 0.74/0.85 (^[X: $i] : refl(((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X)))) <=> ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X)))))),
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% 0.74/0.85 tff(2287,plain,
% 0.74/0.85 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2286])).
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% 0.74/0.85 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))),
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% 0.74/0.85 inference(bind,[status(th)],[])).
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% 0.74/0.85 (![X: $i] : (((((~ap(X)) | r(X)) | (~p(X))) | q(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2289])).
% 0.74/0.85 tff(2291,axiom,(![X: $i] : (((((~ap(X)) | r(X)) | (~p(X))) | q(X)) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c214')).
% 0.74/0.85 tff(2292,plain,
% 0.74/0.85 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2291, 2290])).
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% 0.74/0.85 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))),
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% 0.74/0.85 inference(skolemize,[status(sab)],[2293])).
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% 0.74/0.85 inference(modus_ponens,[status(thm)],[2294, 2287])).
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% 0.74/0.85 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2297,plain,
% 0.74/0.85 (((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))) <=> (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2298,plain,
% 0.74/0.85 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.85 inference(monotonicity,[status(thm)],[2297])).
% 0.74/0.85 tff(2299,plain,
% 0.74/0.85 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(transitivity,[status(thm)],[2298, 2296])).
% 0.74/0.85 tff(2300,plain,
% 0.74/0.85 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
% 0.74/0.85 tff(2301,plain,
% 0.74/0.85 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.74/0.85 tff(2302,plain,
% 0.74/0.85 (r(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2301, 2295, 495])).
% 0.74/0.85 tff(2303,plain,
% 0.74/0.85 (~pp(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2302, 2239, 2234, 2216])).
% 0.74/0.85 tff(2304,plain,
% 0.74/0.85 (((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2305,plain,
% 0.74/0.85 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
% 0.74/0.85 tff(2306,plain,
% 0.74/0.85 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2305, 2304])).
% 0.74/0.85 tff(2307,plain,
% 0.74/0.85 (q(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2306, 206, 499])).
% 0.74/0.85 tff(2308,plain,
% 0.74/0.85 (~q(s(s(s(s(s(s(s(a))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2307, 2239])).
% 0.74/0.85 tff(2309,plain,
% 0.74/0.85 (^[X: $i] : refl((pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X)))) <=> (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X)))))),
% 0.74/0.85 inference(bind,[status(th)],[])).
% 0.74/0.85 tff(2310,plain,
% 0.74/0.85 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2309])).
% 0.74/0.85 tff(2311,plain,
% 0.74/0.85 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2312,plain,
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% 0.74/0.85 inference(bind,[status(th)],[])).
% 0.74/0.85 tff(2313,plain,
% 0.74/0.85 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2312])).
% 0.74/0.85 tff(2314,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | (~pr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c140')).
% 0.74/0.85 tff(2315,plain,
% 0.74/0.85 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2314, 2313])).
% 0.74/0.85 tff(2316,plain,
% 0.74/0.85 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2315, 2311])).
% 0.74/0.85 tff(2317,plain,(
% 0.74/0.85 ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(skolemize,[status(sab)],[2316])).
% 0.74/0.85 tff(2318,plain,
% 0.74/0.85 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2317, 2310])).
% 0.74/0.85 tff(2319,plain,
% 0.74/0.85 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2320,plain,
% 0.74/0.85 ((pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))) <=> (pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2321,plain,
% 0.74/0.85 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.74/0.85 inference(monotonicity,[status(thm)],[2320])).
% 0.74/0.85 tff(2322,plain,
% 0.74/0.85 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.85 inference(transitivity,[status(thm)],[2321, 2319])).
% 0.74/0.85 tff(2323,plain,
% 0.74/0.85 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.74/0.85 inference(quant_inst,[status(thm)],[])).
% 0.74/0.85 tff(2324,plain,
% 0.74/0.85 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(modus_ponens,[status(thm)],[2323, 2322])).
% 0.74/0.85 tff(2325,plain,
% 0.74/0.85 (pp(s(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2324, 2318, 673])).
% 0.74/0.85 tff(2326,plain,
% 0.74/0.85 (~pr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.74/0.85 inference(unit_resolution,[status(thm)],[2325, 2308, 2303, 2285, 2275, 2262, 2257])).
% 0.74/0.85 tff(2327,plain,
% 0.74/0.85 (^[X: $i] : refl((pr(X) | rq(X) | qp(X)) <=> (pr(X) | rq(X) | qp(X)))),
% 0.74/0.85 inference(bind,[status(th)],[])).
% 0.74/0.85 tff(2328,plain,
% 0.74/0.85 (![X: $i] : (pr(X) | rq(X) | qp(X)) <=> ![X: $i] : (pr(X) | rq(X) | qp(X))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2327])).
% 0.74/0.85 tff(2329,plain,
% 0.74/0.85 (![X: $i] : (pr(X) | rq(X) | qp(X)) <=> ![X: $i] : (pr(X) | rq(X) | qp(X))),
% 0.74/0.85 inference(rewrite,[status(thm)],[])).
% 0.74/0.85 tff(2330,plain,
% 0.74/0.85 (^[X: $i] : rewrite(((qp(X) | rq(X)) | pr(X)) <=> (pr(X) | rq(X) | qp(X)))),
% 0.74/0.85 inference(bind,[status(th)],[])).
% 0.74/0.85 tff(2331,plain,
% 0.74/0.85 (![X: $i] : ((qp(X) | rq(X)) | pr(X)) <=> ![X: $i] : (pr(X) | rq(X) | qp(X))),
% 0.74/0.85 inference(quant_intro,[status(thm)],[2330])).
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% 0.83/0.85 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))),
% 0.83/0.85 inference(modus_ponens,[status(thm)],[2394, 2390])).
% 0.83/0.85 tff(2396,plain,(
% 0.83/0.85 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))),
% 0.83/0.85 inference(skolemize,[status(sab)],[2395])).
% 0.83/0.85 tff(2397,plain,
% 0.83/0.85 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))),
% 0.83/0.85 inference(modus_ponens,[status(thm)],[2396, 2389])).
% 0.83/0.85 tff(2398,plain,
% 0.83/0.85 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
% 0.83/0.85 inference(rewrite,[status(thm)],[])).
% 0.83/0.85 tff(2399,plain,
% 0.83/0.85 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | (~rq(s(s(s(s(a))))))) <=> (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
% 0.83/0.85 inference(rewrite,[status(thm)],[])).
% 0.83/0.85 tff(2400,plain,
% 0.83/0.85 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))))),
% 0.83/0.85 inference(monotonicity,[status(thm)],[2399])).
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% 0.83/0.85 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
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% 0.83/0.85 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
% 0.83/0.85 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.85 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | (~rq(s(X))))) | rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))),
% 0.83/0.85 inference(modus_ponens,[status(thm)],[2402, 2401])).
% 0.83/0.85 tff(2404,plain,
% 0.83/0.85 (rr(s(s(s(a)))) | (~r(s(s(s(a))))) | pp(s(s(s(a)))) | p(s(s(s(a)))) | q(s(s(s(a)))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))),
% 0.83/0.85 inference(unit_resolution,[status(thm)],[2403, 2397, 149])).
% 0.83/0.85 tff(2405,plain,
% 0.83/0.85 (~rq(s(s(s(s(a)))))),
% 0.83/0.85 inference(unit_resolution,[status(thm)],[2404, 138, 211, 175, 2046, 2054, 174])).
% 0.83/0.85 tff(2406,plain,
% 0.83/0.85 (^[X: $i] : refl((ap(X) | (~rpq1(X))) <=> (ap(X) | (~rpq1(X))))),
% 0.83/0.85 inference(bind,[status(th)],[])).
% 0.83/0.85 tff(2407,plain,
% 0.83/0.85 (![X: $i] : (ap(X) | (~rpq1(X))) <=> ![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.85 inference(quant_intro,[status(thm)],[2406])).
% 0.83/0.85 tff(2408,plain,
% 0.83/0.85 (![X: $i] : (ap(X) | (~rpq1(X))) <=> ![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.85 inference(rewrite,[status(thm)],[])).
% 0.83/0.85 tff(2409,plain,
% 0.83/0.85 (^[X: $i] : rewrite(((~rpq1(X)) | ap(X)) <=> (ap(X) | (~rpq1(X))))),
% 0.83/0.85 inference(bind,[status(th)],[])).
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% 0.83/0.85 (![X: $i] : ((~rpq1(X)) | ap(X)) <=> ![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.85 inference(quant_intro,[status(thm)],[2409])).
% 0.83/0.85 tff(2411,axiom,(![X: $i] : ((~rpq1(X)) | ap(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c068')).
% 0.83/0.85 tff(2412,plain,
% 0.83/0.85 (![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.85 inference(modus_ponens,[status(thm)],[2411, 2410])).
% 0.83/0.85 tff(2413,plain,
% 0.83/0.85 (![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.85 inference(modus_ponens,[status(thm)],[2412, 2408])).
% 0.83/0.85 tff(2414,plain,(
% 0.83/0.85 ![X: $i] : (ap(X) | (~rpq1(X)))),
% 0.83/0.86 inference(skolemize,[status(sab)],[2413])).
% 0.83/0.86 tff(2415,plain,
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2414, 2407])).
% 0.83/0.86 tff(2416,plain,
% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq1(X)))) | (ap(s(s(s(s(a))))) | (~rpq1(s(s(s(s(a)))))))) <=> ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(a))))) | (~rpq1(s(s(s(s(a)))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2417,plain,
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2418,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(a))))) | (~rpq1(s(s(s(s(a))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2417, 2416])).
% 0.83/0.86 tff(2419,plain,
% 0.83/0.86 (~rpq1(s(s(s(s(a)))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2418, 2415, 567])).
% 0.83/0.86 tff(2420,plain,
% 0.83/0.86 (^[X: $i] : refl((ap(X) | (~rpq4(X))) <=> (ap(X) | (~rpq4(X))))),
% 0.83/0.86 inference(bind,[status(th)],[])).
% 0.83/0.86 tff(2421,plain,
% 0.83/0.86 (![X: $i] : (ap(X) | (~rpq4(X))) <=> ![X: $i] : (ap(X) | (~rpq4(X)))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2420])).
% 0.83/0.86 tff(2422,plain,
% 0.83/0.86 (![X: $i] : (ap(X) | (~rpq4(X))) <=> ![X: $i] : (ap(X) | (~rpq4(X)))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2423,plain,
% 0.83/0.86 (^[X: $i] : rewrite(((~rpq4(X)) | ap(X)) <=> (ap(X) | (~rpq4(X))))),
% 0.83/0.86 inference(bind,[status(th)],[])).
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% 0.83/0.86 (![X: $i] : ((~rpq4(X)) | ap(X)) <=> ![X: $i] : (ap(X) | (~rpq4(X)))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2423])).
% 0.83/0.86 tff(2425,axiom,(![X: $i] : ((~rpq4(X)) | ap(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c089')).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2425, 2424])).
% 0.83/0.86 tff(2427,plain,
% 0.83/0.86 (![X: $i] : (ap(X) | (~rpq4(X)))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2426, 2422])).
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% 0.83/0.86 ![X: $i] : (ap(X) | (~rpq4(X)))),
% 0.83/0.86 inference(skolemize,[status(sab)],[2427])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2428, 2421])).
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% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(a))))) | (~rpq4(s(s(s(s(a)))))))) <=> ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(a))))) | (~rpq4(s(s(s(s(a)))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(a))))) | (~rpq4(s(s(s(s(a))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2431, 2430])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2432, 2429, 567])).
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% 0.83/0.86 (![X: $i] : (ap(X) | (~rpq3(X))) <=> ![X: $i] : (ap(X) | (~rpq3(X)))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2434])).
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% 0.83/0.86 (![X: $i] : (ap(X) | (~rpq3(X))) <=> ![X: $i] : (ap(X) | (~rpq3(X)))),
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% 0.83/0.86 (^[X: $i] : rewrite(((~rpq3(X)) | ap(X)) <=> (ap(X) | (~rpq3(X))))),
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% 0.83/0.86 inference(quant_intro,[status(thm)],[2437])).
% 0.83/0.86 tff(2439,axiom,(![X: $i] : ((~rpq3(X)) | ap(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c082')).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2440, 2436])).
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% 0.83/0.86 inference(skolemize,[status(sab)],[2441])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2442, 2435])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2445, 2444])).
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% 0.83/0.86 tff(2453,axiom,(![X: $i] : ((~rpq2(X)) | ap(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c075')).
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2459, 2458])).
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% 0.83/0.86 inference(quant_intro,[status(thm)],[2462])).
% 0.83/0.86 tff(2464,plain,
% 0.83/0.86 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X)))) <=> ![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2465,plain,
% 0.83/0.86 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((rpq1(X) | rpq2(X)) | rpq3(X)) <=> (rpq1(X) | rpq2(X) | rpq3(X))), ((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) <=> ((rpq1(X) | rpq2(X) | rpq3(X)) | rpq4(X)))), rewrite(((rpq1(X) | rpq2(X) | rpq3(X)) | rpq4(X)) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X))), ((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X)))), (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) <=> ((rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X)) | rq(X)))), rewrite(((rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X)) | rq(X)) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X))), (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X)))), ((((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) | (~rq(s(X)))) <=> ((rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X)) | (~rq(s(X)))))), rewrite(((rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X)) | (~rq(s(X)))) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))), ((((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) | (~rq(s(X)))) <=> (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))))),
% 0.83/0.86 inference(bind,[status(th)],[])).
% 0.83/0.86 tff(2466,plain,
% 0.83/0.86 (![X: $i] : (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) | (~rq(s(X)))) <=> ![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2465])).
% 0.83/0.86 tff(2467,axiom,(![X: $i] : (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | rq(X)) | (~rq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c268')).
% 0.83/0.86 tff(2468,plain,
% 0.83/0.86 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2467, 2466])).
% 0.83/0.86 tff(2469,plain,
% 0.83/0.86 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2468, 2464])).
% 0.83/0.86 tff(2470,plain,(
% 0.83/0.86 ![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(skolemize,[status(sab)],[2469])).
% 0.83/0.86 tff(2471,plain,
% 0.83/0.86 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2470, 2463])).
% 0.83/0.86 tff(2472,plain,
% 0.83/0.86 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2473,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2474,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2473, 2472])).
% 0.83/0.86 tff(2475,plain,
% 0.83/0.86 (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2474, 2471])).
% 0.83/0.86 tff(2476,plain,
% 0.83/0.86 (rq(s(s(s(s(a))))) | (~rq(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2475, 2461, 2447, 2433, 2419])).
% 0.83/0.86 tff(2477,plain,
% 0.83/0.86 (~rq(s(s(s(s(s(a))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2476, 2405])).
% 0.83/0.86 tff(2478,plain,
% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq1(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq1(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq1(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2479,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq1(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq1(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2480,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq1(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2479, 2478])).
% 0.83/0.86 tff(2481,plain,
% 0.83/0.86 (~rpq1(s(s(s(s(s(a))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2480, 2415, 646])).
% 0.83/0.86 tff(2482,plain,
% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq2(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq2(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq2(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq2(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2483,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq2(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq2(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2484,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq2(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq2(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 0.83/0.86 tff(2485,plain,
% 0.83/0.86 (~rpq2(s(s(s(s(s(a))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2484, 2457, 646])).
% 0.83/0.86 tff(2486,plain,
% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq3(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq3(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq3(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq3(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2487,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq3(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq3(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2488,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq3(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq3(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2487, 2486])).
% 0.83/0.86 tff(2489,plain,
% 0.83/0.86 (~rpq3(s(s(s(s(s(a))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2488, 2443, 646])).
% 0.83/0.86 tff(2490,plain,
% 0.83/0.86 (((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq4(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq4(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2491,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(a)))))) | (~rpq4(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2492,plain,
% 0.83/0.86 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(a)))))) | (~rpq4(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 0.83/0.86 tff(2493,plain,
% 0.83/0.86 (~rpq4(s(s(s(s(s(a))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2492, 2429, 646])).
% 0.83/0.86 tff(2494,plain,
% 0.83/0.86 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2495,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2496,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 0.83/0.86 tff(2497,plain,
% 0.83/0.86 (rq(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2496, 2471, 2493, 2489, 2485, 2481])).
% 0.83/0.86 tff(2498,plain,
% 0.83/0.86 (~rq(s(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2497, 2477])).
% 0.83/0.86 tff(2499,plain,
% 0.83/0.86 (^[X: $i] : refl((r(X) | (~rpq2(X))) <=> (r(X) | (~rpq2(X))))),
% 0.83/0.86 inference(bind,[status(th)],[])).
% 0.83/0.86 tff(2500,plain,
% 0.83/0.86 (![X: $i] : (r(X) | (~rpq2(X))) <=> ![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2499])).
% 0.83/0.86 tff(2501,plain,
% 0.83/0.86 (![X: $i] : (r(X) | (~rpq2(X))) <=> ![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2502,plain,
% 0.83/0.86 (^[X: $i] : rewrite(((~rpq2(X)) | r(X)) <=> (r(X) | (~rpq2(X))))),
% 0.83/0.86 inference(bind,[status(th)],[])).
% 0.83/0.86 tff(2503,plain,
% 0.83/0.86 (![X: $i] : ((~rpq2(X)) | r(X)) <=> ![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(quant_intro,[status(thm)],[2502])).
% 0.83/0.86 tff(2504,axiom,(![X: $i] : ((~rpq2(X)) | r(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c069')).
% 0.83/0.86 tff(2505,plain,
% 0.83/0.86 (![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2504, 2503])).
% 0.83/0.86 tff(2506,plain,
% 0.83/0.86 (![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2505, 2501])).
% 0.83/0.86 tff(2507,plain,(
% 0.83/0.86 ![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(skolemize,[status(sab)],[2506])).
% 0.83/0.86 tff(2508,plain,
% 0.83/0.86 (![X: $i] : (r(X) | (~rpq2(X)))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2507, 2500])).
% 0.83/0.86 tff(2509,plain,
% 0.83/0.86 (((~![X: $i] : (r(X) | (~rpq2(X)))) | (r(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (r(X) | (~rpq2(X)))) | r(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2510,plain,
% 0.83/0.86 ((~![X: $i] : (r(X) | (~rpq2(X)))) | (r(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2511,plain,
% 0.83/0.86 ((~![X: $i] : (r(X) | (~rpq2(X)))) | r(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2510, 2509])).
% 0.83/0.86 tff(2512,plain,
% 0.83/0.86 (~rpq2(s(s(s(s(s(s(a)))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2511, 2508, 2234])).
% 0.83/0.86 tff(2513,plain,
% 0.83/0.86 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(s(a))))))))))),
% 0.83/0.86 inference(rewrite,[status(thm)],[])).
% 0.83/0.86 tff(2514,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(s(a))))))))))),
% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
% 0.83/0.86 tff(2515,plain,
% 0.83/0.86 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | rq(X) | (~rq(s(X))))) | rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 0.83/0.86 tff(2516,plain,
% 0.83/0.86 (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(s(a)))))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2515, 2471])).
% 0.83/0.86 tff(2517,plain,
% 0.83/0.86 (~rq(s(s(s(s(s(s(s(a))))))))),
% 0.83/0.86 inference(unit_resolution,[status(thm)],[2516, 2512, 2498, 2387, 2373, 2359])).
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2519, 2518])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2520, 2415, 716])).
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2523, 2522])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2524, 2429, 716])).
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% 0.83/0.86 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2527, 2526])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2528, 2443, 716])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2531, 2530])).
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% 0.83/0.86 inference(modus_ponens,[status(thm)],[2535, 2534])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2536, 2471])).
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% 0.83/0.86 inference(unit_resolution,[status(thm)],[2537, 2533, 2529, 2525, 2521])).
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% 0.83/0.86 tff(2540,plain,(p(s(a)) | rr(s(s(s(a)))) | q(s(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.83/0.86 tff(2541,plain,
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% 0.83/0.86 tff(2542,assumption,(rr(s(s(s(a))))), introduced(assumption)).
% 0.83/0.86 tff(2543,assumption,(~p(s(s(a)))), introduced(assumption)).
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% 0.83/0.86 inference(quant_intro,[status(thm)],[2544])).
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% 0.83/0.86 tff(2549,axiom,(![X: $i] : (((((~ar(X)) | q(X)) | (~r(X))) | p(X)) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c156')).
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% 0.83/0.86 inference(rewrite,[status(thm)],[])).
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% 0.83/0.86 tff(2567,axiom,(![X: $i] : (((((~ar(X)) | q(X)) | r(X)) | p(X)) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c154')).
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% 0.83/0.87 tff(2636,axiom,(![X: $i] : (((((~ap(X)) | r(X)) | p(X)) | q(X)) | p(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c211')).
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% 0.83/0.87 inference(modus_ponens,[status(thm)],[2665, 2664])).
% 0.83/0.87 tff(2667,plain,
% 0.83/0.87 ((~p(s(s(a)))) | p(s(s(s(a))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2666, 1671, 169])).
% 0.83/0.87 tff(2668,plain,
% 0.83/0.87 (p(s(s(s(a))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2667, 2584])).
% 0.83/0.87 tff(2669,plain,
% 0.83/0.87 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2670,plain,
% 0.83/0.87 (((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a))))))) <=> (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2671,plain,
% 0.83/0.87 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a))))))))),
% 0.83/0.87 inference(monotonicity,[status(thm)],[2670])).
% 0.83/0.87 tff(2672,plain,
% 0.83/0.87 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))),
% 0.83/0.87 inference(transitivity,[status(thm)],[2671, 2669])).
% 0.83/0.87 tff(2673,plain,
% 0.83/0.87 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a)))))))),
% 0.83/0.87 inference(quant_inst,[status(thm)],[])).
% 0.83/0.87 tff(2674,plain,
% 0.83/0.87 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a))))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 0.83/0.87 tff(2675,plain,
% 0.83/0.87 (r(s(s(s(a)))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~pp(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2674, 2295, 149])).
% 0.83/0.87 tff(2676,plain,
% 0.83/0.87 (~pp(s(s(s(s(a)))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2675, 2622, 2668, 211])).
% 0.83/0.87 tff(2677,plain,
% 0.83/0.87 (^[X: $i] : refl((pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X))) <=> (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X))))),
% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2678,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2677])).
% 0.83/0.87 tff(2679,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2680,plain,
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% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2681,plain,
% 0.83/0.87 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2680])).
% 0.83/0.87 tff(2682,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | qq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c139')).
% 0.83/0.87 tff(2683,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 0.83/0.87 tff(2684,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2683, 2679])).
% 0.83/0.87 tff(2685,plain,(
% 0.83/0.87 ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(skolemize,[status(sab)],[2684])).
% 0.83/0.87 tff(2686,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2685, 2678])).
% 0.83/0.87 tff(2687,plain,
% 0.83/0.87 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2688,plain,
% 0.83/0.87 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))) <=> (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2689,plain,
% 0.83/0.87 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))))),
% 0.83/0.87 inference(monotonicity,[status(thm)],[2688])).
% 0.83/0.87 tff(2690,plain,
% 0.83/0.87 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(transitivity,[status(thm)],[2689, 2687])).
% 0.83/0.87 tff(2691,plain,
% 0.83/0.87 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(quant_inst,[status(thm)],[])).
% 0.83/0.87 tff(2692,plain,
% 0.83/0.87 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 0.83/0.87 tff(2693,plain,
% 0.83/0.87 (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2692, 2686, 450])).
% 0.83/0.87 tff(2694,plain,
% 0.83/0.87 (qq(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2693, 1776, 2676, 2663, 2650, 2658, 440])).
% 0.83/0.87 tff(2695,plain,
% 0.83/0.87 (qq(s(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[490, 2694])).
% 0.83/0.87 tff(2696,plain,
% 0.83/0.87 (^[X: $i] : refl((pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X))) <=> (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X))))),
% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2697,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2696])).
% 0.83/0.87 tff(2698,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2699,plain,
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% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2700,plain,
% 0.83/0.87 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2699])).
% 0.83/0.87 tff(2701,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | pp(X)) | q(X)) | qq(X)) | r(X)) | (~rr(X))) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c138')).
% 0.83/0.87 tff(2702,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2701, 2700])).
% 0.83/0.87 tff(2703,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2702, 2698])).
% 0.83/0.87 tff(2704,plain,(
% 0.83/0.87 ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(skolemize,[status(sab)],[2703])).
% 0.83/0.87 tff(2705,plain,
% 0.83/0.87 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2704, 2697])).
% 0.83/0.87 tff(2706,plain,
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% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2707,plain,
% 0.83/0.87 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | q(s(s(s(s(s(a))))))) <=> (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2708,plain,
% 0.83/0.87 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))))),
% 0.83/0.87 inference(monotonicity,[status(thm)],[2707])).
% 0.83/0.87 tff(2709,plain,
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% 0.83/0.87 inference(transitivity,[status(thm)],[2708, 2706])).
% 0.83/0.87 tff(2710,plain,
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% 0.83/0.87 inference(quant_inst,[status(thm)],[])).
% 0.83/0.87 tff(2711,plain,
% 0.83/0.87 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 0.83/0.87 tff(2712,plain,
% 0.83/0.87 (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2711, 2705, 450])).
% 0.83/0.87 tff(2713,plain,
% 0.83/0.87 (q(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2712, 2650, 1776, 2676, 2663, 2658, 440])).
% 0.83/0.87 tff(2714,plain,
% 0.83/0.87 (q(s(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[548, 2713])).
% 0.83/0.87 tff(2715,plain,
% 0.83/0.87 (((~![X: $i] : (ar(X) | r(X) | (~r(s(X))))) | (ar(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~r(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (ar(X) | r(X) | (~r(s(X))))) | ar(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~r(s(s(s(s(s(a))))))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2716,plain,
% 0.83/0.87 ((~![X: $i] : (ar(X) | r(X) | (~r(s(X))))) | (ar(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~r(s(s(s(s(s(a))))))))),
% 0.83/0.87 inference(quant_inst,[status(thm)],[])).
% 0.83/0.87 tff(2717,plain,
% 0.83/0.87 ((~![X: $i] : (ar(X) | r(X) | (~r(s(X))))) | ar(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~r(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2716, 2715])).
% 0.83/0.87 tff(2718,plain,
% 0.83/0.87 (r(s(s(s(s(a))))) | (~r(s(s(s(s(s(a)))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2717, 305, 558])).
% 0.83/0.87 tff(2719,plain,
% 0.83/0.87 (~r(s(s(s(s(s(a))))))),
% 0.83/0.87 inference(unit_resolution,[status(thm)],[2718, 2663])).
% 0.83/0.87 tff(2720,plain,
% 0.83/0.87 (^[X: $i] : refl(((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X)))) <=> ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X)))))),
% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2721,plain,
% 0.83/0.87 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2720])).
% 0.83/0.87 tff(2722,plain,
% 0.83/0.87 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2723,plain,
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% 0.83/0.87 inference(bind,[status(th)],[])).
% 0.83/0.87 tff(2724,plain,
% 0.83/0.87 (![X: $i] : (((((~ar(X)) | (~q(X))) | r(X)) | (~p(X))) | (~r(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(quant_intro,[status(thm)],[2723])).
% 0.83/0.87 tff(2725,axiom,(![X: $i] : (((((~ar(X)) | (~q(X))) | r(X)) | (~p(X))) | (~r(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c159')).
% 0.83/0.87 tff(2726,plain,
% 0.83/0.87 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 0.83/0.87 tff(2727,plain,
% 0.83/0.87 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2726, 2722])).
% 0.83/0.87 tff(2728,plain,(
% 0.83/0.87 ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(skolemize,[status(sab)],[2727])).
% 0.83/0.87 tff(2729,plain,
% 0.83/0.87 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))),
% 0.83/0.87 inference(modus_ponens,[status(thm)],[2728, 2721])).
% 0.83/0.87 tff(2730,plain,
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% 0.83/0.87 inference(rewrite,[status(thm)],[])).
% 0.83/0.87 tff(2731,plain,
% 0.83/0.87 (((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))) <=> ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(monotonicity,[status(thm)],[2731])).
% 0.83/0.88 tff(2733,plain,
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% 0.83/0.88 inference(transitivity,[status(thm)],[2732, 2730])).
% 0.83/0.88 tff(2734,plain,
% 0.83/0.88 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 0.83/0.88 inference(quant_inst,[status(thm)],[])).
% 0.83/0.88 tff(2735,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2734, 2733])).
% 0.83/0.88 tff(2736,plain,
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2735, 2729, 472])).
% 0.83/0.88 tff(2737,plain,
% 0.83/0.88 (~r(s(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2736, 2651, 2713, 2719])).
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% 0.83/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 0.83/0.88 tff(2741,plain,
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2740, 281, 567])).
% 0.83/0.88 tff(2742,plain,
% 0.83/0.88 (~pp(s(s(s(s(s(a))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2741, 2676])).
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2744, 2743])).
% 0.83/0.88 tff(2746,plain,
% 0.83/0.88 (pp(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2745, 281, 646])).
% 0.83/0.88 tff(2747,plain,
% 0.83/0.88 (~pp(s(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2746, 2742])).
% 0.83/0.88 tff(2748,assumption,(~r(s(s(s(s(a)))))), introduced(assumption)).
% 0.83/0.88 tff(2749,assumption,(rr(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 0.83/0.88 tff(2750,assumption,(q(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2751,plain,
% 0.83/0.88 (~r(s(s(s(s(s(a))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2718, 2748])).
% 0.83/0.88 tff(2752,plain,
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% 0.83/0.88 inference(bind,[status(th)],[])).
% 0.83/0.88 tff(2753,plain,
% 0.83/0.88 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(quant_intro,[status(thm)],[2752])).
% 0.83/0.88 tff(2754,plain,
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(bind,[status(th)],[])).
% 0.83/0.88 tff(2756,plain,
% 0.83/0.88 (![X: $i] : (((((~ar(X)) | (~q(X))) | r(X)) | (~p(X))) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(quant_intro,[status(thm)],[2755])).
% 0.83/0.88 tff(2757,axiom,(![X: $i] : (((((~ar(X)) | (~q(X))) | r(X)) | (~p(X))) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c160')).
% 0.83/0.88 tff(2758,plain,
% 0.83/0.88 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2757, 2756])).
% 0.83/0.88 tff(2759,plain,
% 0.83/0.88 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2758, 2754])).
% 0.83/0.88 tff(2760,plain,(
% 0.83/0.88 ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(skolemize,[status(sab)],[2759])).
% 0.83/0.88 tff(2761,plain,
% 0.83/0.88 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2760, 2753])).
% 0.83/0.88 tff(2762,plain,
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
% 0.83/0.88 tff(2763,plain,
% 0.83/0.88 (((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))) <=> ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(monotonicity,[status(thm)],[2763])).
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% 0.83/0.88 inference(transitivity,[status(thm)],[2764, 2762])).
% 0.83/0.88 tff(2766,plain,
% 0.83/0.88 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 0.83/0.88 inference(quant_inst,[status(thm)],[])).
% 0.83/0.88 tff(2767,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2766, 2765])).
% 0.83/0.88 tff(2768,plain,
% 0.83/0.88 ((~q(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2767, 2761, 472])).
% 0.83/0.88 tff(2769,plain,
% 0.83/0.88 (~p(s(s(s(s(s(a))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2768, 2751, 2750, 2749])).
% 0.83/0.88 tff(2770,plain,
% 0.83/0.88 (~p(s(s(s(s(a)))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2113, 2769])).
% 0.83/0.88 tff(2771,plain,
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
% 0.83/0.88 tff(2772,plain,
% 0.83/0.88 (((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))) <=> (p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a))))))))),
% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(monotonicity,[status(thm)],[2772])).
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% 0.83/0.88 inference(transitivity,[status(thm)],[2773, 2771])).
% 0.83/0.88 tff(2775,plain,
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% 0.83/0.88 inference(quant_inst,[status(thm)],[])).
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% 0.83/0.88 ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 0.83/0.88 tff(2777,plain,
% 0.83/0.88 (p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2776, 1265, 450])).
% 0.83/0.88 tff(2778,plain,
% 0.83/0.88 (~q(s(s(s(s(a)))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2777, 2770, 2074, 2748])).
% 0.83/0.88 tff(2779,plain,
% 0.83/0.88 (^[X: $i] : refl(((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X)))) <=> ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X)))))),
% 0.83/0.88 inference(bind,[status(th)],[])).
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% 0.83/0.88 inference(quant_intro,[status(thm)],[2779])).
% 0.83/0.88 tff(2781,plain,
% 0.83/0.88 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X))))),
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% 0.83/0.88 inference(bind,[status(th)],[])).
% 0.83/0.88 tff(2783,plain,
% 0.83/0.88 (![X: $i] : (((((~aq(X)) | p(X)) | q(X)) | r(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X))))),
% 0.83/0.88 inference(quant_intro,[status(thm)],[2782])).
% 0.83/0.88 tff(2784,axiom,(![X: $i] : (((((~aq(X)) | p(X)) | q(X)) | r(X)) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c096')).
% 0.83/0.88 tff(2785,plain,
% 0.83/0.88 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2784, 2783])).
% 0.83/0.88 tff(2786,plain,
% 0.83/0.88 (![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X))))),
% 0.83/0.88 inference(modus_ponens,[status(thm)],[2785, 2781])).
% 0.83/0.88 tff(2787,plain,(
% 0.83/0.88 ![X: $i] : ((~aq(X)) | p(X) | r(X) | q(X) | (~qq(s(X))))),
% 0.83/0.88 inference(skolemize,[status(sab)],[2786])).
% 0.83/0.88 tff(2788,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2787, 2780])).
% 0.83/0.88 tff(2789,plain,
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(rewrite,[status(thm)],[])).
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2793, 2792])).
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2794, 2788, 450])).
% 0.83/0.88 tff(2796,plain,
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2795, 2778, 2770, 2074, 2748])).
% 0.83/0.88 tff(2797,plain,(r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))), inference(lemma,lemma(discharge,[]))).
% 0.83/0.88 tff(2798,plain,
% 0.83/0.88 (~rr(s(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2797, 2694, 2663, 2713])).
% 0.83/0.88 tff(2799,assumption,(~r(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 0.83/0.88 tff(2800,assumption,(~p(s(s(s(s(s(s(s(a))))))))), introduced(assumption)).
% 0.83/0.88 tff(2801,assumption,(~rr(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 0.83/0.88 tff(2802,assumption,(~qq(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 0.83/0.88 tff(2803,assumption,(~q(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 0.83/0.88 tff(2804,plain,
% 0.83/0.88 (~p(s(s(s(s(s(s(a)))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2256, 2799, 2803, 2800])).
% 0.83/0.88 tff(2805,plain,
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% 0.83/0.88 tff(2809,plain,
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% 0.83/0.88 tff(2811,plain,
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% 0.83/0.88 tff(2812,plain,
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2811, 2804, 2799, 2803, 2800])).
% 0.83/0.88 tff(2813,plain,(r(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(s(a))))))))), inference(lemma,lemma(discharge,[]))).
% 0.83/0.88 tff(2814,plain,
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% 0.83/0.88 inference(unit_resolution,[status(thm)],[2813, 2799, 2800])).
% 0.83/0.88 tff(2815,plain,
% 0.83/0.88 (q(s(s(s(s(s(a))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[2238, 2814])).
% 0.83/0.88 tff(2816,plain,
% 0.83/0.88 (~qq(s(s(s(s(s(a))))))),
% 0.83/0.88 inference(unit_resolution,[status(thm)],[490, 2802])).
% 0.83/0.88 tff(2817,assumption,(~p(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2818,assumption,(~qq(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2819,assumption,(r(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2820,plain,
% 0.83/0.88 (^[X: $i] : refl(((~ar(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | r(s(X))) <=> ((~ar(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | r(s(X))))),
% 0.83/0.88 inference(bind,[status(th)],[])).
% 0.83/0.88 tff(2821,plain,
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% 0.83/0.88 inference(quant_intro,[status(thm)],[2820])).
% 0.83/0.88 tff(2822,plain,
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% 0.83/0.88 tff(2823,plain,
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% 0.83/0.88 inference(quant_intro,[status(thm)],[2823])).
% 0.83/0.88 tff(2825,axiom,(![X: $i] : (((((((~ar(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | p(X)) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c177')).
% 0.83/0.88 tff(2826,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2825, 2824])).
% 0.83/0.88 tff(2827,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2826, 2822])).
% 0.83/0.88 tff(2828,plain,(
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% 0.83/0.88 inference(skolemize,[status(sab)],[2827])).
% 0.83/0.88 tff(2829,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2828, 2821])).
% 0.83/0.88 tff(2830,plain,
% 0.83/0.88 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 0.83/0.88 inference(rewrite,[status(thm)],[])).
% 0.83/0.88 tff(2831,plain,
% 0.83/0.88 (((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))) <=> (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 0.83/0.88 inference(rewrite,[status(thm)],[])).
% 0.83/0.88 tff(2832,plain,
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% 0.83/0.88 inference(monotonicity,[status(thm)],[2831])).
% 0.83/0.88 tff(2833,plain,
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% 0.83/0.88 tff(2836,plain,
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% 0.83/0.88 inference(bind,[status(th)],[])).
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% 0.83/0.88 inference(quant_intro,[status(thm)],[2838])).
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% 0.83/0.88 inference(bind,[status(th)],[])).
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% 0.83/0.88 inference(quant_intro,[status(thm)],[2841])).
% 0.83/0.88 tff(2843,axiom,(![X: $i] : (((((((~ar(X)) | (~q(X))) | qq(X)) | (~r(X))) | rr(X)) | p(X)) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c165')).
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2843, 2842])).
% 0.83/0.88 tff(2845,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2844, 2840])).
% 0.83/0.88 tff(2846,plain,(
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% 0.83/0.88 inference(skolemize,[status(sab)],[2845])).
% 0.83/0.88 tff(2847,plain,
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2846, 2839])).
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% 0.83/0.88 tff(2858,assumption,(~pp(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2859,assumption,(~r(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.83/0.88 tff(2860,plain,
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% 0.83/0.88 inference(skolemize,[status(sab)],[2867])).
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% 0.83/0.88 inference(modus_ponens,[status(thm)],[2868, 2861])).
% 0.83/0.88 tff(2870,plain,
% 0.83/0.88 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.83/0.89 inference(rewrite,[status(thm)],[])).
% 0.83/0.89 tff(2871,plain,
% 0.83/0.89 ((pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))) <=> ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.83/0.89 inference(rewrite,[status(thm)],[])).
% 0.83/0.89 tff(2872,plain,
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% 0.83/0.89 inference(monotonicity,[status(thm)],[2871])).
% 0.83/0.89 tff(2873,plain,
% 0.83/0.89 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.83/0.89 inference(transitivity,[status(thm)],[2872, 2870])).
% 0.83/0.89 tff(2874,plain,
% 0.83/0.89 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.83/0.89 inference(quant_inst,[status(thm)],[])).
% 0.83/0.89 tff(2875,plain,
% 0.83/0.89 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))),
% 0.83/0.89 inference(modus_ponens,[status(thm)],[2874, 2873])).
% 0.83/0.89 tff(2876,plain,
% 0.83/0.89 ((~q(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))),
% 0.83/0.89 inference(unit_resolution,[status(thm)],[2875, 2869, 472])).
% 0.83/0.89 tff(2877,plain,
% 0.83/0.89 (rr(s(s(s(s(s(a))))))),
% 0.83/0.89 inference(unit_resolution,[status(thm)],[2876, 2859, 2858, 2750, 2817, 2801])).
% 0.83/0.89 tff(2878,plain,
% 0.83/0.89 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2879,plain,
% 0.87/0.89 ((pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a)))))))) <=> ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2880,plain,
% 0.87/0.89 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | ((~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a)))))))))),
% 0.87/0.89 inference(monotonicity,[status(thm)],[2879])).
% 0.87/0.89 tff(2881,plain,
% 0.87/0.89 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(transitivity,[status(thm)],[2880, 2878])).
% 0.87/0.89 tff(2882,plain,
% 0.87/0.89 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(quant_inst,[status(thm)],[])).
% 0.87/0.89 tff(2883,plain,
% 0.87/0.89 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | rr(s(X)))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a)))))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2882, 2881])).
% 0.87/0.89 tff(2884,plain,
% 0.87/0.89 ((~q(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a)))))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2883, 1015, 472])).
% 0.87/0.89 tff(2885,plain,
% 0.87/0.89 ($false),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2884, 2877, 2859, 2858, 2750, 2817, 2801])).
% 0.87/0.89 tff(2886,plain,(r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.89 tff(2887,plain,
% 0.87/0.89 (pp(s(s(s(s(s(a))))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2886, 2857, 2750, 2817, 2801])).
% 0.87/0.89 tff(2888,plain,
% 0.87/0.89 (^[X: $i] : refl(((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X))))),
% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2889,plain,
% 0.87/0.89 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2888])).
% 0.87/0.89 tff(2890,plain,
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% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2891,plain,
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% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2892,plain,
% 0.87/0.89 (![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | r(s(X))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2891])).
% 0.87/0.89 tff(2893,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c196')).
% 0.87/0.89 tff(2894,plain,
% 0.87/0.89 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 0.87/0.89 tff(2895,plain,
% 0.87/0.89 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2894, 2890])).
% 0.87/0.89 tff(2896,plain,(
% 0.87/0.89 ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(skolemize,[status(sab)],[2895])).
% 0.87/0.89 tff(2897,plain,
% 0.87/0.89 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2896, 2889])).
% 0.87/0.89 tff(2898,plain,
% 0.87/0.89 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2899,plain,
% 0.87/0.89 (((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))) <=> (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2900,plain,
% 0.87/0.89 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))))),
% 0.87/0.89 inference(monotonicity,[status(thm)],[2899])).
% 0.87/0.89 tff(2901,plain,
% 0.87/0.89 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(transitivity,[status(thm)],[2900, 2898])).
% 0.87/0.89 tff(2902,plain,
% 0.87/0.89 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 0.87/0.89 inference(quant_inst,[status(thm)],[])).
% 0.87/0.89 tff(2903,plain,
% 0.87/0.89 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2902, 2901])).
% 0.87/0.89 tff(2904,plain,
% 0.87/0.89 (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2903, 2897, 472])).
% 0.87/0.89 tff(2905,plain,
% 0.87/0.89 (rr(s(s(s(s(s(a))))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2904, 2887, 2818, 2857, 2750, 2817, 2799])).
% 0.87/0.89 tff(2906,plain,
% 0.87/0.89 (rr(s(s(s(s(a)))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[591, 2905])).
% 0.87/0.89 tff(2907,plain,
% 0.87/0.89 (rr(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[434, 2906])).
% 0.87/0.89 tff(2908,plain,
% 0.87/0.89 (~p(s(s(s(s(a)))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2113, 2817])).
% 0.87/0.89 tff(2909,plain,
% 0.87/0.89 (~r(s(s(s(s(a)))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[562, 2857])).
% 0.87/0.89 tff(2910,plain,
% 0.87/0.89 (~r(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[164, 2909])).
% 0.87/0.89 tff(2911,plain,
% 0.87/0.89 (q(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2649, 2910, 2908])).
% 0.87/0.89 tff(2912,plain,
% 0.87/0.89 (q(s(s(a)))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[210, 2911])).
% 0.87/0.89 tff(2913,plain,
% 0.87/0.89 (pp(s(s(s(s(a)))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2741, 2887])).
% 0.87/0.89 tff(2914,plain,
% 0.87/0.89 (q(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2649, 3, 446])).
% 0.87/0.89 tff(2915,plain,
% 0.87/0.89 (^[X: $i] : refl(((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X)))) <=> ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X)))))),
% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2916,plain,
% 0.87/0.89 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2915])).
% 0.87/0.89 tff(2917,plain,
% 0.87/0.89 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
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% 0.87/0.89 tff(2918,plain,
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% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2919,plain,
% 0.87/0.89 (![X: $i] : (((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | (~pp(X))) | (~q(X))) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2918])).
% 0.87/0.89 tff(2920,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | (~pp(X))) | (~q(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c222')).
% 0.87/0.89 tff(2921,plain,
% 0.87/0.89 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2920, 2919])).
% 0.87/0.89 tff(2922,plain,
% 0.87/0.89 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2921, 2917])).
% 0.87/0.89 tff(2923,plain,(
% 0.87/0.89 ![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(skolemize,[status(sab)],[2922])).
% 0.87/0.89 tff(2924,plain,
% 0.87/0.89 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2923, 2916])).
% 0.87/0.89 tff(2925,plain,
% 0.87/0.89 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2926,plain,
% 0.87/0.89 (((~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a))))))) <=> (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2927,plain,
% 0.87/0.89 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))))),
% 0.87/0.89 inference(monotonicity,[status(thm)],[2926])).
% 0.87/0.89 tff(2928,plain,
% 0.87/0.89 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 0.87/0.89 inference(transitivity,[status(thm)],[2927, 2925])).
% 0.87/0.89 tff(2929,plain,
% 0.87/0.89 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 0.87/0.89 inference(quant_inst,[status(thm)],[])).
% 0.87/0.89 tff(2930,plain,
% 0.87/0.89 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2929, 2928])).
% 0.87/0.89 tff(2931,plain,
% 0.87/0.89 (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2930, 2924, 149])).
% 0.87/0.89 tff(2932,plain,
% 0.87/0.89 (~pp(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2931, 213, 3, 2542, 2914, 441])).
% 0.87/0.89 tff(2933,plain,
% 0.87/0.89 (^[X: $i] : refl((pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X))) <=> (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X))))),
% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2934,plain,
% 0.87/0.89 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2933])).
% 0.87/0.89 tff(2935,plain,
% 0.87/0.89 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2936,plain,
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% 0.87/0.89 inference(bind,[status(th)],[])).
% 0.87/0.89 tff(2937,plain,
% 0.87/0.89 (![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(quant_intro,[status(thm)],[2936])).
% 0.87/0.89 tff(2938,axiom,(![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | p(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c251')).
% 0.87/0.89 tff(2939,plain,
% 0.87/0.89 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2938, 2937])).
% 0.87/0.89 tff(2940,plain,
% 0.87/0.89 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(modus_ponens,[status(thm)],[2939, 2935])).
% 0.87/0.89 tff(2941,plain,(
% 0.87/0.89 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))),
% 0.87/0.89 inference(skolemize,[status(sab)],[2940])).
% 0.87/0.89 tff(2942,plain,
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% 0.87/0.89 inference(modus_ponens,[status(thm)],[2941, 2934])).
% 0.87/0.89 tff(2943,plain,
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% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2944,plain,
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% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2945,plain,
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% 0.87/0.89 tff(2948,plain,
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% 0.87/0.89 inference(modus_ponens,[status(thm)],[2947, 2946])).
% 0.87/0.89 tff(2949,plain,
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% 0.87/0.89 inference(unit_resolution,[status(thm)],[2948, 2942, 149])).
% 0.87/0.89 tff(2950,plain,
% 0.87/0.89 (qq(s(s(s(a))))),
% 0.87/0.89 inference(unit_resolution,[status(thm)],[2949, 2932, 3, 2542, 2914, 213, 446])).
% 0.87/0.89 tff(2951,plain,
% 0.87/0.89 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
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% 0.87/0.89 tff(2952,plain,
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% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2953,plain,
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% 0.87/0.89 tff(2954,plain,
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% 0.87/0.89 tff(2958,plain,
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% 0.87/0.89 tff(2959,plain,(p(s(s(s(a)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | p(s(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.89 tff(2960,plain,
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% 0.87/0.89 tff(2961,plain,
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% 0.87/0.89 inference(unit_resolution,[status(thm)],[173, 2960])).
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% 0.87/0.89 inference(rewrite,[status(thm)],[])).
% 0.87/0.89 tff(2964,plain,
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% 0.87/0.89 inference(monotonicity,[status(thm)],[2963])).
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% 0.87/0.89 tff(2968,plain,
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% 0.87/0.89 tff(2969,plain,
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% 0.87/0.89 tff(2970,plain,
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% 0.87/0.90 inference(unit_resolution,[status(thm)],[3056, 3031, 2750, 2801, 2074, 2817, 3049])).
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% 0.87/0.90 tff(3061,plain,
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% 0.87/0.90 inference(unit_resolution,[status(thm)],[2215, 3060])).
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% 0.87/0.90 inference(monotonicity,[status(thm)],[3073])).
% 0.87/0.90 tff(3075,plain,
% 0.87/0.90 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | p(s(X)))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 0.87/0.90 inference(transitivity,[status(thm)],[3074, 3072])).
% 0.87/0.90 tff(3076,plain,
% 0.87/0.90 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 0.87/0.90 inference(quant_inst,[status(thm)],[])).
% 0.87/0.90 tff(3077,plain,
% 0.87/0.90 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | p(s(X)))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 0.87/0.90 inference(modus_ponens,[status(thm)],[3076, 3075])).
% 0.87/0.90 tff(3078,plain,
% 0.87/0.90 (r(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[3077, 3071, 495])).
% 0.87/0.90 tff(3079,plain,
% 0.87/0.90 (~pp(s(s(s(s(s(s(a)))))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[3078, 3061, 2799, 2814, 3025, 2800])).
% 0.87/0.90 tff(3080,plain,
% 0.87/0.90 (~pp(s(s(s(s(s(a))))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[2344, 3079])).
% 0.87/0.90 tff(3081,plain,
% 0.87/0.90 (~pp(s(s(s(s(a)))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[586, 3080])).
% 0.87/0.90 tff(3082,plain,
% 0.87/0.90 (p(s(s(s(s(a)))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[571, 3060])).
% 0.87/0.90 tff(3083,plain,
% 0.87/0.90 (~r(s(s(s(s(a)))))),
% 0.87/0.90 inference(unit_resolution,[status(thm)],[2108, 3026, 3082])).
% 0.87/0.90 tff(3084,plain,
% 0.87/0.90 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X)))))),
% 0.87/0.90 inference(bind,[status(th)],[])).
% 0.87/0.90 tff(3085,plain,
% 0.87/0.90 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.90 inference(quant_intro,[status(thm)],[3084])).
% 0.87/0.90 tff(3086,plain,
% 0.87/0.90 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.90 inference(rewrite,[status(thm)],[])).
% 0.87/0.90 tff(3087,plain,
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3088,plain,
% 0.87/0.91 (![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | qq(X)) | r(X)) | rr(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3087])).
% 0.87/0.91 tff(3089,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | qq(X)) | r(X)) | rr(X)) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c111')).
% 0.87/0.91 tff(3090,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3089, 3088])).
% 0.87/0.91 tff(3091,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3090, 3086])).
% 0.87/0.91 tff(3092,plain,(
% 0.87/0.91 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3091])).
% 0.87/0.91 tff(3093,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3092, 3085])).
% 0.87/0.91 tff(3094,plain,
% 0.87/0.91 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3095,plain,
% 0.87/0.91 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))) <=> ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3096,plain,
% 0.87/0.91 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))))),
% 0.87/0.91 inference(monotonicity,[status(thm)],[3095])).
% 0.87/0.91 tff(3097,plain,
% 0.87/0.91 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 0.87/0.91 inference(transitivity,[status(thm)],[3096, 3094])).
% 0.87/0.91 tff(3098,plain,
% 0.87/0.91 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 0.87/0.91 inference(quant_inst,[status(thm)],[])).
% 0.87/0.91 tff(3099,plain,
% 0.87/0.91 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3098, 3097])).
% 0.87/0.91 tff(3100,plain,
% 0.87/0.91 ((~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3099, 3093, 450])).
% 0.87/0.91 tff(3101,plain,
% 0.87/0.91 (qq(s(s(s(s(a)))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3100, 444, 2073, 2748, 443, 2750])).
% 0.87/0.91 tff(3102,plain,
% 0.87/0.91 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X)))))),
% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3103,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3102])).
% 0.87/0.91 tff(3104,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3105,plain,
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3106,plain,
% 0.87/0.91 (![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3105])).
% 0.87/0.91 tff(3107,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c121')).
% 0.87/0.91 tff(3108,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3107, 3106])).
% 0.87/0.91 tff(3109,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3108, 3104])).
% 0.87/0.91 tff(3110,plain,(
% 0.87/0.91 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3109])).
% 0.87/0.91 tff(3111,plain,
% 0.87/0.91 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3110, 3103])).
% 0.87/0.91 tff(3112,plain,
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% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3113,plain,
% 0.87/0.91 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | (~qq(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))) <=> ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(a)))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3114,plain,
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% 0.87/0.91 inference(monotonicity,[status(thm)],[3113])).
% 0.87/0.91 tff(3115,plain,
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% 0.87/0.91 inference(transitivity,[status(thm)],[3114, 3112])).
% 0.87/0.91 tff(3116,plain,
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% 0.87/0.91 inference(quant_inst,[status(thm)],[])).
% 0.87/0.91 tff(3117,plain,
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% 0.87/0.91 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 0.87/0.91 tff(3118,plain,
% 0.87/0.91 ((~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(a))))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3117, 3111, 450])).
% 0.87/0.91 tff(3119,plain,
% 0.87/0.91 ($false),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3118, 3101, 444, 2748, 2073, 443, 2750])).
% 0.87/0.91 tff(3120,plain,(q(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.91 tff(3121,plain,
% 0.87/0.91 (q(s(s(s(s(a)))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3120, 443, 2073, 2748, 2750])).
% 0.87/0.91 tff(3122,plain,
% 0.87/0.91 (q(s(s(s(a))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[439, 3121])).
% 0.87/0.91 tff(3123,plain,
% 0.87/0.91 (~r(s(s(s(a))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[164, 2748])).
% 0.87/0.91 tff(3124,plain,
% 0.87/0.91 (~rr(s(s(s(a))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[2657, 443])).
% 0.87/0.91 tff(3125,assumption,(q(s(s(s(a))))), introduced(assumption)).
% 0.87/0.91 tff(3126,plain,
% 0.87/0.91 (^[X: $i] : refl((pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X)))) <=> (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X)))))),
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% 0.87/0.91 tff(3127,plain,
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% 0.87/0.91 inference(quant_intro,[status(thm)],[3126])).
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3130,plain,
% 0.87/0.91 (![X: $i] : (((((((~ap(X)) | r(X)) | rr(X)) | p(X)) | pp(X)) | (~q(X))) | (~p(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X))))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3129])).
% 0.87/0.91 tff(3131,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | rr(X)) | p(X)) | pp(X)) | (~q(X))) | (~p(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c219')).
% 0.87/0.91 tff(3132,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3131, 3130])).
% 0.87/0.91 tff(3133,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3132, 3128])).
% 0.87/0.91 tff(3134,plain,(
% 0.87/0.91 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X))))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3133])).
% 0.87/0.91 tff(3135,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~p(s(X))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3134, 3127])).
% 0.87/0.91 tff(3136,plain,
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% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3137,plain,
% 0.87/0.91 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | rr(s(s(s(a)))) | (~p(s(s(s(s(a))))))) <=> (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~p(s(s(s(s(a)))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
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% 0.87/0.91 inference(monotonicity,[status(thm)],[3137])).
% 0.87/0.91 tff(3139,plain,
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% 0.87/0.91 tff(3141,plain,
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% 0.87/0.91 tff(3142,plain,
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% 0.87/0.91 inference(unit_resolution,[status(thm)],[3141, 3135, 149])).
% 0.87/0.91 tff(3143,plain,
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3148,plain,
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% 0.87/0.91 inference(quant_intro,[status(thm)],[3147])).
% 0.87/0.91 tff(3149,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~q(X))) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c242')).
% 0.87/0.91 tff(3150,plain,
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% 0.87/0.91 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 0.87/0.91 tff(3151,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3150, 3146])).
% 0.87/0.91 tff(3152,plain,(
% 0.87/0.91 ![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3151])).
% 0.87/0.91 tff(3153,plain,
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% 0.87/0.91 inference(modus_ponens,[status(thm)],[3152, 3145])).
% 0.87/0.91 tff(3154,plain,
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% 0.87/0.91 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | rr(s(s(s(a)))) | (~pp(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~pp(X)) | pp(s(X)))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a)))))))),
% 0.87/0.91 inference(monotonicity,[status(thm)],[3155])).
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% 0.87/0.91 inference(unit_resolution,[status(thm)],[3159, 3153, 149])).
% 0.87/0.91 tff(3161,plain,
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% 0.87/0.91 tff(3162,plain,(p(s(s(s(a)))) | r(s(s(s(a)))) | rr(s(s(s(a)))) | (~q(s(s(s(a))))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a))))))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.91 tff(3163,plain,
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% 0.87/0.91 inference(unit_resolution,[status(thm)],[3162, 3124, 3123, 3122, 212, 2073])).
% 0.87/0.91 tff(3164,assumption,(p(s(s(s(a))))), introduced(assumption)).
% 0.87/0.91 tff(3165,assumption,(~pp(s(s(s(a))))), introduced(assumption)).
% 0.87/0.91 tff(3166,plain,
% 0.87/0.91 (^[X: $i] : refl((pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | pp(s(X))) <=> (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | pp(s(X))))),
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% 0.87/0.91 inference(quant_intro,[status(thm)],[3166])).
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3170,plain,
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% 0.87/0.91 inference(quant_intro,[status(thm)],[3169])).
% 0.87/0.91 tff(3171,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | (~p(X))) | pp(X)) | (~q(X))) | qq(X)) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c232')).
% 0.87/0.91 tff(3172,plain,
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% 0.87/0.91 inference(skolemize,[status(sab)],[3173])).
% 0.87/0.91 tff(3175,plain,
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% 0.87/0.91 tff(3176,plain,
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% 0.87/0.91 tff(3177,plain,
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% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3187,plain,
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3188,plain,
% 0.87/0.91 (![X: $i] : ((((((((~ap(X)) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | pp(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3187])).
% 0.87/0.91 tff(3189,axiom,(![X: $i] : ((((((((~ap(X)) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c261')).
% 0.87/0.91 tff(3190,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3189, 3188])).
% 0.87/0.91 tff(3191,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3190, 3186])).
% 0.87/0.91 tff(3192,plain,(
% 0.87/0.91 ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3191])).
% 0.87/0.91 tff(3193,plain,
% 0.87/0.91 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3192, 3185])).
% 0.87/0.91 tff(3194,plain,
% 0.87/0.91 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3195,plain,
% 0.87/0.91 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | pp(s(s(s(s(a)))))) <=> (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a))))))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3196,plain,
% 0.87/0.91 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a)))))))),
% 0.87/0.91 inference(monotonicity,[status(thm)],[3195])).
% 0.87/0.91 tff(3197,plain,
% 0.87/0.91 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a))))))),
% 0.87/0.91 inference(transitivity,[status(thm)],[3196, 3194])).
% 0.87/0.91 tff(3198,plain,
% 0.87/0.91 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 0.87/0.91 inference(quant_inst,[status(thm)],[])).
% 0.87/0.91 tff(3199,plain,
% 0.87/0.91 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | pp(s(X)))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a)))))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 0.87/0.91 tff(3200,plain,
% 0.87/0.91 (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | pp(s(s(s(s(a)))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3199, 3193, 149])).
% 0.87/0.91 tff(3201,plain,
% 0.87/0.91 ($false),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3200, 3183, 3165, 3, 175, 3125, 3164, 212])).
% 0.87/0.91 tff(3202,plain,(pp(s(s(s(a)))) | r(s(s(s(a)))) | rr(s(s(s(a)))) | (~q(s(s(s(a))))) | (~p(s(s(s(a))))) | pp(s(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 0.87/0.91 tff(3203,plain,
% 0.87/0.91 (pp(s(s(s(a))))),
% 0.87/0.91 inference(unit_resolution,[status(thm)],[3202, 3124, 3123, 3122, 3163, 212])).
% 0.87/0.91 tff(3204,plain,
% 0.87/0.91 (^[X: $i] : refl(((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X))) <=> ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X))))),
% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3205,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3204])).
% 0.87/0.91 tff(3206,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(rewrite,[status(thm)],[])).
% 0.87/0.91 tff(3207,plain,
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% 0.87/0.91 inference(bind,[status(th)],[])).
% 0.87/0.91 tff(3208,plain,
% 0.87/0.91 (![X: $i] : (((((((~ap(X)) | r(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | pp(s(X))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(quant_intro,[status(thm)],[3207])).
% 0.87/0.91 tff(3209,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c240')).
% 0.87/0.91 tff(3210,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3209, 3208])).
% 0.87/0.91 tff(3211,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3210, 3206])).
% 0.87/0.91 tff(3212,plain,(
% 0.87/0.91 ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(skolemize,[status(sab)],[3211])).
% 0.87/0.91 tff(3213,plain,
% 0.87/0.91 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))),
% 0.87/0.91 inference(modus_ponens,[status(thm)],[3212, 3205])).
% 0.87/0.92 tff(3214,plain,
% 0.87/0.92 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3215,plain,
% 0.87/0.92 (((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | pp(s(s(s(s(a)))))) <=> (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3216,plain,
% 0.87/0.92 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a)))))))),
% 0.87/0.92 inference(monotonicity,[status(thm)],[3215])).
% 0.87/0.92 tff(3217,plain,
% 0.87/0.92 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 0.87/0.92 inference(transitivity,[status(thm)],[3216, 3214])).
% 0.87/0.92 tff(3218,plain,
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% 0.87/0.92 inference(quant_intro,[status(thm)],[3242])).
% 0.87/0.92 tff(3244,axiom,(![X: $i] : (((((~ap(X)) | r(X)) | p(X)) | q(X)) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c212')).
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% 0.87/0.92 tff(3262,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | (~qq(X))) | r(X)) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c110')).
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% 0.87/0.92 tff(3272,plain,
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% 0.87/0.92 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 0.87/0.92 tff(3273,plain,
% 0.87/0.92 ((~p(s(a))) | (~pp(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a)))) | (~qq(s(a)))),
% 0.87/0.92 inference(unit_resolution,[status(thm)],[3272, 3266, 18])).
% 0.87/0.92 tff(3274,plain,
% 0.87/0.92 (~qq(s(a))),
% 0.87/0.92 inference(unit_resolution,[status(thm)],[3273, 3256, 1922, 314, 45, 312])).
% 0.87/0.92 tff(3275,assumption,(q(s(s(a)))), introduced(assumption)).
% 0.87/0.92 tff(3276,plain,
% 0.87/0.92 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X)))))),
% 0.87/0.92 inference(bind,[status(th)],[])).
% 0.87/0.92 tff(3277,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(quant_intro,[status(thm)],[3276])).
% 0.87/0.92 tff(3278,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3279,plain,
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% 0.87/0.92 inference(bind,[status(th)],[])).
% 0.87/0.92 tff(3280,plain,
% 0.87/0.92 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(quant_intro,[status(thm)],[3279])).
% 0.87/0.92 tff(3281,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c141')).
% 0.87/0.92 tff(3282,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3281, 3280])).
% 0.87/0.92 tff(3283,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3282, 3278])).
% 0.87/0.92 tff(3284,plain,(
% 0.87/0.92 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(skolemize,[status(sab)],[3283])).
% 0.87/0.92 tff(3285,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3284, 3277])).
% 0.87/0.92 tff(3286,plain,
% 0.87/0.92 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a)))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3287,plain,
% 0.87/0.92 (((~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | (~pp(s(a))) | (~q(s(s(a))))) <=> ((~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a)))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3288,plain,
% 0.87/0.92 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | (~pp(s(a))) | (~q(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a))))))),
% 0.87/0.92 inference(monotonicity,[status(thm)],[3287])).
% 0.87/0.92 tff(3289,plain,
% 0.87/0.92 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | (~pp(s(a))) | (~q(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a)))))),
% 0.87/0.92 inference(transitivity,[status(thm)],[3288, 3286])).
% 0.87/0.92 tff(3290,plain,
% 0.87/0.92 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | (~pp(s(a))) | (~q(s(s(a)))))),
% 0.87/0.92 inference(quant_inst,[status(thm)],[])).
% 0.87/0.92 tff(3291,plain,
% 0.87/0.92 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3290, 3289])).
% 0.87/0.92 tff(3292,plain,
% 0.87/0.92 ((~p(s(a))) | (~pp(s(a))) | (~q(s(a))) | qq(s(a)) | rr(s(a)) | r(s(a)) | (~q(s(s(a))))),
% 0.87/0.92 inference(unit_resolution,[status(thm)],[3291, 3285, 18])).
% 0.87/0.92 tff(3293,plain,
% 0.87/0.92 (rr(s(a))),
% 0.87/0.92 inference(unit_resolution,[status(thm)],[3292, 3274, 1922, 314, 3256, 45, 3275])).
% 0.87/0.92 tff(3294,plain,
% 0.87/0.92 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X)))) <=> ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X)))))),
% 0.87/0.92 inference(bind,[status(th)],[])).
% 0.87/0.92 tff(3295,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(quant_intro,[status(thm)],[3294])).
% 0.87/0.92 tff(3296,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3297,plain,
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% 0.87/0.92 inference(bind,[status(th)],[])).
% 0.87/0.92 tff(3298,plain,
% 0.87/0.92 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | (~rr(X))) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(quant_intro,[status(thm)],[3297])).
% 0.87/0.92 tff(3299,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | (~rr(X))) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c128')).
% 0.87/0.92 tff(3300,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 0.87/0.92 tff(3301,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3300, 3296])).
% 0.87/0.92 tff(3302,plain,(
% 0.87/0.92 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(skolemize,[status(sab)],[3301])).
% 0.87/0.92 tff(3303,plain,
% 0.87/0.92 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))),
% 0.87/0.92 inference(modus_ponens,[status(thm)],[3302, 3295])).
% 0.87/0.92 tff(3304,plain,
% 0.87/0.92 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))) | ((~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))) | (~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | (~qq(s(s(a)))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3305,plain,
% 0.87/0.92 (((~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~pp(s(a))) | (~qq(s(s(a))))) <=> ((~p(s(a))) | (~pp(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | (~qq(s(s(a)))))),
% 0.87/0.92 inference(rewrite,[status(thm)],[])).
% 0.87/0.92 tff(3306,plain,
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% 0.87/0.92 inference(unit_resolution,[status(thm)],[3327, 3083, 3082, 3081, 2815])).
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% 0.87/0.92 (~r(s(s(s(s(s(s(s(a))))))))),
% 0.87/0.92 inference(unit_resolution,[status(thm)],[2261, 2799])).
% 0.87/0.92 tff(3330,plain,
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% 0.87/0.92 inference(unit_resolution,[status(thm)],[3332, 1001, 3329])).
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% 0.87/0.92 inference(modus_ponens,[status(thm)],[3335, 3334])).
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% 0.87/0.92 inference(unit_resolution,[status(thm)],[3336, 1126, 2800])).
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% 0.87/0.92 inference(unit_resolution,[status(thm)],[3345, 1060, 3342])).
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% 0.91/0.93 inference(bind,[status(th)],[])).
% 0.91/0.93 tff(3428,plain,
% 0.91/0.93 (![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~qp(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))),
% 0.91/0.93 inference(quant_intro,[status(thm)],[3427])).
% 0.91/0.93 tff(3429,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~qp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c198')).
% 0.91/0.93 tff(3430,plain,
% 0.91/0.93 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 0.91/0.93 tff(3431,plain,
% 0.91/0.93 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[3430, 3426])).
% 0.91/0.93 tff(3432,plain,(
% 0.91/0.93 ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))),
% 0.91/0.93 inference(skolemize,[status(sab)],[3431])).
% 0.91/0.93 tff(3433,plain,
% 0.91/0.93 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[3432, 3425])).
% 0.91/0.93 tff(3434,plain,
% 0.91/0.93 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(3435,plain,
% 0.91/0.93 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(3436,plain,
% 0.91/0.93 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 0.91/0.93 inference(monotonicity,[status(thm)],[3435])).
% 0.91/0.93 tff(3437,plain,
% 0.91/0.93 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.93 inference(transitivity,[status(thm)],[3436, 3434])).
% 0.91/0.93 tff(3438,plain,
% 0.91/0.93 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(3439,plain,
% 0.91/0.93 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[3438, 3437])).
% 0.91/0.93 tff(3440,plain,
% 0.91/0.93 (qq(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[3439, 3433, 695])).
% 0.91/0.93 tff(3441,plain,
% 0.91/0.93 (~qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.93 inference(unit_resolution,[status(thm)],[3440, 3423, 3410, 3405, 3404, 3396, 3394])).
% 0.91/0.93 tff(3442,assumption,(~pr(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.91/0.93 tff(3443,assumption,(~rq(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.91/0.93 tff(3444,assumption,(~qp(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.91/0.93 tff(3445,plain,
% 0.91/0.93 (((~![X: $i] : (pr(X) | rq(X) | qp(X))) | (qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pr(X) | rq(X) | qp(X))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(3446,plain,
% 0.91/0.93 ((pr(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(rewrite,[status(thm)],[])).
% 0.91/0.93 tff(3447,plain,
% 0.91/0.93 (((~![X: $i] : (pr(X) | rq(X) | qp(X))) | (pr(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pr(X) | rq(X) | qp(X))) | (qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.93 inference(monotonicity,[status(thm)],[3446])).
% 0.91/0.93 tff(3448,plain,
% 0.91/0.93 (((~![X: $i] : (pr(X) | rq(X) | qp(X))) | (pr(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pr(X) | rq(X) | qp(X))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(transitivity,[status(thm)],[3447, 3445])).
% 0.91/0.93 tff(3449,plain,
% 0.91/0.93 ((~![X: $i] : (pr(X) | rq(X) | qp(X))) | (pr(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.93 inference(quant_inst,[status(thm)],[])).
% 0.91/0.93 tff(3450,plain,
% 0.91/0.93 ((~![X: $i] : (pr(X) | rq(X) | qp(X))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a)))))))))) | pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.93 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 0.91/0.94 tff(3451,plain,
% 0.91/0.94 ($false),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3450, 2336, 3444, 3443, 3442])).
% 0.91/0.94 tff(3452,plain,(pr(s(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.91/0.94 tff(3453,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3452, 3441, 3386])).
% 0.91/0.94 tff(3454,plain,
% 0.91/0.94 (^[X: $i] : refl((pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X)))) <=> (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X)))))),
% 0.91/0.94 inference(bind,[status(th)],[])).
% 0.91/0.94 tff(3455,plain,
% 0.91/0.94 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X)))) <=> ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(quant_intro,[status(thm)],[3454])).
% 0.91/0.94 tff(3456,plain,
% 0.91/0.94 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X)))) <=> ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(3457,plain,
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% 0.91/0.94 inference(bind,[status(th)],[])).
% 0.91/0.94 tff(3458,plain,
% 0.91/0.94 (![X: $i] : (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | pr(X)) | (~pr(s(X)))) <=> ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(quant_intro,[status(thm)],[3457])).
% 0.91/0.94 tff(3459,axiom,(![X: $i] : (((((pqr1(X) | pqr2(X)) | pqr3(X)) | pqr4(X)) | pr(X)) | (~pr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c152')).
% 0.91/0.94 tff(3460,plain,
% 0.91/0.94 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3459, 3458])).
% 0.91/0.94 tff(3461,plain,
% 0.91/0.94 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3460, 3456])).
% 0.91/0.94 tff(3462,plain,(
% 0.91/0.94 ![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(skolemize,[status(sab)],[3461])).
% 0.91/0.94 tff(3463,plain,
% 0.91/0.94 (![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3462, 3455])).
% 0.91/0.94 tff(3464,plain,
% 0.91/0.94 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(3465,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(3466,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3465, 3464])).
% 0.91/0.94 tff(3467,plain,
% 0.91/0.94 (pqr1(s(s(s(s(s(s(s(s(a))))))))) | pqr2(s(s(s(s(s(s(s(s(a))))))))) | pqr3(s(s(s(s(s(s(s(s(a))))))))) | pqr4(s(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3466, 3463])).
% 0.91/0.94 tff(3468,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3467, 1527, 1513, 1509, 1495])).
% 0.91/0.94 tff(3469,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3468, 3453])).
% 0.91/0.94 tff(3470,plain,
% 0.91/0.94 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(s(a)))))))) | pqr2(s(s(s(s(s(s(s(a)))))))) | pqr3(s(s(s(s(s(s(s(a)))))))) | pqr4(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(s(a)))))))) | pqr2(s(s(s(s(s(s(s(a)))))))) | pqr3(s(s(s(s(s(s(s(a)))))))) | pqr4(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(3471,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(s(a)))))))) | pqr2(s(s(s(s(s(s(s(a)))))))) | pqr3(s(s(s(s(s(s(s(a)))))))) | pqr4(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(3472,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(s(a)))))))) | pqr2(s(s(s(s(s(s(s(a)))))))) | pqr3(s(s(s(s(s(s(s(a)))))))) | pqr4(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3471, 3470])).
% 0.91/0.94 tff(3473,plain,
% 0.91/0.94 (pqr1(s(s(s(s(s(s(s(a)))))))) | pqr2(s(s(s(s(s(s(s(a)))))))) | pqr3(s(s(s(s(s(s(s(a)))))))) | pqr4(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(a)))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3472, 3463])).
% 0.91/0.94 tff(3474,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(s(a))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3473, 3469, 3346, 3341, 3337, 3333])).
% 0.91/0.94 tff(3475,plain,
% 0.91/0.94 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(a))))))) | pqr2(s(s(s(s(s(s(a))))))) | pqr3(s(s(s(s(s(s(a))))))) | pqr4(s(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))) | (~pr(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(a))))))) | pqr2(s(s(s(s(s(s(a))))))) | pqr3(s(s(s(s(s(s(a))))))) | pqr4(s(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))) | (~pr(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(3476,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(s(a))))))) | pqr2(s(s(s(s(s(s(a))))))) | pqr3(s(s(s(s(s(s(a))))))) | pqr4(s(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))) | (~pr(s(s(s(s(s(s(s(a))))))))))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(3477,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(s(a))))))) | pqr2(s(s(s(s(s(s(a))))))) | pqr3(s(s(s(s(s(s(a))))))) | pqr4(s(s(s(s(s(s(a))))))) | pr(s(s(s(s(s(s(a))))))) | (~pr(s(s(s(s(s(s(s(a)))))))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 0.91/0.94 tff(3478,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(a))))))) | (~pr(s(s(s(s(s(s(s(a)))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3477, 3463, 1589, 1585, 1581, 1577])).
% 0.91/0.94 tff(3479,plain,
% 0.91/0.94 (pr(s(s(s(s(s(s(a)))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3478, 3474])).
% 0.91/0.94 tff(3480,plain,
% 0.91/0.94 (((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a)))))))))),
% 0.91/0.94 inference(rewrite,[status(thm)],[])).
% 0.91/0.94 tff(3481,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | (pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a)))))))))),
% 0.91/0.94 inference(quant_inst,[status(thm)],[])).
% 0.91/0.94 tff(3482,plain,
% 0.91/0.94 ((~![X: $i] : (pqr1(X) | pqr2(X) | pqr3(X) | pqr4(X) | pr(X) | (~pr(s(X))))) | pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a))))))))),
% 0.91/0.94 inference(modus_ponens,[status(thm)],[3481, 3480])).
% 0.91/0.94 tff(3483,plain,
% 0.91/0.94 (pqr1(s(s(s(s(s(a)))))) | pqr2(s(s(s(s(s(a)))))) | pqr3(s(s(s(s(s(a)))))) | pqr4(s(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3482, 3463])).
% 0.91/0.94 tff(3484,plain,
% 0.91/0.94 (pr(s(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(s(a))))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3483, 1567, 1563, 1559, 1555])).
% 0.91/0.94 tff(3485,plain,
% 0.91/0.94 (pr(s(s(s(s(s(a))))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[3484, 3479])).
% 0.91/0.94 tff(3486,plain,
% 0.91/0.94 (~r(s(s(s(s(a)))))),
% 0.91/0.94 inference(unit_resolution,[status(thm)],[2108, 2074, 2073])).
% 0.91/0.94 tff(3487,assumption,(rr(s(s(s(s(a)))))), introduced(assumption)).
% 0.91/0.94 tff(3488,assumption,(pr(s(s(s(s(s(a))))))), introduced(assumption)).
% 0.91/0.94 tff(3489,plain,
% 0.91/0.94 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X)))) <=> ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X)))))),
% 0.91/0.94 inference(bind,[status(th)],[])).
% 0.91/0.94 tff(3490,plain,
% 0.91/0.94 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.91/0.94 inference(quant_intro,[status(thm)],[3489])).
% 0.91/0.94 tff(3491,plain,
% 0.91/0.94 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
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% 0.91/0.94 tff(3492,plain,
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% 0.92/0.94 inference(bind,[status(th)],[])).
% 0.92/0.94 tff(3493,plain,
% 0.92/0.94 (![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | (~rr(X))) | (~qq(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.92/0.94 inference(quant_intro,[status(thm)],[3492])).
% 0.92/0.94 tff(3494,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | (~rr(X))) | (~qq(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c114')).
% 0.92/0.94 tff(3495,plain,
% 0.92/0.94 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 0.92/0.94 tff(3496,plain,
% 0.92/0.94 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[3495, 3491])).
% 0.92/0.94 tff(3497,plain,(
% 0.92/0.94 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.92/0.94 inference(skolemize,[status(sab)],[3496])).
% 0.92/0.94 tff(3498,plain,
% 0.92/0.94 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~qq(s(X))))),
% 0.92/0.94 inference(modus_ponens,[status(thm)],[3497, 3490])).
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% 0.92/0.94 inference(modus_ponens,[status(thm)],[3511, 3510])).
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% 0.92/0.94 tff(3516,plain,
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% 0.92/0.94 tff(3517,plain,
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% 0.92/0.94 inference(unit_resolution,[status(thm)],[439, 3516])).
% 0.92/0.94 tff(3518,plain,
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% 0.92/0.94 inference(unit_resolution,[status(thm)],[210, 3517])).
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% 0.92/0.94 inference(unit_resolution,[status(thm)],[434, 3328])).
% 0.92/0.94 tff(3520,plain,
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% 0.92/0.94 inference(unit_resolution,[status(thm)],[164, 3083])).
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% 0.92/0.94 tff(3526,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | (~pp(X))) | (~q(X))) | (~p(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c221')).
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% 0.92/0.94 tff(3532,plain,
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% 0.92/0.94 inference(monotonicity,[status(thm)],[3532])).
% 0.92/0.94 tff(3534,plain,
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% 0.92/0.94 inference(transitivity,[status(thm)],[3533, 3531])).
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% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
% 0.92/0.94 tff(3536,plain,
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% 0.92/0.94 inference(modus_ponens,[status(thm)],[3535, 3534])).
% 0.92/0.94 tff(3537,plain,
% 0.92/0.94 (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[3536, 3530, 149])).
% 0.92/0.94 tff(3538,plain,
% 0.92/0.94 (~pp(s(s(s(a))))),
% 0.92/0.94 inference(unit_resolution,[status(thm)],[3537, 213, 3, 2542, 3125, 2073])).
% 0.92/0.94 tff(3539,plain,
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% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(3540,plain,
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% 0.92/0.94 inference(rewrite,[status(thm)],[])).
% 0.92/0.94 tff(3541,plain,
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% 0.92/0.94 inference(monotonicity,[status(thm)],[3540])).
% 0.92/0.94 tff(3542,plain,
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% 0.92/0.94 inference(transitivity,[status(thm)],[3541, 3539])).
% 0.92/0.94 tff(3543,plain,
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% 0.92/0.94 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.94 inference(modus_ponens,[status(thm)],[3543, 3542])).
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% 0.92/0.94 inference(unit_resolution,[status(thm)],[3544, 827, 149])).
% 0.92/0.94 tff(3546,plain,
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% 0.92/0.94 tff(3547,plain,
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% 0.92/0.94 tff(3548,plain,
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% 0.92/0.94 inference(quant_intro,[status(thm)],[3547])).
% 0.92/0.94 tff(3549,plain,
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3551,plain,
% 0.92/0.95 (![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | pp(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3550])).
% 0.92/0.95 tff(3552,axiom,(![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | pp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c252')).
% 0.92/0.95 tff(3553,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))),
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% 0.92/0.95 tff(3554,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3553, 3549])).
% 0.92/0.95 tff(3555,plain,(
% 0.92/0.95 ![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))),
% 0.92/0.95 inference(skolemize,[status(sab)],[3554])).
% 0.92/0.95 tff(3556,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3555, 3548])).
% 0.92/0.95 tff(3557,plain,
% 0.92/0.95 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3558,plain,
% 0.92/0.95 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(s(a)))))) <=> (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3559,plain,
% 0.92/0.95 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a)))))))),
% 0.92/0.95 inference(monotonicity,[status(thm)],[3558])).
% 0.92/0.95 tff(3560,plain,
% 0.92/0.95 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | pp(s(X)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 0.92/0.95 inference(transitivity,[status(thm)],[3559, 3557])).
% 0.92/0.95 tff(3561,plain,
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% 0.92/0.95 tff(3562,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 0.92/0.95 tff(3563,plain,
% 0.92/0.95 (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | pp(s(s(s(s(a)))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3562, 3556, 149])).
% 0.92/0.95 tff(3564,plain,
% 0.92/0.95 ($false),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3563, 3546, 3538, 212, 3, 2542, 3125, 213])).
% 0.92/0.95 tff(3565,plain,(p(s(s(s(a)))) | pp(s(s(s(s(a))))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~q(s(s(s(a))))) | (~p(s(s(s(s(a))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.95 tff(3566,plain,
% 0.92/0.95 (p(s(s(s(a))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3565, 3081, 3520, 3519, 3517, 3082])).
% 0.92/0.95 tff(3567,plain,
% 0.92/0.95 (p(s(s(a)))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[173, 3566])).
% 0.92/0.95 tff(3568,plain,
% 0.92/0.95 (r(s(s(a)))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2968, 3567, 3519, 3518])).
% 0.92/0.95 tff(3569,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[2983, 3568, 3567, 3519, 3518])).
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[3570, 2798, 2737])).
% 0.92/0.95 tff(3572,plain,
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% 0.92/0.95 inference(bind,[status(th)],[])).
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% 0.92/0.95 inference(quant_intro,[status(thm)],[3572])).
% 0.92/0.95 tff(3574,plain,
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% 0.92/0.95 tff(3578,plain,
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% 0.92/0.95 inference(monotonicity,[status(thm)],[3583])).
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% 0.92/0.95 inference(transitivity,[status(thm)],[3584, 3582])).
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3586, 3585])).
% 0.92/0.95 tff(3588,plain,
% 0.92/0.95 (rr(s(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3587, 3581, 495])).
% 0.92/0.95 tff(3589,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[3588, 3571, 2798, 2747, 2737, 2714, 2695, 2652])).
% 0.92/0.95 tff(3590,plain,(qq(s(s(a))) | q(s(s(a))) | r(s(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.95 tff(3591,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[3590, 2, 1])).
% 0.92/0.95 tff(3592,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[2649, 3, 211])).
% 0.92/0.95 tff(3593,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[2662, 3])).
% 0.92/0.95 tff(3594,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[2675, 3, 2668, 211])).
% 0.92/0.95 tff(3595,plain,
% 0.92/0.95 (~pp(s(s(s(s(s(a))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2741, 3594])).
% 0.92/0.95 tff(3596,plain,
% 0.92/0.95 (qq(s(s(s(a))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2045, 3591])).
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3598, 3597])).
% 0.92/0.95 tff(3600,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[3599, 486, 415])).
% 0.92/0.95 tff(3601,plain,
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% 0.92/0.95 inference(unit_resolution,[status(thm)],[3600, 3596])).
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3606,plain,
% 0.92/0.95 (![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | qq(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3605])).
% 0.92/0.95 tff(3607,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | qq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c122')).
% 0.92/0.95 tff(3608,plain,
% 0.92/0.95 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 0.92/0.95 tff(3609,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3608, 3604])).
% 0.92/0.95 tff(3610,plain,(
% 0.92/0.95 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))),
% 0.92/0.95 inference(skolemize,[status(sab)],[3609])).
% 0.92/0.95 tff(3611,plain,
% 0.92/0.95 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3610, 3603])).
% 0.92/0.95 tff(3612,plain,
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% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3613,plain,
% 0.92/0.95 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | (~qq(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))) <=> ((~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3614,plain,
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% 0.92/0.95 inference(monotonicity,[status(thm)],[3613])).
% 0.92/0.95 tff(3615,plain,
% 0.92/0.95 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(a))))) | (~qq(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 0.92/0.95 inference(transitivity,[status(thm)],[3614, 3612])).
% 0.92/0.95 tff(3616,plain,
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% 0.92/0.95 inference(quant_inst,[status(thm)],[])).
% 0.92/0.95 tff(3617,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3616, 3615])).
% 0.92/0.95 tff(3618,plain,
% 0.92/0.95 ((~p(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3617, 3611, 450])).
% 0.92/0.95 tff(3619,plain,
% 0.92/0.95 (qq(s(s(s(s(s(a))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3618, 443, 3601, 2748, 2073, 440])).
% 0.92/0.95 tff(3620,plain,
% 0.92/0.95 (~q(s(s(s(s(s(a))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3120, 443, 2073, 440, 2748])).
% 0.92/0.95 tff(3621,plain,
% 0.92/0.95 (p(s(s(s(s(s(a))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2113, 2073])).
% 0.92/0.95 tff(3622,plain,
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3623,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3622])).
% 0.92/0.95 tff(3624,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3626,plain,
% 0.92/0.95 (![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | rr(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3625])).
% 0.92/0.95 tff(3627,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c194')).
% 0.92/0.95 tff(3628,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 0.92/0.95 tff(3629,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3628, 3624])).
% 0.92/0.95 tff(3630,plain,(
% 0.92/0.95 ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))),
% 0.92/0.95 inference(skolemize,[status(sab)],[3629])).
% 0.92/0.95 tff(3631,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3630, 3623])).
% 0.92/0.95 tff(3632,plain,
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% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3633,plain,
% 0.92/0.95 ((pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))) <=> (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a))))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3634,plain,
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% 0.92/0.95 inference(monotonicity,[status(thm)],[3633])).
% 0.92/0.95 tff(3635,plain,
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% 0.92/0.95 inference(transitivity,[status(thm)],[3634, 3632])).
% 0.92/0.95 tff(3636,plain,
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% 0.92/0.95 inference(quant_inst,[status(thm)],[])).
% 0.92/0.95 tff(3637,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3636, 3635])).
% 0.92/0.95 tff(3638,plain,
% 0.92/0.95 (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3637, 3631, 472])).
% 0.92/0.95 tff(3639,plain,
% 0.92/0.95 (rr(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3638, 592, 3621, 3620, 2751, 2858, 3619])).
% 0.92/0.95 tff(3640,plain,
% 0.92/0.95 (rr(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2274, 3639])).
% 0.92/0.95 tff(3641,plain,
% 0.92/0.95 (((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3642,plain,
% 0.92/0.95 ((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | (ar(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.95 inference(quant_inst,[status(thm)],[])).
% 0.92/0.95 tff(3643,plain,
% 0.92/0.95 ((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | ar(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3642, 3641])).
% 0.92/0.95 tff(3644,plain,
% 0.92/0.95 ((~rr(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3643, 948, 767])).
% 0.92/0.95 tff(3645,plain,
% 0.92/0.95 (rr(s(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3644, 3640])).
% 0.92/0.95 tff(3646,plain,
% 0.92/0.95 (^[X: $i] : refl((pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X))) <=> (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X))))),
% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3647,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3646])).
% 0.92/0.95 tff(3648,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3649,plain,
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3650,plain,
% 0.92/0.95 (![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | r(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3649])).
% 0.92/0.95 tff(3651,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c193')).
% 0.92/0.95 tff(3652,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3651, 3650])).
% 0.92/0.95 tff(3653,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3652, 3648])).
% 0.92/0.95 tff(3654,plain,(
% 0.92/0.95 ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))),
% 0.92/0.95 inference(skolemize,[status(sab)],[3653])).
% 0.92/0.95 tff(3655,plain,
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% 0.92/0.95 inference(modus_ponens,[status(thm)],[3654, 3647])).
% 0.92/0.95 tff(3656,plain,
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% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3657,plain,
% 0.92/0.95 ((pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(s(a)))))))) <=> (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | r(s(s(s(s(s(s(a))))))))),
% 0.92/0.95 inference(rewrite,[status(thm)],[])).
% 0.92/0.95 tff(3658,plain,
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% 0.92/0.95 inference(monotonicity,[status(thm)],[3657])).
% 0.92/0.95 tff(3659,plain,
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% 0.92/0.95 inference(transitivity,[status(thm)],[3658, 3656])).
% 0.92/0.95 tff(3660,plain,
% 0.92/0.95 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(s(a))))))))),
% 0.92/0.95 inference(quant_inst,[status(thm)],[])).
% 0.92/0.95 tff(3661,plain,
% 0.92/0.95 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | r(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 0.92/0.95 tff(3662,plain,
% 0.92/0.95 (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | pp(s(s(s(s(s(a)))))) | r(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3661, 3655, 472])).
% 0.92/0.95 tff(3663,plain,
% 0.92/0.95 (r(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[3662, 592, 3621, 3620, 2751, 2858, 3619])).
% 0.92/0.95 tff(3664,plain,
% 0.92/0.95 (r(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[618, 3663])).
% 0.92/0.95 tff(3665,plain,
% 0.92/0.95 (r(s(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[771, 3664])).
% 0.92/0.95 tff(3666,plain,
% 0.92/0.95 (qq(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[490, 3619])).
% 0.92/0.95 tff(3667,plain,
% 0.92/0.95 (p(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2215, 3621])).
% 0.92/0.95 tff(3668,plain,
% 0.92/0.95 (~q(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2238, 3620])).
% 0.92/0.95 tff(3669,plain,
% 0.92/0.95 (~pp(s(s(s(s(s(s(a)))))))),
% 0.92/0.95 inference(unit_resolution,[status(thm)],[2746, 2858])).
% 0.92/0.95 tff(3670,plain,
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% 0.92/0.95 inference(bind,[status(th)],[])).
% 0.92/0.95 tff(3671,plain,
% 0.92/0.95 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))),
% 0.92/0.95 inference(quant_intro,[status(thm)],[3670])).
% 0.92/0.95 tff(3672,plain,
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% 0.92/0.95 tff(3673,plain,
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% 0.92/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.96 inference(modus_ponens,[status(thm)],[3741, 3740])).
% 0.92/0.96 tff(3743,plain,
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% 0.92/0.96 inference(unit_resolution,[status(thm)],[3742, 190, 699])).
% 0.92/0.96 tff(3744,plain,
% 0.92/0.96 (~qq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.96 inference(unit_resolution,[status(thm)],[3743, 3739])).
% 0.92/0.96 tff(3745,plain,
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% 0.92/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.96 inference(modus_ponens,[status(thm)],[3746, 3745])).
% 0.92/0.96 tff(3748,plain,
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% 0.92/0.96 inference(unit_resolution,[status(thm)],[3747, 206, 699])).
% 0.92/0.96 tff(3749,plain,
% 0.92/0.96 (~q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.96 inference(unit_resolution,[status(thm)],[3748, 3701])).
% 0.92/0.96 tff(3750,plain,
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% 0.92/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.96 inference(modus_ponens,[status(thm)],[3751, 3750])).
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% 0.92/0.96 inference(unit_resolution,[status(thm)],[3752, 1671, 725])).
% 0.92/0.96 tff(3754,plain,
% 0.92/0.96 (p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.96 inference(unit_resolution,[status(thm)],[3753, 3692])).
% 0.92/0.96 tff(3755,plain,
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% 0.92/0.96 inference(bind,[status(th)],[])).
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% 0.92/0.96 inference(quant_intro,[status(thm)],[3755])).
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% 0.92/0.96 inference(bind,[status(th)],[])).
% 0.92/0.96 tff(3759,plain,
% 0.92/0.96 (![X: $i] : (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | r(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3758])).
% 0.92/0.97 tff(3760,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | pp(X)) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c181')).
% 0.92/0.97 tff(3761,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3760, 3759])).
% 0.92/0.97 tff(3762,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3761, 3757])).
% 0.92/0.97 tff(3763,plain,(
% 0.92/0.97 ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))),
% 0.92/0.97 inference(skolemize,[status(sab)],[3762])).
% 0.92/0.97 tff(3764,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3763, 3756])).
% 0.92/0.97 tff(3765,plain,
% 0.92/0.97 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3766,plain,
% 0.92/0.97 ((pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3767,plain,
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% 0.92/0.97 inference(monotonicity,[status(thm)],[3766])).
% 0.92/0.97 tff(3768,plain,
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% 0.92/0.97 inference(transitivity,[status(thm)],[3767, 3765])).
% 0.92/0.97 tff(3769,plain,
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3770,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3769, 3768])).
% 0.92/0.97 tff(3771,plain,
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% 0.92/0.97 inference(unit_resolution,[status(thm)],[3770, 3764, 695])).
% 0.92/0.97 tff(3772,plain,
% 0.92/0.97 (r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3771, 3710, 3701, 3692, 3665, 3645])).
% 0.92/0.97 tff(3773,plain,
% 0.92/0.97 (^[X: $i] : refl((pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X))) <=> (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X))))),
% 0.92/0.97 inference(bind,[status(th)],[])).
% 0.92/0.97 tff(3774,plain,
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% 0.92/0.97 inference(quant_intro,[status(thm)],[3773])).
% 0.92/0.97 tff(3775,plain,
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% 0.92/0.97 inference(quant_intro,[status(thm)],[3813])).
% 0.92/0.97 tff(3815,plain,
% 0.92/0.97 (![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
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% 0.92/0.97 inference(bind,[status(th)],[])).
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% 0.92/0.97 (![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | qp(s(X))) <=> ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3816])).
% 0.92/0.97 tff(3818,axiom,(![X: $i] : ((((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | rr(X)) | (~p(X))) | pp(X)) | qp(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c195')).
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3819, 3815])).
% 0.92/0.97 tff(3821,plain,(
% 0.92/0.97 ![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))),
% 0.92/0.97 inference(skolemize,[status(sab)],[3820])).
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3821, 3814])).
% 0.92/0.97 tff(3823,plain,
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% 0.92/0.97 inference(rewrite,[status(thm)],[])).
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% 0.92/0.97 inference(monotonicity,[status(thm)],[3824])).
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% 0.92/0.97 inference(transitivity,[status(thm)],[3825, 3823])).
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3827, 3826])).
% 0.92/0.97 tff(3829,plain,
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% 0.92/0.97 tff(3830,plain,
% 0.92/0.97 (qp(s(s(s(s(s(s(a)))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3829, 592, 3621, 3620, 2751, 2858, 3619])).
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.97 inference(unit_resolution,[status(thm)],[3834, 2168, 2164, 2160, 2156])).
% 0.92/0.97 tff(3836,plain,
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% 0.92/0.97 inference(unit_resolution,[status(thm)],[3835, 3830])).
% 0.92/0.97 tff(3837,plain,
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% 0.92/0.97 tff(3841,plain,
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% 0.92/0.97 inference(unit_resolution,[status(thm)],[3840, 3836])).
% 0.92/0.97 tff(3842,plain,
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% 0.92/0.97 inference(bind,[status(th)],[])).
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% 0.92/0.97 inference(quant_intro,[status(thm)],[3842])).
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% 0.92/0.97 tff(3845,plain,
% 0.92/0.97 (^[X: $i] : rewrite(((~qrp4(X)) | pp(X)) <=> (pp(X) | (~qrp4(X))))),
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% 0.92/0.97 inference(quant_intro,[status(thm)],[3845])).
% 0.92/0.97 tff(3847,axiom,(![X: $i] : ((~qrp4(X)) | pp(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c060')).
% 0.92/0.97 tff(3848,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3847, 3846])).
% 0.92/0.97 tff(3849,plain,
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% 0.92/0.97 tff(3850,plain,(
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% 0.92/0.97 inference(skolemize,[status(sab)],[3849])).
% 0.92/0.97 tff(3851,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3850, 3843])).
% 0.92/0.97 tff(3852,plain,
% 0.92/0.97 (((~![X: $i] : (pp(X) | (~qrp4(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~qrp4(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~qrp4(X)))) | pp(s(s(s(s(s(s(s(s(a))))))))) | (~qrp4(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3853,plain,
% 0.92/0.97 ((~![X: $i] : (pp(X) | (~qrp4(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~qrp4(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3854,plain,
% 0.92/0.97 ((~![X: $i] : (pp(X) | (~qrp4(X)))) | pp(s(s(s(s(s(s(s(s(a))))))))) | (~qrp4(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3853, 3852])).
% 0.92/0.97 tff(3855,plain,
% 0.92/0.97 (~qrp4(s(s(s(s(s(s(s(s(a)))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3854, 3851, 3710])).
% 0.92/0.97 tff(3856,plain,
% 0.92/0.97 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | (~qp(X)) | qp(s(X)))) | (qrp1(s(s(s(s(s(s(s(s(a))))))))) | qrp2(s(s(s(s(s(s(s(s(a))))))))) | qrp3(s(s(s(s(s(s(s(s(a))))))))) | qrp4(s(s(s(s(s(s(s(s(a))))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | (~qp(X)) | qp(s(X)))) | qrp1(s(s(s(s(s(s(s(s(a))))))))) | qrp2(s(s(s(s(s(s(s(s(a))))))))) | qrp3(s(s(s(s(s(s(s(s(a))))))))) | qrp4(s(s(s(s(s(s(s(s(a))))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3857,plain,
% 0.92/0.97 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | (~qp(X)) | qp(s(X)))) | (qrp1(s(s(s(s(s(s(s(s(a))))))))) | qrp2(s(s(s(s(s(s(s(s(a))))))))) | qrp3(s(s(s(s(s(s(s(s(a))))))))) | qrp4(s(s(s(s(s(s(s(s(a))))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3858,plain,
% 0.92/0.97 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | (~qp(X)) | qp(s(X)))) | qrp1(s(s(s(s(s(s(s(s(a))))))))) | qrp2(s(s(s(s(s(s(s(s(a))))))))) | qrp3(s(s(s(s(s(s(s(s(a))))))))) | qrp4(s(s(s(s(s(s(s(s(a))))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 0.92/0.97 tff(3859,plain,
% 0.92/0.97 (qrp1(s(s(s(s(s(s(s(s(a))))))))) | qrp2(s(s(s(s(s(s(s(s(a))))))))) | qrp3(s(s(s(s(s(s(s(s(a))))))))) | qrp4(s(s(s(s(s(s(s(s(a))))))))) | (~qp(s(s(s(s(s(s(s(s(a)))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3858, 1404])).
% 0.92/0.97 tff(3860,plain,
% 0.92/0.97 (qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3859, 3855, 3841, 3812, 3808, 3804])).
% 0.92/0.97 tff(3861,plain,
% 0.92/0.97 (qq(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[503, 3666])).
% 0.92/0.97 tff(3862,plain,
% 0.92/0.97 (~pqr1(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[514, 511, 3861])).
% 0.92/0.97 tff(3863,plain,
% 0.92/0.97 (~pqr2(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[1615, 1612, 3861])).
% 0.92/0.97 tff(3864,plain,
% 0.92/0.97 (~pqr3(s(s(s(s(s(s(s(a))))))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[1604, 1601, 3861])).
% 0.92/0.97 tff(3865,plain,
% 0.92/0.97 (^[X: $i] : refl((q(X) | (~pqr4(X))) <=> (q(X) | (~pqr4(X))))),
% 0.92/0.97 inference(bind,[status(th)],[])).
% 0.92/0.97 tff(3866,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr4(X))) <=> ![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3865])).
% 0.92/0.97 tff(3867,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr4(X))) <=> ![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3868,plain,
% 0.92/0.97 (^[X: $i] : rewrite(((~pqr4(X)) | q(X)) <=> (q(X) | (~pqr4(X))))),
% 0.92/0.97 inference(bind,[status(th)],[])).
% 0.92/0.97 tff(3869,plain,
% 0.92/0.97 (![X: $i] : ((~pqr4(X)) | q(X)) <=> ![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3868])).
% 0.92/0.97 tff(3870,axiom,(![X: $i] : ((~pqr4(X)) | q(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c029')).
% 0.92/0.97 tff(3871,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3870, 3869])).
% 0.92/0.97 tff(3872,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3871, 3867])).
% 0.92/0.97 tff(3873,plain,(
% 0.92/0.97 ![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(skolemize,[status(sab)],[3872])).
% 0.92/0.97 tff(3874,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr4(X)))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3873, 3866])).
% 0.92/0.97 tff(3875,plain,
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% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3876,plain,
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3877,plain,
% 0.92/0.97 ((~![X: $i] : (q(X) | (~pqr4(X)))) | q(s(s(s(s(a))))) | (~pqr4(s(s(s(s(a))))))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3876, 3875])).
% 0.92/0.97 tff(3878,plain,
% 0.92/0.97 (~pqr4(s(s(s(s(a)))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3877, 3874, 440])).
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% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3880,plain,
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.97 ((~![X: $i] : ((~pqr1(X)) | (~qq(X)))) | (~pqr1(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 0.92/0.97 inference(modus_ponens,[status(thm)],[3880, 3879])).
% 0.92/0.97 tff(3882,plain,
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% 0.92/0.97 inference(unit_resolution,[status(thm)],[3881, 511, 3601])).
% 0.92/0.97 tff(3883,plain,
% 0.92/0.97 (^[X: $i] : refl((q(X) | (~pqr2(X))) <=> (q(X) | (~pqr2(X))))),
% 0.92/0.97 inference(bind,[status(th)],[])).
% 0.92/0.97 tff(3884,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr2(X))) <=> ![X: $i] : (q(X) | (~pqr2(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3883])).
% 0.92/0.97 tff(3885,plain,
% 0.92/0.97 (![X: $i] : (q(X) | (~pqr2(X))) <=> ![X: $i] : (q(X) | (~pqr2(X)))),
% 0.92/0.97 inference(rewrite,[status(thm)],[])).
% 0.92/0.97 tff(3886,plain,
% 0.92/0.97 (^[X: $i] : rewrite(((~pqr2(X)) | q(X)) <=> (q(X) | (~pqr2(X))))),
% 0.92/0.97 inference(bind,[status(th)],[])).
% 0.92/0.97 tff(3887,plain,
% 0.92/0.97 (![X: $i] : ((~pqr2(X)) | q(X)) <=> ![X: $i] : (q(X) | (~pqr2(X)))),
% 0.92/0.97 inference(quant_intro,[status(thm)],[3886])).
% 0.92/0.97 tff(3888,axiom,(![X: $i] : ((~pqr2(X)) | q(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c015')).
% 0.92/0.97 tff(3889,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3888, 3887])).
% 0.92/0.97 tff(3890,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3889, 3885])).
% 0.92/0.97 tff(3891,plain,(
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% 0.92/0.97 inference(skolemize,[status(sab)],[3890])).
% 0.92/0.97 tff(3892,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3891, 3884])).
% 0.92/0.97 tff(3893,plain,
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% 0.92/0.97 inference(rewrite,[status(thm)],[])).
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3895,plain,
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% 0.92/0.97 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 0.92/0.97 tff(3896,plain,
% 0.92/0.97 (~pqr2(s(s(s(s(a)))))),
% 0.92/0.97 inference(unit_resolution,[status(thm)],[3895, 3892, 440])).
% 0.92/0.97 tff(3897,plain,
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% 0.92/0.97 inference(rewrite,[status(thm)],[])).
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% 0.92/0.97 inference(quant_inst,[status(thm)],[])).
% 0.92/0.97 tff(3899,plain,
% 0.92/0.98 ((~![X: $i] : ((~pqr3(X)) | (~qq(X)))) | (~pqr3(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 0.92/0.98 inference(modus_ponens,[status(thm)],[3898, 3897])).
% 0.92/0.98 tff(3900,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3899, 1601, 3601])).
% 0.92/0.98 tff(3901,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[108, 2])).
% 0.92/0.98 tff(3902,plain,
% 0.92/0.98 (p(s(a))),
% 0.92/0.98 inference(unit_resolution,[status(thm)],[2540, 175, 1])).
% 0.92/0.98 tff(3903,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[1675, 3902])).
% 0.92/0.98 tff(3904,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[290, 1723])).
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% 0.92/0.98 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (q(s(s(a))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | q(s(s(a))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | rr(s(s(s(a)))))),
% 0.92/0.98 inference(rewrite,[status(thm)],[])).
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% 0.92/0.98 ((pp(s(s(a))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | r(s(s(a))) | q(s(s(a))) | (~qq(s(s(a)))) | rr(s(s(a))) | rr(s(s(s(a))))) <=> (q(s(s(a))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | (~p(s(s(a)))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | rr(s(s(s(a)))))),
% 0.92/0.98 inference(rewrite,[status(thm)],[])).
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% 0.92/0.98 inference(monotonicity,[status(thm)],[3906])).
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% 0.92/0.98 inference(transitivity,[status(thm)],[3907, 3905])).
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3909, 3908])).
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% 0.92/0.98 tff(3913,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[1905, 3912])).
% 0.92/0.98 tff(3914,assumption,(rr(s(a))), introduced(assumption)).
% 0.92/0.98 tff(3915,plain,
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3917,plain,
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% 0.92/0.98 inference(monotonicity,[status(thm)],[3916])).
% 0.92/0.98 tff(3918,plain,
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% 0.92/0.98 inference(transitivity,[status(thm)],[3917, 3915])).
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3919, 3918])).
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3920, 3498, 18])).
% 0.92/0.98 tff(3922,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3921, 313, 312, 1922, 45, 3914])).
% 0.92/0.98 tff(3923,plain,
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3924,plain,
% 0.92/0.98 ((pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | q(s(s(a)))) <=> (pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a))))),
% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3925,plain,
% 0.92/0.98 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | q(s(s(a))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a)))))),
% 0.92/0.98 inference(monotonicity,[status(thm)],[3924])).
% 0.92/0.98 tff(3926,plain,
% 0.92/0.98 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | q(s(s(a))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a))))),
% 0.92/0.98 inference(transitivity,[status(thm)],[3925, 3923])).
% 0.92/0.98 tff(3927,plain,
% 0.92/0.98 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | (pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | q(s(s(a))))),
% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
% 0.92/0.98 tff(3928,plain,
% 0.92/0.98 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | q(X) | qq(X) | (~rr(X)) | q(s(X)))) | pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a)))),
% 0.92/0.98 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 0.92/0.98 tff(3929,plain,
% 0.92/0.98 (pp(s(a)) | (~p(s(a))) | q(s(a)) | qq(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a)))),
% 0.92/0.98 inference(unit_resolution,[status(thm)],[3928, 2705, 18])).
% 0.92/0.98 tff(3930,plain,
% 0.92/0.98 ($false),
% 0.92/0.98 inference(unit_resolution,[status(thm)],[3929, 3922, 313, 1922, 1723, 3914, 45, 1])).
% 0.92/0.98 tff(3931,plain,(q(s(a)) | (~p(s(a))) | pp(s(a)) | (~rr(s(a))) | r(s(a)) | q(s(s(a))) | (~qq(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.98 tff(3932,plain,
% 0.92/0.98 (q(s(a))),
% 0.92/0.98 inference(unit_resolution,[status(thm)],[3931, 1723, 3902, 3913, 3901, 1, 2041])).
% 0.92/0.98 tff(3933,plain,
% 0.92/0.98 (^[X: $i] : refl((pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X))) <=> (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X))))),
% 0.92/0.98 inference(bind,[status(th)],[])).
% 0.92/0.98 tff(3934,plain,
% 0.92/0.98 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))),
% 0.92/0.98 inference(quant_intro,[status(thm)],[3933])).
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% 0.92/0.98 inference(bind,[status(th)],[])).
% 0.92/0.98 tff(3937,plain,
% 0.92/0.98 (![X: $i] : (((((((~aq(X)) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | r(X)) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))),
% 0.92/0.98 inference(quant_intro,[status(thm)],[3936])).
% 0.92/0.98 tff(3938,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | r(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c119')).
% 0.92/0.98 tff(3939,plain,
% 0.92/0.98 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))),
% 0.92/0.98 inference(modus_ponens,[status(thm)],[3938, 3937])).
% 0.92/0.98 tff(3940,plain,
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3939, 3935])).
% 0.92/0.98 tff(3941,plain,(
% 0.92/0.98 ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))),
% 0.92/0.98 inference(skolemize,[status(sab)],[3940])).
% 0.92/0.98 tff(3942,plain,
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3941, 3934])).
% 0.92/0.98 tff(3943,plain,
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3944,plain,
% 0.92/0.98 ((pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | (~qq(s(a))) | q(s(s(a)))) <=> (pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | q(s(s(a))) | (~qq(s(a))))),
% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3945,plain,
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% 0.92/0.98 inference(monotonicity,[status(thm)],[3944])).
% 0.92/0.98 tff(3946,plain,
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% 0.92/0.98 inference(transitivity,[status(thm)],[3945, 3943])).
% 0.92/0.98 tff(3947,plain,
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
% 0.92/0.98 tff(3948,plain,
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% 0.92/0.98 tff(3949,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3948, 3942, 18])).
% 0.92/0.98 tff(3950,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3949, 3932, 1723, 3902, 3901, 1])).
% 0.92/0.98 tff(3951,plain,
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% 0.92/0.98 tff(3952,plain,
% 0.92/0.98 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))),
% 0.92/0.98 inference(quant_intro,[status(thm)],[3951])).
% 0.92/0.98 tff(3953,plain,
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
% 0.92/0.98 tff(3954,plain,
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% 0.92/0.98 inference(bind,[status(th)],[])).
% 0.92/0.98 tff(3955,plain,
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% 0.92/0.98 inference(quant_intro,[status(thm)],[3954])).
% 0.92/0.98 tff(3956,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | pp(X)) | (~q(X))) | qq(X)) | r(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c107')).
% 0.92/0.98 tff(3957,plain,
% 0.92/0.98 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))),
% 0.92/0.98 inference(modus_ponens,[status(thm)],[3956, 3955])).
% 0.92/0.98 tff(3958,plain,
% 0.92/0.98 (![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))),
% 0.92/0.98 inference(modus_ponens,[status(thm)],[3957, 3953])).
% 0.92/0.98 tff(3959,plain,(
% 0.92/0.98 ![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))),
% 0.92/0.98 inference(skolemize,[status(sab)],[3958])).
% 0.92/0.98 tff(3960,plain,
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3959, 3952])).
% 0.92/0.98 tff(3961,plain,
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% 0.92/0.98 tff(3962,plain,
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% 0.92/0.98 inference(monotonicity,[status(thm)],[3962])).
% 0.92/0.98 tff(3964,plain,
% 0.92/0.98 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(a)) | (~aq(s(a))) | (~p(s(a))) | r(s(a)) | (~q(s(a))) | qq(s(a)) | q(s(s(a))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | pp(s(a)) | (~p(s(a))) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | r(s(a)) | q(s(s(a))))),
% 0.92/0.98 inference(transitivity,[status(thm)],[3963, 3961])).
% 0.92/0.98 tff(3965,plain,
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% 0.92/0.98 tff(3967,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3966, 3960, 18])).
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% 0.92/0.98 tff(3969,plain,(pp(s(a)) | q(s(s(a))) | rr(s(s(s(a)))) | r(s(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.98 tff(3970,plain,
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% 0.92/0.98 tff(3971,plain,
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% 0.92/0.98 tff(3972,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3254, 3970, 3971])).
% 0.92/0.98 tff(3973,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[1915, 3972])).
% 0.92/0.98 tff(3974,plain,
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% 0.92/0.98 tff(3975,plain,
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% 0.92/0.98 inference(quant_intro,[status(thm)],[3976])).
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% 0.92/0.98 inference(bind,[status(th)],[])).
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% 0.92/0.98 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | pr(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))),
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% 0.92/0.98 tff(3981,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | pr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c143')).
% 0.92/0.98 tff(3982,plain,
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% 0.92/0.98 inference(skolemize,[status(sab)],[3983])).
% 0.92/0.98 tff(3985,plain,
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% 0.92/0.98 tff(3986,plain,
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% 0.92/0.98 inference(rewrite,[status(thm)],[])).
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% 0.92/0.98 tff(3992,plain,
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[3991, 3985, 18])).
% 0.92/0.98 tff(3993,plain,
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[3999, 3998])).
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.98 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[4007, 4006])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[4011, 4010])).
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[4012, 1169])).
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[4014, 3993])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[4017, 4016])).
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% 0.92/0.98 inference(modus_ponens,[status(thm)],[4021, 4020])).
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% 0.92/0.98 inference(unit_resolution,[status(thm)],[4030, 1505, 415])).
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% 0.92/0.99 tff(4053,assumption,(qrp3(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
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% 0.92/0.99 tff(4058,plain,(~qrp3(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.99 tff(4059,assumption,(pqr2(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
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% 0.92/0.99 inference(rewrite,[status(thm)],[])).
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% 0.92/0.99 inference(quant_inst,[status(thm)],[])).
% 0.92/0.99 tff(4062,plain,
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% 0.92/0.99 inference(modus_ponens,[status(thm)],[4061, 4060])).
% 0.92/0.99 tff(4063,plain,
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% 0.92/0.99 tff(4065,assumption,(pqr4(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4066,plain,
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% 0.92/0.99 inference(quant_inst,[status(thm)],[])).
% 0.92/0.99 tff(4068,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[4068, 1505, 960, 4065])).
% 0.92/0.99 tff(4070,plain,(~pqr4(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.99 tff(4071,assumption,(~pqr3(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4072,assumption,(~pqr4(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4073,assumption,(~pqr2(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4074,assumption,(~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4075,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[1172, 1169, 1159, 4074, 4073, 4072, 4071])).
% 0.92/0.99 tff(4076,assumption,(~qrp1(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4077,assumption,(~qrp2(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4078,assumption,(~qrp3(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4079,assumption,(~qrp4(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4080,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[1407, 1404, 1394, 4079, 4078, 4077, 4076])).
% 0.92/0.99 tff(4081,assumption,(rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.92/0.99 tff(4082,plain,
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% 0.92/0.99 inference(transitivity,[status(thm)],[4084, 4082])).
% 0.92/0.99 tff(4086,plain,
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% 0.92/0.99 inference(quant_inst,[status(thm)],[])).
% 0.92/0.99 tff(4087,plain,
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% 0.92/0.99 inference(modus_ponens,[status(thm)],[4086, 4085])).
% 0.92/0.99 tff(4088,plain,
% 0.92/0.99 ($false),
% 0.92/0.99 inference(unit_resolution,[status(thm)],[4087, 1472, 4081, 4080, 4075])).
% 0.92/0.99 tff(4089,plain,(pqr3(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))) | qrp4(s(s(s(s(s(s(s(s(s(a)))))))))) | qrp3(s(s(s(s(s(s(s(s(s(a)))))))))) | qrp2(s(s(s(s(s(s(s(s(s(a)))))))))) | qrp1(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.99 tff(4090,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[4090, 4046, 3860, 3790, 3730, 3726, 3722])).
% 0.92/0.99 tff(4092,plain,(rr(s(s(s(s(a))))) | pp(s(s(s(s(s(a)))))) | r(s(s(a))) | q(s(s(a))) | r(s(s(s(s(a))))) | (~p(s(s(s(s(a))))))), inference(lemma,lemma(discharge,[]))).
% 0.92/0.99 tff(4093,plain,
% 0.92/0.99 (rr(s(s(s(s(a)))))),
% 0.92/0.99 inference(unit_resolution,[status(thm)],[4092, 3595, 2, 1, 3593, 3592])).
% 0.92/0.99 tff(4094,plain,
% 0.92/0.99 (rr(s(s(s(a))))),
% 0.92/0.99 inference(unit_resolution,[status(thm)],[434, 4093])).
% 0.92/0.99 tff(4095,plain,
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% 0.92/0.99 inference(bind,[status(th)],[])).
% 0.92/0.99 tff(4096,plain,
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% 0.92/0.99 inference(quant_intro,[status(thm)],[4095])).
% 0.92/0.99 tff(4097,plain,
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% 0.92/0.99 inference(rewrite,[status(thm)],[])).
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% 0.92/0.99 tff(4099,plain,
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% 0.92/0.99 inference(quant_intro,[status(thm)],[4098])).
% 0.92/0.99 tff(4100,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | (~qq(X))) | r(X)) | (~rr(X))) | (~p(X))) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c164')).
% 0.92/0.99 tff(4101,plain,
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% 0.92/0.99 tff(4102,plain,
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% 0.92/0.99 tff(4103,plain,(
% 0.92/0.99 ![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~rr(s(X))))),
% 0.92/0.99 inference(skolemize,[status(sab)],[4102])).
% 0.92/0.99 tff(4104,plain,
% 0.92/0.99 (![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~rr(s(X))))),
% 0.92/0.99 inference(modus_ponens,[status(thm)],[4103, 4096])).
% 0.92/0.99 tff(4105,plain,
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% 0.92/0.99 inference(rewrite,[status(thm)],[])).
% 0.92/0.99 tff(4106,plain,
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% 0.92/0.99 inference(monotonicity,[status(thm)],[4106])).
% 0.92/0.99 tff(4108,plain,
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% 0.92/0.99 inference(transitivity,[status(thm)],[4107, 4105])).
% 0.92/0.99 tff(4109,plain,
% 0.92/0.99 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | (~rr(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | (~p(s(s(a)))) | r(s(s(a))) | q(s(s(a))) | (~qq(s(s(a)))) | (~rr(s(s(a)))) | (~rr(s(s(s(a))))))),
% 0.92/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.92/0.99 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 0.92/0.99 tff(4111,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[4110, 4104, 120])).
% 0.92/0.99 tff(4112,plain,
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% 0.92/0.99 inference(unit_resolution,[status(thm)],[4111, 4094, 1, 3591, 2584, 2])).
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% 0.92/1.00 inference(unit_resolution,[status(thm)],[4185, 3679, 149])).
% 0.92/1.00 tff(4187,plain,
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% 0.92/1.00 tff(4188,plain,
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% 0.92/1.00 inference(rewrite,[status(thm)],[])).
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% 0.92/1.00 tff(4196,plain,
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% 0.92/1.00 tff(4197,plain,
% 0.92/1.00 (~pp(s(s(s(s(s(a))))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[2741, 4196])).
% 0.92/1.00 tff(4198,plain,
% 0.92/1.00 (p(s(s(s(s(s(a))))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[2113, 4187])).
% 0.92/1.00 tff(4199,plain,
% 0.92/1.00 (r(s(s(s(s(s(a))))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[562, 4141])).
% 0.92/1.00 tff(4200,plain,
% 0.92/1.00 (rr(s(s(s(s(a)))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[2657, 4179])).
% 0.92/1.00 tff(4201,plain,
% 0.92/1.00 (((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | (ar(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (ar(X) | (~rr(X)) | rr(s(X)))) | ar(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))))),
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% 0.92/1.00 inference(modus_ponens,[status(thm)],[4202, 4201])).
% 0.92/1.00 tff(4204,plain,
% 0.92/1.00 ((~rr(s(s(s(s(a)))))) | rr(s(s(s(s(s(a))))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[4203, 948, 558])).
% 0.92/1.00 tff(4205,plain,
% 0.92/1.00 (rr(s(s(s(s(s(a))))))),
% 0.92/1.00 inference(unit_resolution,[status(thm)],[4204, 4200])).
% 0.92/1.00 tff(4206,plain,
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% 0.92/1.00 tff(4216,plain,
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% 0.92/1.00 inference(bind,[status(th)],[])).
% 0.92/1.00 tff(4217,plain,
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% 0.92/1.00 tff(4270,plain,(
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% 0.92/1.00 inference(unit_resolution,[status(thm)],[4278, 4257, 4245, 4213, 4261, 4260, 4259])).
% 0.92/1.00 tff(4280,plain,
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% 0.92/1.00 inference(rewrite,[status(thm)],[])).
% 0.92/1.00 tff(4282,plain,
% 0.92/1.00 ((pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a)))))))))) <=> ((~r(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))))),
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% 0.92/1.00 tff(4283,plain,
% 0.92/1.00 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | ((~r(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a)))))))))))),
% 0.92/1.00 inference(monotonicity,[status(thm)],[4282])).
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% 0.92/1.00 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~p(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))))),
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% 0.92/1.00 tff(4288,plain,
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% 0.92/1.00 inference(unit_resolution,[status(thm)],[4287, 4257, 4245, 4213, 4261, 4260, 4259])).
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% 0.92/1.00 inference(bind,[status(th)],[])).
% 0.92/1.00 tff(4290,plain,
% 0.92/1.00 (![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))),
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% 0.92/1.00 tff(4292,plain,
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% 0.98/1.00 inference(bind,[status(th)],[])).
% 0.98/1.00 tff(4293,plain,
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% 0.98/1.00 tff(4294,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | (~pp(X))) | q(X)) | qq(X)) | (~r(X))) | (~rr(X))) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c133')).
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% 0.98/1.00 inference(modus_ponens,[status(thm)],[4295, 4291])).
% 0.98/1.00 tff(4297,plain,(
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% 0.98/1.00 inference(skolemize,[status(sab)],[4296])).
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% 0.98/1.01 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.01 tff(4305,plain,
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% 0.98/1.01 tff(4306,plain,
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% 0.98/1.01 inference(unit_resolution,[status(thm)],[4305, 4288, 4280, 4279, 4246, 4258, 4214])).
% 0.98/1.01 tff(4307,plain,
% 0.98/1.01 (~p(s(s(s(s(s(s(s(s(a)))))))))),
% 0.98/1.01 inference(unit_resolution,[status(thm)],[757, 4288])).
% 0.98/1.01 tff(4308,plain,
% 0.98/1.01 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.98/1.01 inference(rewrite,[status(thm)],[])).
% 0.98/1.01 tff(4309,plain,
% 0.98/1.01 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.98/1.01 inference(rewrite,[status(thm)],[])).
% 0.98/1.01 tff(4310,plain,
% 0.98/1.01 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))))),
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% 0.98/1.01 tff(4311,plain,
% 0.98/1.01 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
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% 0.98/1.01 inference(quant_inst,[status(thm)],[])).
% 0.98/1.01 tff(4313,plain,
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% 0.98/1.01 tff(4315,plain,
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% 0.98/1.01 tff(4317,plain,
% 0.98/1.01 (((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a))))))))))) <=> (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.98/1.01 inference(rewrite,[status(thm)],[])).
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% 0.98/1.01 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.98/1.01 inference(monotonicity,[status(thm)],[4317])).
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% 0.98/1.01 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.98/1.01 inference(transitivity,[status(thm)],[4318, 4316])).
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% 0.98/1.02 inference(quant_intro,[status(thm)],[4397])).
% 0.98/1.02 tff(4399,plain,
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% 0.98/1.02 inference(rewrite,[status(thm)],[])).
% 0.98/1.02 tff(4400,plain,
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% 0.98/1.02 inference(bind,[status(th)],[])).
% 0.98/1.02 tff(4401,plain,
% 0.98/1.02 (![X: $i] : (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | (~rq(X))) | rq(s(X))) <=> ![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))),
% 0.98/1.02 inference(quant_intro,[status(thm)],[4400])).
% 0.98/1.02 tff(4402,axiom,(![X: $i] : (((((rpq1(X) | rpq2(X)) | rpq3(X)) | rpq4(X)) | (~rq(X))) | rq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c267')).
% 0.98/1.02 tff(4403,plain,
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% 0.98/1.02 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 0.98/1.02 tff(4404,plain,
% 0.98/1.02 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))),
% 0.98/1.02 inference(modus_ponens,[status(thm)],[4403, 4399])).
% 0.98/1.02 tff(4405,plain,(
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% 0.98/1.02 inference(skolemize,[status(sab)],[4404])).
% 0.98/1.02 tff(4406,plain,
% 0.98/1.02 (![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))),
% 0.98/1.02 inference(modus_ponens,[status(thm)],[4405, 4398])).
% 0.98/1.02 tff(4407,plain,
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% 0.98/1.02 tff(4408,plain,
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% 0.98/1.02 tff(4409,plain,
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% 0.98/1.02 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 0.98/1.02 tff(4410,plain,
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% 0.98/1.02 tff(4411,plain,
% 0.98/1.02 ((~rq(s(s(s(s(s(s(s(a))))))))) | rq(s(s(s(s(s(s(s(s(a)))))))))),
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% 0.98/1.02 tff(4412,plain,
% 0.98/1.02 (rq(s(s(s(s(s(s(s(s(a)))))))))),
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% 0.98/1.02 tff(4413,plain,
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% 0.98/1.02 inference(rewrite,[status(thm)],[])).
% 0.98/1.02 tff(4414,plain,
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% 0.98/1.02 tff(4415,plain,
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% 0.98/1.02 tff(4416,plain,
% 0.98/1.02 ((~rq(s(s(s(s(s(s(s(s(a)))))))))) | rq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.98/1.02 inference(unit_resolution,[status(thm)],[4415, 4406, 3381, 3377, 3373, 3369])).
% 0.98/1.02 tff(4417,plain,
% 0.98/1.02 (rq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.98/1.02 inference(unit_resolution,[status(thm)],[4416, 4412])).
% 0.98/1.02 tff(4418,assumption,(rpq4(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4419,assumption,(pp(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4420,plain,
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% 0.98/1.02 inference(rewrite,[status(thm)],[])).
% 0.98/1.02 tff(4421,plain,
% 0.98/1.02 ((~![X: $i] : ((~pp(X)) | (~rpq4(X)))) | ((~pp(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(a))))))))))))),
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% 0.98/1.02 tff(4423,plain,
% 0.98/1.02 ($false),
% 0.98/1.02 inference(unit_resolution,[status(thm)],[4422, 2355, 4419, 4418])).
% 0.98/1.02 tff(4424,plain,((~rpq4(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.02 tff(4425,plain,
% 0.98/1.02 (~rpq4(s(s(s(s(s(s(s(s(s(a))))))))))),
% 0.98/1.02 inference(unit_resolution,[status(thm)],[4424, 4330])).
% 0.98/1.02 tff(4426,plain,
% 0.98/1.02 (^[X: $i] : refl(((~r(X)) | (~rpq1(X))) <=> ((~r(X)) | (~rpq1(X))))),
% 0.98/1.02 inference(bind,[status(th)],[])).
% 0.98/1.02 tff(4427,plain,
% 0.98/1.02 (![X: $i] : ((~r(X)) | (~rpq1(X))) <=> ![X: $i] : ((~r(X)) | (~rpq1(X)))),
% 0.98/1.02 inference(quant_intro,[status(thm)],[4426])).
% 0.98/1.02 tff(4428,plain,
% 0.98/1.02 (![X: $i] : ((~r(X)) | (~rpq1(X))) <=> ![X: $i] : ((~r(X)) | (~rpq1(X)))),
% 0.98/1.02 inference(rewrite,[status(thm)],[])).
% 0.98/1.02 tff(4429,plain,
% 0.98/1.02 (^[X: $i] : rewrite(((~rpq1(X)) | (~r(X))) <=> ((~r(X)) | (~rpq1(X))))),
% 0.98/1.02 inference(bind,[status(th)],[])).
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% 0.98/1.02 (![X: $i] : ((~rpq1(X)) | (~r(X))) <=> ![X: $i] : ((~r(X)) | (~rpq1(X)))),
% 0.98/1.02 inference(quant_intro,[status(thm)],[4429])).
% 0.98/1.02 tff(4431,axiom,(![X: $i] : ((~rpq1(X)) | (~r(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c062')).
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% 0.98/1.02 inference(modus_ponens,[status(thm)],[4431, 4430])).
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% 0.98/1.02 inference(modus_ponens,[status(thm)],[4434, 4427])).
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% 0.98/1.02 tff(4439,plain,
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% 0.98/1.02 tff(4441,assumption,(~rpq3(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4442,assumption,(~rpq1(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4443,assumption,(~rpq2(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4444,assumption,(rq(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4445,assumption,(~rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 0.98/1.02 tff(4446,plain,
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% 0.98/1.02 inference(rewrite,[status(thm)],[])).
% 0.98/1.02 tff(4447,plain,
% 0.98/1.02 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq2(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq3(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rq(s(s(s(s(s(s(s(s(s(a))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 0.98/1.02 inference(quant_inst,[status(thm)],[])).
% 0.98/1.02 tff(4448,plain,
% 0.98/1.02 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq2(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq3(s(s(s(s(s(s(s(s(s(a)))))))))) | rpq4(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rq(s(s(s(s(s(s(s(s(s(a))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 0.98/1.02 inference(modus_ponens,[status(thm)],[4447, 4446])).
% 0.98/1.02 tff(4449,plain,
% 0.98/1.02 ($false),
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4617, 3822, 120])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4618, 4177, 1, 3591, 2584, 4159, 2])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4621, 4620])).
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% 0.98/1.03 (~qrp1(s(s(s(a))))),
% 0.98/1.03 inference(unit_resolution,[status(thm)],[4622, 1311, 160])).
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% 0.98/1.03 inference(rewrite,[status(thm)],[])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4625, 4624])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4626, 1353, 160])).
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% 0.98/1.03 inference(rewrite,[status(thm)],[])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4629, 4628])).
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% 0.98/1.03 (~qrp3(s(s(s(a))))),
% 0.98/1.03 inference(unit_resolution,[status(thm)],[4630, 1339, 160])).
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% 0.98/1.03 inference(rewrite,[status(thm)],[])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4633, 4632])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4634, 1325, 160])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4638, 1404])).
% 0.98/1.03 tff(4640,plain,
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4639, 4635, 4631, 4627, 4623])).
% 0.98/1.03 tff(4641,plain,
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4640, 4619])).
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% 0.98/1.03 inference(rewrite,[status(thm)],[])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4643, 4642])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4644, 1311, 558])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4647, 4646])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4648, 1325, 558])).
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% 0.98/1.03 inference(rewrite,[status(thm)],[])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4652, 1339, 558])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4655, 4654])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4656, 1353, 558])).
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% 0.98/1.03 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.03 inference(modus_ponens,[status(thm)],[4659, 4658])).
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% 0.98/1.03 ((~qp(s(s(s(s(a)))))) | qp(s(s(s(s(s(a))))))),
% 0.98/1.03 inference(unit_resolution,[status(thm)],[4660, 1404, 4657, 4653, 4649, 4645])).
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% 0.98/1.03 (qp(s(s(s(s(s(a))))))),
% 0.98/1.03 inference(unit_resolution,[status(thm)],[4661, 4641])).
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% 0.98/1.03 inference(unit_resolution,[status(thm)],[4675, 1])).
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% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4867,plain,
% 0.98/1.05 (((~aq(s(a))) | p(s(a)) | (~q(s(a))) | (~qq(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a))))) <=> (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4868,plain,
% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | (~q(s(a))) | (~qq(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a)))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4867])).
% 0.98/1.05 tff(4869,plain,
% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | (~q(s(a))) | (~qq(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a))))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4868, 4866])).
% 0.98/1.05 tff(4870,plain,
% 0.98/1.05 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | (~q(s(a))) | (~qq(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4871,plain,
% 0.98/1.05 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4870, 4869])).
% 0.98/1.05 tff(4872,plain,
% 0.98/1.05 (p(s(a)) | (~q(s(a))) | (~rr(s(a))) | (~r(s(a))) | (~qq(s(s(a)))) | (~qq(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4871, 4865, 18])).
% 0.98/1.05 tff(4873,plain,
% 0.98/1.05 (~qq(s(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4872, 4855, 4817, 4815, 4768, 4806])).
% 0.98/1.05 tff(4874,plain,
% 0.98/1.05 (^[X: $i] : refl((pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X)))) <=> (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X)))))),
% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4875,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4874])).
% 0.98/1.05 tff(4876,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4877,plain,
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% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4878,plain,
% 0.98/1.05 (![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | (~q(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4877])).
% 0.98/1.05 tff(4879,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c144')).
% 0.98/1.05 tff(4880,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4879, 4878])).
% 0.98/1.05 tff(4881,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4880, 4876])).
% 0.98/1.05 tff(4882,plain,(
% 0.98/1.05 ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(skolemize,[status(sab)],[4881])).
% 0.98/1.05 tff(4883,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4882, 4875])).
% 0.98/1.05 tff(4884,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4885,plain,
% 0.98/1.05 ((pp(s(a)) | (~aq(s(a))) | p(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a))))) <=> (pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4886,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(a)) | (~aq(s(a))) | p(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a))))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4885])).
% 0.98/1.05 tff(4887,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(a)) | (~aq(s(a))) | p(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4886, 4884])).
% 0.98/1.05 tff(4888,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(a)) | (~aq(s(a))) | p(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a)))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4889,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(a)) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4888, 4887])).
% 0.98/1.05 tff(4890,plain,
% 0.98/1.05 (pp(s(a)) | p(s(a)) | (~q(s(a))) | qq(s(a)) | (~rr(s(a))) | (~r(s(a))) | (~q(s(s(a))))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4889, 4883, 18])).
% 0.98/1.05 tff(4891,plain,
% 0.98/1.05 ($false),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4890, 4873, 4855, 4817, 4816, 4815, 4768, 3275])).
% 0.98/1.05 tff(4892,plain,(pp(s(s(a))) | (~q(s(s(a)))) | p(s(s(a))) | rr(s(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.05 tff(4893,plain,
% 0.98/1.05 (pp(s(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4892, 175, 44, 4749])).
% 0.98/1.05 tff(4894,plain,
% 0.98/1.05 (pp(s(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[290, 4893])).
% 0.98/1.05 tff(4895,plain,
% 0.98/1.05 (~r(s(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[1719, 45])).
% 0.98/1.05 tff(4896,plain,
% 0.98/1.05 (q(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[3254, 3232, 4894])).
% 0.98/1.05 tff(4897,plain,
% 0.98/1.05 (q(s(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[1915, 4896])).
% 0.98/1.05 tff(4898,plain,
% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4899,plain,
% 0.98/1.05 (((~aq(s(a))) | p(s(a)) | r(s(a)) | (~q(s(a))) | (~qq(s(s(a))))) <=> (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4900,plain,
% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | (~q(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | (p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a))))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4899])).
% 0.98/1.05 tff(4901,plain,
% 0.98/1.05 (((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | (~q(s(a))) | (~qq(s(s(a)))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a)))))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4900, 4898])).
% 0.98/1.05 tff(4902,plain,
% 0.98/1.05 ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | ((~aq(s(a))) | p(s(a)) | r(s(a)) | (~q(s(a))) | (~qq(s(s(a)))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4903,plain,
% 0.98/1.05 ((~![X: $i] : ((~aq(X)) | p(X) | r(X) | (~q(X)) | (~qq(s(X))))) | p(s(a)) | (~aq(s(a))) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 0.98/1.05 tff(4904,plain,
% 0.98/1.05 (p(s(a)) | (~q(s(a))) | r(s(a)) | (~qq(s(s(a))))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4903, 1265, 18])).
% 0.98/1.05 tff(4905,plain,
% 0.98/1.05 (~qq(s(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4904, 4897, 4, 45])).
% 0.98/1.05 tff(4906,plain,
% 0.98/1.05 (^[X: $i] : refl(((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X))))),
% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4907,plain,
% 0.98/1.05 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4906])).
% 0.98/1.05 tff(4908,plain,
% 0.98/1.05 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4909,plain,
% 0.98/1.05 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ar(X)) | (~q(X))) | qq(X)) <=> ((~ar(X)) | (~q(X)) | qq(X))), (((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) <=> (((~ar(X)) | (~q(X)) | qq(X)) | r(X)))), rewrite((((~ar(X)) | (~q(X)) | qq(X)) | r(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | qq(X))), (((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | qq(X)))), ((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) <=> (((~ar(X)) | r(X) | (~q(X)) | qq(X)) | rr(X)))), rewrite((((~ar(X)) | r(X) | (~q(X)) | qq(X)) | rr(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | qq(X) | rr(X))), ((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | qq(X) | rr(X)))), (((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) <=> (((~ar(X)) | r(X) | (~q(X)) | qq(X) | rr(X)) | p(X)))), rewrite((((~ar(X)) | r(X) | (~q(X)) | qq(X) | rr(X)) | p(X)) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X))), (((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X)))), ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) <=> (((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X)) | (~pp(X))))), rewrite((((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X)) | (~pp(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)))), ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X))))), (((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | rr(s(X))) <=> (((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X))) | rr(s(X))))), rewrite((((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X))) | rr(s(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))), (((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | rr(s(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))))),
% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4910,plain,
% 0.98/1.05 (![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | rr(s(X))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4909])).
% 0.98/1.05 tff(4911,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | rr(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c197')).
% 0.98/1.05 tff(4912,plain,
% 0.98/1.05 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4911, 4910])).
% 0.98/1.05 tff(4913,plain,
% 0.98/1.05 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4912, 4908])).
% 0.98/1.05 tff(4914,plain,(
% 0.98/1.05 ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(skolemize,[status(sab)],[4913])).
% 0.98/1.05 tff(4915,plain,
% 0.98/1.05 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4914, 4907])).
% 0.98/1.05 tff(4916,plain,
% 0.98/1.05 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4917,plain,
% 0.98/1.05 (((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a))))) <=> (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4918,plain,
% 0.98/1.05 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a))))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4917])).
% 0.98/1.05 tff(4919,plain,
% 0.98/1.05 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4918, 4916])).
% 0.98/1.05 tff(4920,plain,
% 0.98/1.05 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a)))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4921,plain,
% 0.98/1.05 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4920, 4919])).
% 0.98/1.05 tff(4922,plain,
% 0.98/1.05 (qq(s(s(a))) | (~q(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | rr(s(s(s(a))))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4921, 4915, 120])).
% 0.98/1.05 tff(4923,plain,
% 0.98/1.05 (rr(s(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4922, 4905, 4749, 4895, 44, 4893, 175])).
% 0.98/1.05 tff(4924,plain,
% 0.98/1.05 (rr(s(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[1905, 4923])).
% 0.98/1.05 tff(4925,plain,
% 0.98/1.05 (rr(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[1910, 4924])).
% 0.98/1.05 tff(4926,plain,
% 0.98/1.05 (q(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[3254, 3233, 314])).
% 0.98/1.05 tff(4927,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a)))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4928,plain,
% 0.98/1.05 (((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(a)) | (~pp(s(a)))) <=> ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4929,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(a)) | (~pp(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4928])).
% 0.98/1.05 tff(4930,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(a)) | (~pp(s(a))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a)))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4929, 4927])).
% 0.98/1.05 tff(4931,plain,
% 0.98/1.05 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(a)) | (~pp(s(a))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4932,plain,
% 0.98/1.05 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~pp(s(X))))) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4931, 4930])).
% 0.98/1.05 tff(4933,plain,
% 0.98/1.05 (p(a) | r(a) | (~q(a)) | (~rr(a)) | (~pp(s(a))) | (~pp(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4932, 14, 2924])).
% 0.98/1.05 tff(4934,plain,
% 0.98/1.05 (~pp(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4933, 1924, 3233, 4926, 1919, 314])).
% 0.98/1.05 tff(4935,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4936,plain,
% 0.98/1.05 ((pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | (~rr(a)) | p(s(a))) <=> (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4937,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | (~rr(a)) | p(s(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4936])).
% 0.98/1.05 tff(4938,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | (~rr(a)) | p(s(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a)))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4937, 4935])).
% 0.98/1.05 tff(4939,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | (~rr(a)) | p(s(a)))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4940,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | p(s(X)))) | pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4939, 4938])).
% 0.98/1.05 tff(4941,plain,
% 0.98/1.05 (pp(a) | p(a) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~rr(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4940, 14, 2942])).
% 0.98/1.05 tff(4942,plain,
% 0.98/1.05 (qq(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4941, 4934, 4926, 3233, 1919, 1924, 4])).
% 0.98/1.05 tff(4943,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4944,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4945,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | p(a) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4944, 4943])).
% 0.98/1.05 tff(4946,plain,
% 0.98/1.05 (pp(a) | p(a) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4945, 14, 873])).
% 0.98/1.05 tff(4947,plain,
% 0.98/1.05 ($false),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4946, 4942, 4934, 4926, 3233, 1924, 1919, 314])).
% 0.98/1.05 tff(4948,plain,(p(a) | r(a) | (~rr(a)) | (~pp(s(a))) | p(s(a))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.05 tff(4949,plain,
% 0.98/1.05 (p(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4948, 3232, 4925, 4894, 4])).
% 0.98/1.05 tff(4950,plain,
% 0.98/1.05 (p(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4948, 3233, 1919, 314, 4])).
% 0.98/1.05 tff(4951,assumption,(~pp(a)), introduced(assumption)).
% 0.98/1.05 tff(4952,plain,
% 0.98/1.05 (^[X: $i] : refl((pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X)))) <=> (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X)))))),
% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4953,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4952])).
% 0.98/1.05 tff(4954,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4955,plain,
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% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4956,plain,
% 0.98/1.05 (![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | (~pp(s(X)))) <=> ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4955])).
% 0.98/1.05 tff(4957,axiom,(![X: $i] : ((((((((~ap(X)) | r(X)) | (~rr(X))) | (~p(X))) | pp(X)) | (~q(X))) | (~qq(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c248')).
% 0.98/1.05 tff(4958,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4957, 4956])).
% 0.98/1.05 tff(4959,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4958, 4954])).
% 0.98/1.05 tff(4960,plain,(
% 0.98/1.05 ![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(skolemize,[status(sab)],[4959])).
% 0.98/1.05 tff(4961,plain,
% 0.98/1.05 (![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4960, 4953])).
% 0.98/1.05 tff(4962,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4963,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | (pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a))))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4964,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~pp(s(X))))) | pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a)))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 0.98/1.05 tff(4965,plain,
% 0.98/1.05 (pp(a) | (~p(a)) | r(a) | (~q(a)) | (~qq(a)) | (~rr(a)) | (~pp(s(a)))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4964, 14, 4961])).
% 0.98/1.05 tff(4966,plain,
% 0.98/1.05 (~qq(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4965, 4951, 4926, 3233, 4950, 1919, 314])).
% 0.98/1.05 tff(4967,plain,
% 0.98/1.05 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4968,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4969,plain,
% 0.98/1.05 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | pp(a) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 0.98/1.05 tff(4970,plain,
% 0.98/1.05 (pp(a) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4969, 14, 3015])).
% 0.98/1.05 tff(4971,plain,
% 0.98/1.05 ($false),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4970, 4966, 4951, 4, 3233, 4926, 4950])).
% 0.98/1.05 tff(4972,plain,(pp(a) | p(s(a)) | r(a) | (~rr(a)) | (~pp(s(a)))), inference(lemma,lemma(discharge,[]))).
% 0.98/1.05 tff(4973,plain,
% 0.98/1.05 (pp(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4972, 3232, 4, 4925, 4894])).
% 0.98/1.05 tff(4974,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a)))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4975,plain,
% 0.98/1.05 (((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | (~pp(a)) | p(s(a))) <=> ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a)))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4976,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | (~pp(a)) | p(s(a)))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a))))),
% 0.98/1.05 inference(monotonicity,[status(thm)],[4975])).
% 0.98/1.05 tff(4977,plain,
% 0.98/1.05 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | (~pp(a)) | p(s(a)))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a)))),
% 0.98/1.05 inference(transitivity,[status(thm)],[4976, 4974])).
% 0.98/1.05 tff(4978,plain,
% 0.98/1.05 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | (~pp(a)) | p(s(a)))),
% 0.98/1.05 inference(quant_inst,[status(thm)],[])).
% 0.98/1.05 tff(4979,plain,
% 0.98/1.05 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (~ap(a)) | (~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a))),
% 0.98/1.05 inference(modus_ponens,[status(thm)],[4978, 4977])).
% 0.98/1.05 tff(4980,plain,
% 0.98/1.05 ((~p(a)) | r(a) | (~q(a)) | qq(a) | p(s(a)) | (~pp(a))),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4979, 14, 2997])).
% 0.98/1.05 tff(4981,plain,
% 0.98/1.05 (qq(a)),
% 0.98/1.05 inference(unit_resolution,[status(thm)],[4980, 4973, 4, 3232, 4896, 4949])).
% 0.98/1.05 tff(4982,plain,
% 0.98/1.05 (^[X: $i] : refl(((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X)))) <=> ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X)))))),
% 0.98/1.05 inference(bind,[status(th)],[])).
% 0.98/1.05 tff(4983,plain,
% 0.98/1.05 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(quant_intro,[status(thm)],[4982])).
% 0.98/1.05 tff(4984,plain,
% 0.98/1.05 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.98/1.05 inference(rewrite,[status(thm)],[])).
% 0.98/1.05 tff(4985,plain,
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% 0.98/1.06 inference(bind,[status(th)],[])).
% 0.98/1.06 tff(4986,plain,
% 0.98/1.06 (![X: $i] : (((((((~ap(X)) | r(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | (~qq(X))) | (~pp(s(X)))) <=> ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.98/1.06 inference(quant_intro,[status(thm)],[4985])).
% 0.98/1.06 tff(4987,axiom,(![X: $i] : (((((((~ap(X)) | r(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | (~qq(X))) | (~pp(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c234')).
% 0.98/1.06 tff(4988,plain,
% 0.98/1.06 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.98/1.06 inference(modus_ponens,[status(thm)],[4987, 4986])).
% 0.98/1.06 tff(4989,plain,
% 0.98/1.06 (![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
% 0.98/1.06 inference(modus_ponens,[status(thm)],[4988, 4984])).
% 0.98/1.06 tff(4990,plain,(
% 0.98/1.06 ![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))),
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% 0.98/1.06 inference(monotonicity,[status(thm)],[5078])).
% 0.98/1.06 tff(5080,plain,
% 0.98/1.06 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 0.98/1.06 inference(transitivity,[status(thm)],[5079, 5077])).
% 0.98/1.06 tff(5081,plain,
% 0.98/1.06 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))),
% 0.98/1.06 inference(quant_inst,[status(thm)],[])).
% 0.98/1.06 tff(5082,plain,
% 0.98/1.06 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 0.98/1.06 inference(modus_ponens,[status(thm)],[5081, 5080])).
% 0.98/1.06 tff(5083,plain,
% 0.98/1.06 (p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~r(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 0.98/1.06 inference(unit_resolution,[status(thm)],[5082, 740, 450])).
% 0.98/1.06 tff(5084,plain,
% 0.98/1.06 (q(s(s(s(s(s(a))))))),
% 0.98/1.06 inference(unit_resolution,[status(thm)],[5083, 5064, 5068, 443, 5067, 5043])).
% 0.98/1.06 tff(5085,plain,
% 0.98/1.06 (((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | ((~r(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 0.98/1.06 inference(rewrite,[status(thm)],[])).
% 0.98/1.06 tff(5086,plain,
% 0.98/1.06 (((~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(s(a))))))) <=> ((~r(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 0.98/1.06 inference(rewrite,[status(thm)],[])).
% 0.98/1.06 tff(5087,plain,
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% 0.98/1.06 inference(monotonicity,[status(thm)],[5086])).
% 0.98/1.06 tff(5088,plain,
% 0.98/1.06 (((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 0.98/1.07 inference(transitivity,[status(thm)],[5087, 5085])).
% 0.98/1.07 tff(5089,plain,
% 0.98/1.07 ((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 0.98/1.07 inference(quant_inst,[status(thm)],[])).
% 0.98/1.07 tff(5090,plain,
% 0.98/1.07 ((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(a))))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a))))))),
% 0.98/1.07 inference(modus_ponens,[status(thm)],[5089, 5088])).
% 0.98/1.07 tff(5091,plain,
% 0.98/1.07 ((~r(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | (~pp(s(s(s(s(a))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[5090, 389, 149])).
% 0.98/1.07 tff(5092,plain,
% 0.98/1.07 (~pp(s(s(s(s(a)))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[5091, 5042, 5049, 174])).
% 0.98/1.07 tff(5093,plain,
% 0.98/1.07 (~pp(s(s(s(s(s(a))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[2741, 5092])).
% 0.98/1.07 tff(5094,plain,
% 0.98/1.07 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))) | ((~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))) | (~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
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% 0.98/1.07 inference(rewrite,[status(thm)],[])).
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% 0.98/1.07 inference(monotonicity,[status(thm)],[5095])).
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% 0.98/1.07 inference(transitivity,[status(thm)],[5096, 5094])).
% 0.98/1.07 tff(5098,plain,
% 0.98/1.07 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))) | (pp(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 0.98/1.07 inference(quant_inst,[status(thm)],[])).
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% 0.98/1.07 inference(modus_ponens,[status(thm)],[5098, 5097])).
% 0.98/1.07 tff(5100,plain,
% 0.98/1.07 ((~q(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[5099, 805, 472])).
% 0.98/1.07 tff(5101,plain,
% 0.98/1.07 (~r(s(s(s(s(s(s(a)))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[5100, 5093, 5084, 5076, 5065, 5044, 592])).
% 0.98/1.07 tff(5102,plain,
% 0.98/1.07 (~r(s(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[2261, 5101])).
% 0.98/1.07 tff(5103,plain,
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% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(5104,plain,
% 0.98/1.07 (((~pqr1(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a))))))))) <=> (r(s(s(s(s(s(s(s(a)))))))) | (~pqr1(s(s(s(s(s(s(s(a))))))))))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(5105,plain,
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% 0.98/1.07 inference(monotonicity,[status(thm)],[5104])).
% 0.98/1.07 tff(5106,plain,
% 0.98/1.07 (((~![X: $i] : ((~pqr1(X)) | r(X))) | ((~pqr1(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~pqr1(X)) | r(X))) | r(s(s(s(s(s(s(s(a)))))))) | (~pqr1(s(s(s(s(s(s(s(a))))))))))),
% 0.98/1.07 inference(transitivity,[status(thm)],[5105, 5103])).
% 0.98/1.07 tff(5107,plain,
% 0.98/1.07 ((~![X: $i] : ((~pqr1(X)) | r(X))) | ((~pqr1(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))))),
% 0.98/1.07 inference(quant_inst,[status(thm)],[])).
% 0.98/1.07 tff(5108,plain,
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% 0.98/1.07 inference(modus_ponens,[status(thm)],[5107, 5106])).
% 0.98/1.07 tff(5109,plain,
% 0.98/1.07 (~pqr1(s(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[5108, 1145, 5102])).
% 0.98/1.07 tff(5110,plain,
% 0.98/1.07 (qq(s(s(s(s(s(s(a)))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[490, 5076])).
% 0.98/1.07 tff(5111,plain,
% 0.98/1.07 (qq(s(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[503, 5110])).
% 0.98/1.07 tff(5112,plain,
% 0.98/1.07 (~pqr2(s(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[1615, 1612, 5111])).
% 0.98/1.07 tff(5113,plain,
% 0.98/1.07 (~pqr3(s(s(s(s(s(s(s(a))))))))),
% 0.98/1.07 inference(unit_resolution,[status(thm)],[1604, 1601, 5111])).
% 0.98/1.07 tff(5114,plain,
% 0.98/1.07 (^[X: $i] : refl((rr(X) | (~pqr4(X))) <=> (rr(X) | (~pqr4(X))))),
% 0.98/1.07 inference(bind,[status(th)],[])).
% 0.98/1.07 tff(5115,plain,
% 0.98/1.07 (![X: $i] : (rr(X) | (~pqr4(X))) <=> ![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(quant_intro,[status(thm)],[5114])).
% 0.98/1.07 tff(5116,plain,
% 0.98/1.07 (![X: $i] : (rr(X) | (~pqr4(X))) <=> ![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(5117,plain,
% 0.98/1.07 (^[X: $i] : rewrite(((~pqr4(X)) | rr(X)) <=> (rr(X) | (~pqr4(X))))),
% 0.98/1.07 inference(bind,[status(th)],[])).
% 0.98/1.07 tff(5118,plain,
% 0.98/1.07 (![X: $i] : ((~pqr4(X)) | rr(X)) <=> ![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(quant_intro,[status(thm)],[5117])).
% 0.98/1.07 tff(5119,axiom,(![X: $i] : ((~pqr4(X)) | rr(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c032')).
% 0.98/1.07 tff(5120,plain,
% 0.98/1.07 (![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(modus_ponens,[status(thm)],[5119, 5118])).
% 0.98/1.07 tff(5121,plain,
% 0.98/1.07 (![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(modus_ponens,[status(thm)],[5120, 5116])).
% 0.98/1.07 tff(5122,plain,(
% 0.98/1.07 ![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(skolemize,[status(sab)],[5121])).
% 0.98/1.07 tff(5123,plain,
% 0.98/1.07 (![X: $i] : (rr(X) | (~pqr4(X)))),
% 0.98/1.07 inference(modus_ponens,[status(thm)],[5122, 5115])).
% 0.98/1.07 tff(5124,plain,
% 0.98/1.07 (((~![X: $i] : (rr(X) | (~pqr4(X)))) | (rr(s(s(s(s(a))))) | (~pqr4(s(s(s(s(a)))))))) <=> ((~![X: $i] : (rr(X) | (~pqr4(X)))) | rr(s(s(s(s(a))))) | (~pqr4(s(s(s(s(a)))))))),
% 0.98/1.07 inference(rewrite,[status(thm)],[])).
% 0.98/1.07 tff(5125,plain,
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% 1.05/1.08 inference(monotonicity,[status(thm)],[5286])).
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% 1.05/1.08 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))),
% 1.05/1.08 inference(transitivity,[status(thm)],[5287, 5285])).
% 1.05/1.08 tff(5289,plain,
% 1.05/1.08 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a))))))))),
% 1.05/1.08 inference(quant_inst,[status(thm)],[])).
% 1.05/1.08 tff(5290,plain,
% 1.05/1.08 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | rr(s(X)))) | qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a)))))))),
% 1.05/1.08 inference(modus_ponens,[status(thm)],[5289, 5288])).
% 1.05/1.08 tff(5291,plain,
% 1.05/1.08 (qq(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(s(a)))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[5290, 4915, 472])).
% 1.05/1.08 tff(5292,plain,
% 1.05/1.08 (rr(s(s(s(s(s(s(a)))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[5291, 5264, 572, 2818, 2750, 592, 2859])).
% 1.05/1.08 tff(5293,plain,
% 1.05/1.08 (rr(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[2274, 5292])).
% 1.05/1.08 tff(5294,plain,
% 1.05/1.08 (~qq(s(s(s(s(s(s(a)))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[2279, 2818])).
% 1.05/1.08 tff(5295,plain,
% 1.05/1.08 (~qq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[2284, 5294])).
% 1.05/1.08 tff(5296,plain,
% 1.05/1.08 (~pp(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.08 inference(unit_resolution,[status(thm)],[711, 5281, 4734, 651])).
% 1.05/1.08 tff(5297,plain,
% 1.05/1.08 (^[X: $i] : refl((pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X)))) <=> (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X)))))),
% 1.05/1.08 inference(bind,[status(th)],[])).
% 1.05/1.08 tff(5298,plain,
% 1.05/1.08 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(quant_intro,[status(thm)],[5297])).
% 1.05/1.08 tff(5299,plain,
% 1.05/1.08 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(rewrite,[status(thm)],[])).
% 1.05/1.08 tff(5300,plain,
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% 1.05/1.08 inference(bind,[status(th)],[])).
% 1.05/1.08 tff(5301,plain,
% 1.05/1.08 (![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | (~pr(s(X)))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(quant_intro,[status(thm)],[5300])).
% 1.05/1.08 tff(5302,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | (~pr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c146')).
% 1.05/1.08 tff(5303,plain,
% 1.05/1.08 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(modus_ponens,[status(thm)],[5302, 5301])).
% 1.05/1.08 tff(5304,plain,
% 1.05/1.08 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(modus_ponens,[status(thm)],[5303, 5299])).
% 1.05/1.08 tff(5305,plain,(
% 1.05/1.08 ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(skolemize,[status(sab)],[5304])).
% 1.05/1.08 tff(5306,plain,
% 1.05/1.08 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))),
% 1.05/1.08 inference(modus_ponens,[status(thm)],[5305, 5298])).
% 1.05/1.08 tff(5307,plain,
% 1.05/1.08 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.08 inference(rewrite,[status(thm)],[])).
% 1.05/1.08 tff(5308,plain,
% 1.05/1.08 ((pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))) <=> (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5309,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.09 inference(monotonicity,[status(thm)],[5308])).
% 1.05/1.09 tff(5310,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.09 inference(transitivity,[status(thm)],[5309, 5307])).
% 1.05/1.09 tff(5311,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.09 inference(quant_inst,[status(thm)],[])).
% 1.05/1.09 tff(5312,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.09 inference(modus_ponens,[status(thm)],[5311, 5310])).
% 1.05/1.09 tff(5313,plain,
% 1.05/1.09 (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5312, 5306, 673])).
% 1.05/1.09 tff(5314,plain,
% 1.05/1.09 (~pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5313, 5296, 5295, 5293, 5284, 5283, 5282])).
% 1.05/1.09 tff(5315,plain,
% 1.05/1.09 (rq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2339, 2336, 5314, 5280])).
% 1.05/1.09 tff(5316,plain,
% 1.05/1.09 (rq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2538, 5315])).
% 1.05/1.09 tff(5317,plain,
% 1.05/1.09 (rq(s(s(s(s(s(s(a)))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2516, 5316, 5270, 5266, 4748, 4733])).
% 1.05/1.09 tff(5318,plain,
% 1.05/1.09 (rq(s(s(s(s(s(a))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2497, 5317])).
% 1.05/1.09 tff(5319,plain,
% 1.05/1.09 (rq(s(s(s(s(a)))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2476, 5318])).
% 1.05/1.09 tff(5320,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5321,plain,
% 1.05/1.09 (((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a)))))) <=> (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5322,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))))),
% 1.05/1.09 inference(monotonicity,[status(thm)],[5321])).
% 1.05/1.09 tff(5323,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(transitivity,[status(thm)],[5322, 5320])).
% 1.05/1.09 tff(5324,plain,
% 1.05/1.09 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 1.05/1.09 inference(quant_inst,[status(thm)],[])).
% 1.05/1.09 tff(5325,plain,
% 1.05/1.09 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))),
% 1.05/1.09 inference(modus_ponens,[status(thm)],[5324, 5323])).
% 1.05/1.09 tff(5326,plain,
% 1.05/1.09 (r(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5325, 2997, 149])).
% 1.05/1.09 tff(5327,plain,
% 1.05/1.09 (~pp(s(s(s(a))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5326, 196, 446, 2914, 3, 3164])).
% 1.05/1.09 tff(5328,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5329,plain,
% 1.05/1.09 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a)))))) <=> (r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5330,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a)))))))),
% 1.05/1.09 inference(monotonicity,[status(thm)],[5329])).
% 1.05/1.09 tff(5331,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))),
% 1.05/1.09 inference(transitivity,[status(thm)],[5330, 5328])).
% 1.05/1.09 tff(5332,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a))))))),
% 1.05/1.09 inference(quant_inst,[status(thm)],[])).
% 1.05/1.09 tff(5333,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | p(s(X)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a)))))),
% 1.05/1.09 inference(modus_ponens,[status(thm)],[5332, 5331])).
% 1.05/1.09 tff(5334,plain,
% 1.05/1.09 (r(s(s(s(a)))) | pp(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | p(s(s(s(s(a)))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5333, 3015, 149])).
% 1.05/1.09 tff(5335,plain,
% 1.05/1.09 ($false),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5334, 5327, 196, 446, 2914, 3, 3164])).
% 1.05/1.09 tff(5336,plain,(qq(s(s(s(a)))) | p(s(s(s(s(a))))) | r(s(s(s(a)))) | (~p(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.09 tff(5337,plain,
% 1.05/1.09 (qq(s(s(s(a))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5336, 5251, 3, 446])).
% 1.05/1.09 tff(5338,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5339,plain,
% 1.05/1.09 (((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a))))))) <=> (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5340,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | (r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))))),
% 1.05/1.09 inference(monotonicity,[status(thm)],[5339])).
% 1.05/1.09 tff(5341,plain,
% 1.05/1.09 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | r(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a))))))),
% 1.05/1.09 inference(transitivity,[status(thm)],[5340, 5338])).
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% 1.05/1.09 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(a))))) | (~pp(s(s(s(s(a)))))))),
% 1.05/1.09 inference(quant_inst,[status(thm)],[])).
% 1.05/1.09 tff(5343,plain,
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% 1.05/1.09 inference(modus_ponens,[status(thm)],[5342, 5341])).
% 1.05/1.09 tff(5344,plain,
% 1.05/1.09 (r(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~pp(s(s(s(a)))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5343, 4991, 149])).
% 1.05/1.09 tff(5345,plain,
% 1.05/1.09 (~pp(s(s(s(a))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5344, 5337, 5251, 2914, 3, 5263])).
% 1.05/1.09 tff(5346,plain,
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% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5347,plain,
% 1.05/1.09 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~rq(s(s(s(s(a))))))) <=> (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
% 1.05/1.09 inference(rewrite,[status(thm)],[])).
% 1.05/1.09 tff(5348,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~rq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))))),
% 1.05/1.09 inference(monotonicity,[status(thm)],[5347])).
% 1.05/1.09 tff(5349,plain,
% 1.05/1.09 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~rq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a)))))))),
% 1.05/1.09 inference(transitivity,[status(thm)],[5348, 5346])).
% 1.05/1.09 tff(5350,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~rq(s(s(s(s(a)))))))),
% 1.05/1.09 inference(quant_inst,[status(thm)],[])).
% 1.05/1.09 tff(5351,plain,
% 1.05/1.09 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~rq(s(X))))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))),
% 1.05/1.09 inference(modus_ponens,[status(thm)],[5350, 5349])).
% 1.05/1.09 tff(5352,plain,
% 1.05/1.09 (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~rq(s(s(s(s(a))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5351, 3356, 149])).
% 1.05/1.09 tff(5353,plain,
% 1.05/1.09 ($false),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5352, 5345, 5337, 2914, 3124, 3, 5251, 5319])).
% 1.05/1.09 tff(5354,plain,(rr(s(s(s(s(a))))) | r(s(s(s(a)))) | p(s(s(s(s(a))))) | r(s(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(a))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.09 tff(5355,plain,
% 1.05/1.09 (rr(s(s(s(s(a)))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5354, 3123, 446, 2751, 4728, 4713])).
% 1.05/1.09 tff(5356,plain,
% 1.05/1.09 (rr(s(s(s(s(s(a))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[4204, 5355])).
% 1.05/1.09 tff(5357,plain,
% 1.05/1.09 (rr(s(s(s(a))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[434, 5355])).
% 1.05/1.09 tff(5358,plain,
% 1.05/1.09 (q(s(s(a)))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[210, 4715])).
% 1.05/1.09 tff(5359,plain,
% 1.05/1.09 (r(s(s(a)))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2968, 2542, 1677, 3275])).
% 1.05/1.09 tff(5360,plain,
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% 1.05/1.09 inference(unit_resolution,[status(thm)],[5392, 3556, 495])).
% 1.05/1.09 tff(5394,plain,
% 1.05/1.09 (pp(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[5393, 5375, 4729, 5374, 4714, 651, 5373])).
% 1.05/1.09 tff(5395,plain,
% 1.05/1.09 (q(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[553, 4729])).
% 1.05/1.09 tff(5396,plain,
% 1.05/1.09 (rr(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2274, 5374])).
% 1.05/1.09 tff(5397,plain,
% 1.05/1.09 (~qq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.09 inference(unit_resolution,[status(thm)],[2284, 4714])).
% 1.05/1.09 tff(5398,plain,
% 1.05/1.09 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X))) <=> ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X))))),
% 1.05/1.09 inference(bind,[status(th)],[])).
% 1.05/1.09 tff(5399,plain,
% 1.05/1.09 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(quant_intro,[status(thm)],[5398])).
% 1.05/1.10 tff(5400,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5401,plain,
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% 1.05/1.10 inference(bind,[status(th)],[])).
% 1.05/1.10 tff(5402,plain,
% 1.05/1.10 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | (~rr(X))) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(quant_intro,[status(thm)],[5401])).
% 1.05/1.10 tff(5403,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | (~rr(X))) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c127')).
% 1.05/1.10 tff(5404,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5403, 5402])).
% 1.05/1.10 tff(5405,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5404, 5400])).
% 1.05/1.10 tff(5406,plain,(
% 1.05/1.10 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(skolemize,[status(sab)],[5405])).
% 1.05/1.10 tff(5407,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5406, 5399])).
% 1.05/1.10 tff(5408,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5409,plain,
% 1.05/1.10 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a)))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5410,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.10 inference(monotonicity,[status(thm)],[5409])).
% 1.05/1.10 tff(5411,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(transitivity,[status(thm)],[5410, 5408])).
% 1.05/1.10 tff(5412,plain,
% 1.05/1.10 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5413,plain,
% 1.05/1.10 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5412, 5411])).
% 1.05/1.10 tff(5414,plain,
% 1.05/1.10 ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5413, 5407, 673])).
% 1.05/1.10 tff(5415,plain,
% 1.05/1.10 (q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5414, 5383, 5397, 5396, 5395, 5385, 5394])).
% 1.05/1.10 tff(5416,plain,
% 1.05/1.10 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5417,plain,
% 1.05/1.10 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5418,plain,
% 1.05/1.10 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.10 inference(monotonicity,[status(thm)],[5417])).
% 1.05/1.10 tff(5419,plain,
% 1.05/1.10 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.10 inference(transitivity,[status(thm)],[5418, 5416])).
% 1.05/1.10 tff(5420,plain,
% 1.05/1.10 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5421,plain,
% 1.05/1.10 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | (~q(X)) | (~r(s(X))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5420, 5419])).
% 1.05/1.10 tff(5422,plain,
% 1.05/1.10 ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5421, 2729, 695])).
% 1.05/1.10 tff(5423,plain,
% 1.05/1.10 (~r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5422, 5415, 5386, 5384])).
% 1.05/1.10 tff(5424,plain,
% 1.05/1.10 (~qrp4(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[1392, 1389, 5423])).
% 1.05/1.10 tff(5425,plain,
% 1.05/1.10 (~qrp2(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[1374, 1371, 5423])).
% 1.05/1.10 tff(5426,plain,
% 1.05/1.10 (rr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3644, 5396])).
% 1.05/1.10 tff(5427,plain,
% 1.05/1.10 (~qrp3(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5205, 1222, 5426])).
% 1.05/1.10 tff(5428,plain,
% 1.05/1.10 (((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5429,plain,
% 1.05/1.10 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5430,plain,
% 1.05/1.10 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5429, 5428])).
% 1.05/1.10 tff(5431,plain,
% 1.05/1.10 (~qrp1(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5430, 1200, 5426])).
% 1.05/1.10 tff(5432,plain,
% 1.05/1.10 (~qrp2(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[4250, 1211, 5426])).
% 1.05/1.10 tff(5433,plain,
% 1.05/1.10 (~qrp4(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[4254, 1233, 5426])).
% 1.05/1.10 tff(5434,plain,
% 1.05/1.10 (((~![X: $i] : (p(X) | (~qrp1(X)))) | (p(s(s(s(s(s(a)))))) | (~qrp1(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (p(X) | (~qrp1(X)))) | p(s(s(s(s(s(a)))))) | (~qrp1(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5435,plain,
% 1.05/1.10 ((~![X: $i] : (p(X) | (~qrp1(X)))) | (p(s(s(s(s(s(a)))))) | (~qrp1(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5436,plain,
% 1.05/1.10 ((~![X: $i] : (p(X) | (~qrp1(X)))) | p(s(s(s(s(s(a)))))) | (~qrp1(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5435, 5434])).
% 1.05/1.10 tff(5437,plain,
% 1.05/1.10 (~qrp1(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5436, 4478, 572])).
% 1.05/1.10 tff(5438,plain,
% 1.05/1.10 (((~![X: $i] : (p(X) | (~qrp4(X)))) | (p(s(s(s(s(s(a)))))) | (~qrp4(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (p(X) | (~qrp4(X)))) | p(s(s(s(s(s(a)))))) | (~qrp4(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5439,plain,
% 1.05/1.10 ((~![X: $i] : (p(X) | (~qrp4(X)))) | (p(s(s(s(s(s(a)))))) | (~qrp4(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5440,plain,
% 1.05/1.10 ((~![X: $i] : (p(X) | (~qrp4(X)))) | p(s(s(s(s(s(a)))))) | (~qrp4(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5439, 5438])).
% 1.05/1.10 tff(5441,plain,
% 1.05/1.10 (~qrp4(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5440, 4492, 572])).
% 1.05/1.10 tff(5442,plain,
% 1.05/1.10 (((~![X: $i] : (r(X) | (~qrp2(X)))) | (r(s(s(s(s(s(a)))))) | (~qrp2(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (r(X) | (~qrp2(X)))) | r(s(s(s(s(s(a)))))) | (~qrp2(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5443,plain,
% 1.05/1.10 ((~![X: $i] : (r(X) | (~qrp2(X)))) | (r(s(s(s(s(s(a)))))) | (~qrp2(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5444,plain,
% 1.05/1.10 ((~![X: $i] : (r(X) | (~qrp2(X)))) | r(s(s(s(s(s(a)))))) | (~qrp2(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5443, 5442])).
% 1.05/1.10 tff(5445,plain,
% 1.05/1.10 (~qrp2(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5444, 1371, 2751])).
% 1.05/1.10 tff(5446,plain,
% 1.05/1.10 (~p(s(a))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[1675, 5362])).
% 1.05/1.10 tff(5447,plain,
% 1.05/1.10 (rr(s(s(s(a))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5248, 4])).
% 1.05/1.10 tff(5448,plain,
% 1.05/1.10 (~pp(s(s(s(a))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[285, 1844])).
% 1.05/1.10 tff(5449,plain,
% 1.05/1.10 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | q(a) | p(s(a)))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | (~ap(a)) | (~p(a)) | r(a) | q(a) | p(s(a)))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5450,plain,
% 1.05/1.10 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | ((~ap(a)) | (~p(a)) | r(a) | q(a) | p(s(a)))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5451,plain,
% 1.05/1.10 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | (~ap(a)) | (~p(a)) | r(a) | q(a) | p(s(a))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5450, 5449])).
% 1.05/1.10 tff(5452,plain,
% 1.05/1.10 ((~p(a)) | r(a) | q(a) | p(s(a))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5451, 14, 2249])).
% 1.05/1.10 tff(5453,plain,
% 1.05/1.10 (~p(a)),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5452, 1920, 4, 3233])).
% 1.05/1.10 tff(5454,plain,
% 1.05/1.10 (((~![X: $i] : ((~ap(X)) | p(X) | r(X) | q(X) | p(s(X)))) | ((~ap(a)) | p(a) | r(a) | q(a) | p(s(a)))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | q(X) | p(s(X)))) | (~ap(a)) | p(a) | r(a) | q(a) | p(s(a)))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5455,plain,
% 1.05/1.10 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | q(X) | p(s(X)))) | ((~ap(a)) | p(a) | r(a) | q(a) | p(s(a)))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5456,plain,
% 1.05/1.10 ((~![X: $i] : ((~ap(X)) | p(X) | r(X) | q(X) | p(s(X)))) | (~ap(a)) | p(a) | r(a) | q(a) | p(s(a))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5455, 5454])).
% 1.05/1.10 tff(5457,plain,
% 1.05/1.10 (p(a) | r(a) | q(a) | p(s(a))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5456, 14, 2640])).
% 1.05/1.10 tff(5458,plain,
% 1.05/1.10 ($false),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5457, 5453, 1920, 4, 3233])).
% 1.05/1.10 tff(5459,plain,(q(a) | p(s(a)) | r(a)), inference(lemma,lemma(discharge,[]))).
% 1.05/1.10 tff(5460,plain,
% 1.05/1.10 (q(a)),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5459, 3232, 4])).
% 1.05/1.10 tff(5461,plain,
% 1.05/1.10 (q(s(a))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[1915, 5460])).
% 1.05/1.10 tff(5462,plain,
% 1.05/1.10 (~qq(s(s(a)))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[4904, 5461, 4, 45])).
% 1.05/1.10 tff(5463,plain,
% 1.05/1.10 (~qq(s(s(s(a))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[194, 5462])).
% 1.05/1.10 tff(5464,plain,
% 1.05/1.10 (~r(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2718, 3593])).
% 1.05/1.10 tff(5465,plain,
% 1.05/1.10 (p(s(s(s(s(a)))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2949, 3, 2542, 196, 3125, 213, 3165])).
% 1.05/1.10 tff(5466,plain,
% 1.05/1.10 (rr(s(s(s(s(a)))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2657, 2542])).
% 1.05/1.10 tff(5467,plain,
% 1.05/1.10 (q(s(s(s(s(a)))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[4719, 3125])).
% 1.05/1.10 tff(5468,plain,
% 1.05/1.10 (pp(s(s(s(s(a)))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3563, 3, 196, 3165, 2542, 3125, 213])).
% 1.05/1.10 tff(5469,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5470,plain,
% 1.05/1.10 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a))))))) <=> ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5471,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(monotonicity,[status(thm)],[5470])).
% 1.05/1.10 tff(5472,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(transitivity,[status(thm)],[5471, 5469])).
% 1.05/1.10 tff(5473,plain,
% 1.05/1.10 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5474,plain,
% 1.05/1.10 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5473, 5472])).
% 1.05/1.10 tff(5475,plain,
% 1.05/1.10 ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5474, 5407, 450])).
% 1.05/1.10 tff(5476,plain,
% 1.05/1.10 (q(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5475, 5468, 5467, 420, 5466, 3593, 5465])).
% 1.05/1.10 tff(5477,plain,
% 1.05/1.10 (p(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2113, 5465])).
% 1.05/1.10 tff(5478,plain,
% 1.05/1.10 (~r(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2736, 5477, 5476, 5464])).
% 1.05/1.10 tff(5479,plain,
% 1.05/1.10 (~rr(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2768, 5476, 5464, 5477])).
% 1.05/1.10 tff(5480,plain,
% 1.05/1.10 (p(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3570, 5479, 5478])).
% 1.05/1.10 tff(5481,plain,
% 1.05/1.10 (p(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3691, 5480])).
% 1.05/1.10 tff(5482,plain,
% 1.05/1.10 (p(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2215, 5477])).
% 1.05/1.10 tff(5483,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | (~pp(X)) | (~qq(s(X))))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~qq(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5484,plain,
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% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5485,plain,
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% 1.05/1.10 inference(monotonicity,[status(thm)],[5484])).
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% 1.05/1.10 inference(transitivity,[status(thm)],[5485, 5483])).
% 1.05/1.10 tff(5487,plain,
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% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
% 1.05/1.10 tff(5488,plain,
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% 1.05/1.10 tff(5489,plain,
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% 1.05/1.10 inference(unit_resolution,[status(thm)],[5488, 3303, 450])).
% 1.05/1.10 tff(5490,plain,
% 1.05/1.10 (~qq(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5489, 5468, 5467, 420, 5466, 3593, 5465])).
% 1.05/1.10 tff(5491,plain,
% 1.05/1.10 (~qq(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2279, 5490])).
% 1.05/1.10 tff(5492,plain,
% 1.05/1.10 (q(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[548, 5476])).
% 1.05/1.10 tff(5493,plain,
% 1.05/1.10 (pp(s(s(s(s(s(a))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[586, 5468])).
% 1.05/1.10 tff(5494,plain,
% 1.05/1.10 (pp(s(s(s(s(s(s(a)))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2344, 5493])).
% 1.05/1.10 tff(5495,plain,
% 1.05/1.10 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5496,plain,
% 1.05/1.10 (((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))) <=> (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(rewrite,[status(thm)],[])).
% 1.05/1.10 tff(5497,plain,
% 1.05/1.10 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(a))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | pp(s(X)))) | (r(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))))),
% 1.05/1.10 inference(monotonicity,[status(thm)],[5496])).
% 1.05/1.10 tff(5498,plain,
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% 1.05/1.10 inference(transitivity,[status(thm)],[5497, 5495])).
% 1.05/1.10 tff(5499,plain,
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% 1.05/1.10 inference(quant_inst,[status(thm)],[])).
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% 1.05/1.10 inference(modus_ponens,[status(thm)],[5499, 5498])).
% 1.05/1.10 tff(5501,plain,
% 1.05/1.10 (r(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5500, 3213, 495])).
% 1.05/1.10 tff(5502,plain,
% 1.05/1.10 (pp(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[5501, 5494, 5492, 5491, 5478, 5482])).
% 1.05/1.10 tff(5503,plain,
% 1.05/1.10 (pp(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3422, 5502])).
% 1.05/1.10 tff(5504,plain,
% 1.05/1.10 (~r(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2261, 5478])).
% 1.05/1.10 tff(5505,plain,
% 1.05/1.10 (~r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[3409, 5504])).
% 1.05/1.10 tff(5506,plain,
% 1.05/1.10 (~rr(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[641, 5479])).
% 1.05/1.10 tff(5507,plain,
% 1.05/1.10 (~rr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[776, 5506])).
% 1.05/1.10 tff(5508,plain,
% 1.05/1.10 (q(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[553, 5492])).
% 1.05/1.10 tff(5509,plain,
% 1.05/1.10 (~qq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.10 inference(unit_resolution,[status(thm)],[2284, 5491])).
% 1.05/1.10 tff(5510,plain,
% 1.05/1.10 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X))) <=> ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X))))),
% 1.05/1.10 inference(bind,[status(th)],[])).
% 1.05/1.10 tff(5511,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(quant_intro,[status(thm)],[5510])).
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% 1.05/1.10 inference(bind,[status(th)],[])).
% 1.05/1.10 tff(5514,plain,
% 1.05/1.10 (![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | qq(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(quant_intro,[status(thm)],[5513])).
% 1.05/1.10 tff(5515,axiom,(![X: $i] : ((((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | qq(X)) | r(X)) | rr(X)) | qq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c142')).
% 1.05/1.10 tff(5516,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5515, 5514])).
% 1.05/1.10 tff(5517,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5516, 5512])).
% 1.05/1.10 tff(5518,plain,(
% 1.05/1.10 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(skolemize,[status(sab)],[5517])).
% 1.05/1.10 tff(5519,plain,
% 1.05/1.10 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))),
% 1.05/1.10 inference(modus_ponens,[status(thm)],[5518, 5511])).
% 1.05/1.10 tff(5520,plain,
% 1.05/1.10 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5521,plain,
% 1.05/1.11 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5522,plain,
% 1.05/1.11 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(monotonicity,[status(thm)],[5521])).
% 1.05/1.11 tff(5523,plain,
% 1.05/1.11 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(transitivity,[status(thm)],[5522, 5520])).
% 1.05/1.11 tff(5524,plain,
% 1.05/1.11 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5525,plain,
% 1.05/1.11 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5524, 5523])).
% 1.05/1.11 tff(5526,plain,
% 1.05/1.11 ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5525, 5519, 673])).
% 1.05/1.11 tff(5527,plain,
% 1.05/1.11 (qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5526, 5502, 5480, 5509, 5506, 5504, 5508])).
% 1.05/1.11 tff(5528,plain,
% 1.05/1.11 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5529,plain,
% 1.05/1.11 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5530,plain,
% 1.05/1.11 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(monotonicity,[status(thm)],[5529])).
% 1.05/1.11 tff(5531,plain,
% 1.05/1.11 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(transitivity,[status(thm)],[5530, 5528])).
% 1.05/1.11 tff(5532,plain,
% 1.05/1.11 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5533,plain,
% 1.05/1.11 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5532, 5531])).
% 1.05/1.11 tff(5534,plain,
% 1.05/1.11 ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5533, 3285, 673])).
% 1.05/1.11 tff(5535,plain,
% 1.05/1.11 (~q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5534, 5502, 5480, 5509, 5506, 5504, 5508])).
% 1.05/1.11 tff(5536,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5537,plain,
% 1.05/1.11 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5538,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.11 inference(monotonicity,[status(thm)],[5537])).
% 1.05/1.11 tff(5539,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(transitivity,[status(thm)],[5538, 5536])).
% 1.05/1.11 tff(5540,plain,
% 1.05/1.11 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5541,plain,
% 1.05/1.11 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5540, 5539])).
% 1.05/1.11 tff(5542,plain,
% 1.05/1.11 (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5541, 4169, 695])).
% 1.05/1.11 tff(5543,plain,
% 1.05/1.11 (~r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5542, 5535, 5527, 5507, 5505, 5503, 5481])).
% 1.05/1.11 tff(5544,plain,
% 1.05/1.11 (((~![X: $i] : (r(X) | (~rpq3(X)))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (r(X) | (~rpq3(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5545,plain,
% 1.05/1.11 ((~![X: $i] : (r(X) | (~rpq3(X)))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5546,plain,
% 1.05/1.11 ((~![X: $i] : (r(X) | (~rpq3(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 1.05/1.11 tff(5547,plain,
% 1.05/1.11 (~rpq3(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5546, 2369, 5543])).
% 1.05/1.11 tff(5548,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5549,plain,
% 1.05/1.11 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5550,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.11 inference(monotonicity,[status(thm)],[5549])).
% 1.05/1.11 tff(5551,plain,
% 1.05/1.11 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(transitivity,[status(thm)],[5550, 5548])).
% 1.05/1.11 tff(5552,plain,
% 1.05/1.11 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5553,plain,
% 1.05/1.11 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5552, 5551])).
% 1.05/1.11 tff(5554,plain,
% 1.05/1.11 (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5553, 4122, 695])).
% 1.05/1.11 tff(5555,plain,
% 1.05/1.11 (~rr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5554, 5535, 5527, 5507, 5505, 5503, 5481])).
% 1.05/1.11 tff(5556,plain,
% 1.05/1.11 (~rpq2(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[4387, 4384, 5555])).
% 1.05/1.11 tff(5557,plain,
% 1.05/1.11 (^[X: $i] : refl((rr(X) | (~rpq1(X))) <=> (rr(X) | (~rpq1(X))))),
% 1.05/1.11 inference(bind,[status(th)],[])).
% 1.05/1.11 tff(5558,plain,
% 1.05/1.11 (![X: $i] : (rr(X) | (~rpq1(X))) <=> ![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(quant_intro,[status(thm)],[5557])).
% 1.05/1.11 tff(5559,plain,
% 1.05/1.11 (![X: $i] : (rr(X) | (~rpq1(X))) <=> ![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5560,plain,
% 1.05/1.11 (^[X: $i] : rewrite(((~rpq1(X)) | rr(X)) <=> (rr(X) | (~rpq1(X))))),
% 1.05/1.11 inference(bind,[status(th)],[])).
% 1.05/1.11 tff(5561,plain,
% 1.05/1.11 (![X: $i] : ((~rpq1(X)) | rr(X)) <=> ![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(quant_intro,[status(thm)],[5560])).
% 1.05/1.11 tff(5562,axiom,(![X: $i] : ((~rpq1(X)) | rr(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c063')).
% 1.05/1.11 tff(5563,plain,
% 1.05/1.11 (![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5562, 5561])).
% 1.05/1.11 tff(5564,plain,
% 1.05/1.11 (![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5563, 5559])).
% 1.05/1.11 tff(5565,plain,(
% 1.05/1.11 ![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(skolemize,[status(sab)],[5564])).
% 1.05/1.11 tff(5566,plain,
% 1.05/1.11 (![X: $i] : (rr(X) | (~rpq1(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5565, 5558])).
% 1.05/1.11 tff(5567,plain,
% 1.05/1.11 (((~![X: $i] : (rr(X) | (~rpq1(X)))) | (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (rr(X) | (~rpq1(X)))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5568,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq1(X)))) | (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5569,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq1(X)))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5568, 5567])).
% 1.05/1.11 tff(5570,plain,
% 1.05/1.11 (~rpq1(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5569, 5566, 5555])).
% 1.05/1.11 tff(5571,plain,
% 1.05/1.11 (pp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[4329, 5503])).
% 1.05/1.11 tff(5572,plain,
% 1.05/1.11 (~rpq4(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[4424, 5571])).
% 1.05/1.11 tff(5573,plain,
% 1.05/1.11 (^[X: $i] : refl((qq(X) | (~rpq4(X))) <=> (qq(X) | (~rpq4(X))))),
% 1.05/1.11 inference(bind,[status(th)],[])).
% 1.05/1.11 tff(5574,plain,
% 1.05/1.11 (![X: $i] : (qq(X) | (~rpq4(X))) <=> ![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(quant_intro,[status(thm)],[5573])).
% 1.05/1.11 tff(5575,plain,
% 1.05/1.11 (![X: $i] : (qq(X) | (~rpq4(X))) <=> ![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5576,plain,
% 1.05/1.11 (^[X: $i] : rewrite(((~rpq4(X)) | qq(X)) <=> (qq(X) | (~rpq4(X))))),
% 1.05/1.11 inference(bind,[status(th)],[])).
% 1.05/1.11 tff(5577,plain,
% 1.05/1.11 (![X: $i] : ((~rpq4(X)) | qq(X)) <=> ![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(quant_intro,[status(thm)],[5576])).
% 1.05/1.11 tff(5578,axiom,(![X: $i] : ((~rpq4(X)) | qq(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c088')).
% 1.05/1.11 tff(5579,plain,
% 1.05/1.11 (![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5578, 5577])).
% 1.05/1.11 tff(5580,plain,
% 1.05/1.11 (![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5579, 5575])).
% 1.05/1.11 tff(5581,plain,(
% 1.05/1.11 ![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(skolemize,[status(sab)],[5580])).
% 1.05/1.11 tff(5582,plain,
% 1.05/1.11 (![X: $i] : (qq(X) | (~rpq4(X)))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5581, 5574])).
% 1.05/1.11 tff(5583,plain,
% 1.05/1.11 (((~![X: $i] : (qq(X) | (~rpq4(X)))) | (qq(s(s(s(s(s(s(a))))))) | (~rpq4(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (qq(X) | (~rpq4(X)))) | qq(s(s(s(s(s(s(a))))))) | (~rpq4(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5584,plain,
% 1.05/1.11 ((~![X: $i] : (qq(X) | (~rpq4(X)))) | (qq(s(s(s(s(s(s(a))))))) | (~rpq4(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5585,plain,
% 1.05/1.11 ((~![X: $i] : (qq(X) | (~rpq4(X)))) | qq(s(s(s(s(s(s(a))))))) | (~rpq4(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5584, 5583])).
% 1.05/1.11 tff(5586,plain,
% 1.05/1.11 (~rpq4(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5585, 5582, 5491])).
% 1.05/1.11 tff(5587,plain,
% 1.05/1.11 (((~![X: $i] : (rr(X) | (~rpq1(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~rpq1(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (rr(X) | (~rpq1(X)))) | rr(s(s(s(s(s(s(a))))))) | (~rpq1(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5588,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq1(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~rpq1(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5589,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq1(X)))) | rr(s(s(s(s(s(s(a))))))) | (~rpq1(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5588, 5587])).
% 1.05/1.11 tff(5590,plain,
% 1.05/1.11 (~rpq1(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5589, 5566, 5479])).
% 1.05/1.11 tff(5591,plain,
% 1.05/1.11 (((~![X: $i] : (rr(X) | (~rpq2(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (rr(X) | (~rpq2(X)))) | rr(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5592,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq2(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5593,plain,
% 1.05/1.11 ((~![X: $i] : (rr(X) | (~rpq2(X)))) | rr(s(s(s(s(s(s(a))))))) | (~rpq2(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5592, 5591])).
% 1.05/1.11 tff(5594,plain,
% 1.05/1.11 (~rpq2(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5593, 4384, 5479])).
% 1.05/1.11 tff(5595,plain,
% 1.05/1.11 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5596,plain,
% 1.05/1.11 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | rq(s(s(s(s(a)))))) <=> (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5597,plain,
% 1.05/1.11 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | rq(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a)))))))),
% 1.05/1.11 inference(monotonicity,[status(thm)],[5596])).
% 1.05/1.11 tff(5598,plain,
% 1.05/1.11 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | rq(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a))))))),
% 1.05/1.11 inference(transitivity,[status(thm)],[5597, 5595])).
% 1.05/1.11 tff(5599,plain,
% 1.05/1.11 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | rq(s(s(s(s(a))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5600,plain,
% 1.05/1.11 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | r(X) | (~q(X)) | qq(X) | (~rr(X)) | rq(s(X)))) | r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a)))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5599, 5598])).
% 1.05/1.11 tff(5601,plain,
% 1.05/1.11 (r(s(s(s(a)))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | p(s(s(s(a)))) | (~q(s(s(s(a))))) | qq(s(s(s(a)))) | rq(s(s(s(s(a)))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5600, 1454, 149])).
% 1.05/1.11 tff(5602,plain,
% 1.05/1.11 (rq(s(s(s(s(a)))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5601, 3, 2542, 196, 3125, 213, 3165])).
% 1.05/1.11 tff(5603,plain,
% 1.05/1.11 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | (~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | (~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5604,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | (~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5605,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | (~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5604, 5603])).
% 1.05/1.11 tff(5606,plain,
% 1.05/1.11 (rpq1(s(s(s(s(a))))) | rpq2(s(s(s(s(a))))) | rpq3(s(s(s(s(a))))) | rpq4(s(s(s(s(a))))) | (~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5605, 4406])).
% 1.05/1.11 tff(5607,plain,
% 1.05/1.11 ((~rq(s(s(s(s(a)))))) | rq(s(s(s(s(s(a))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5606, 2461, 2447, 2433, 2419])).
% 1.05/1.11 tff(5608,plain,
% 1.05/1.11 (rq(s(s(s(s(s(a))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5607, 5602])).
% 1.05/1.11 tff(5609,plain,
% 1.05/1.11 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5610,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5611,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(a)))))) | rpq2(s(s(s(s(s(a)))))) | rpq3(s(s(s(s(s(a)))))) | rpq4(s(s(s(s(s(a)))))) | (~rq(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5610, 5609])).
% 1.05/1.11 tff(5612,plain,
% 1.05/1.11 ((~rq(s(s(s(s(s(a))))))) | rq(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5611, 4406, 2493, 2489, 2485, 2481])).
% 1.05/1.11 tff(5613,plain,
% 1.05/1.11 (rq(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5612, 5608])).
% 1.05/1.11 tff(5614,plain,
% 1.05/1.11 (((~![X: $i] : (qq(X) | (~rpq3(X)))) | (qq(s(s(s(s(s(s(a))))))) | (~rpq3(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (qq(X) | (~rpq3(X)))) | qq(s(s(s(s(s(s(a))))))) | (~rpq3(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5615,plain,
% 1.05/1.11 ((~![X: $i] : (qq(X) | (~rpq3(X)))) | (qq(s(s(s(s(s(s(a))))))) | (~rpq3(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5616,plain,
% 1.05/1.11 ((~![X: $i] : (qq(X) | (~rpq3(X)))) | qq(s(s(s(s(s(s(a))))))) | (~rpq3(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5615, 5614])).
% 1.05/1.11 tff(5617,plain,
% 1.05/1.11 (~rpq3(s(s(s(s(s(s(a)))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5616, 4368, 5491])).
% 1.05/1.11 tff(5618,plain,
% 1.05/1.11 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(a)))))))) | rq(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(a)))))))) | rq(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(rewrite,[status(thm)],[])).
% 1.05/1.11 tff(5619,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(a)))))))) | rq(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(quant_inst,[status(thm)],[])).
% 1.05/1.11 tff(5620,plain,
% 1.05/1.11 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(a)))))))) | rq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(modus_ponens,[status(thm)],[5619, 5618])).
% 1.05/1.11 tff(5621,plain,
% 1.05/1.11 (rpq1(s(s(s(s(s(s(a))))))) | rpq2(s(s(s(s(s(s(a))))))) | rpq3(s(s(s(s(s(s(a))))))) | rpq4(s(s(s(s(s(s(a))))))) | (~rq(s(s(s(s(s(s(a)))))))) | rq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5620, 4406])).
% 1.05/1.11 tff(5622,plain,
% 1.05/1.11 (rq(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[5621, 5617, 5613, 5594, 5590, 5586])).
% 1.05/1.11 tff(5623,plain,
% 1.05/1.11 (rq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[4411, 5622])).
% 1.05/1.11 tff(5624,plain,
% 1.05/1.11 (rq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.11 inference(unit_resolution,[status(thm)],[4416, 5623])).
% 1.05/1.11 tff(5625,plain,
% 1.05/1.11 (~q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[3748, 5535])).
% 1.05/1.12 tff(5626,plain,
% 1.05/1.12 (p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[3753, 5481])).
% 1.05/1.12 tff(5627,plain,
% 1.05/1.12 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5628,plain,
% 1.05/1.12 (((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5629,plain,
% 1.05/1.12 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.12 inference(monotonicity,[status(thm)],[5628])).
% 1.05/1.12 tff(5630,plain,
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% 1.05/1.12 inference(transitivity,[status(thm)],[5629, 5627])).
% 1.05/1.12 tff(5631,plain,
% 1.05/1.12 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5632,plain,
% 1.05/1.12 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | (~pp(s(X))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5631, 5630])).
% 1.05/1.12 tff(5633,plain,
% 1.05/1.12 (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5632, 2295, 817])).
% 1.05/1.12 tff(5634,plain,
% 1.05/1.12 (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5633, 5625, 5543, 5626])).
% 1.05/1.12 tff(5635,plain,
% 1.05/1.12 (qq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[703, 5527])).
% 1.05/1.12 tff(5636,assumption,(~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5637,plain,
% 1.05/1.12 ($false),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1079, 486, 1076, 960, 5636])).
% 1.05/1.12 tff(5638,plain,(qq(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5639,plain,
% 1.05/1.12 (qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5638, 5635])).
% 1.05/1.12 tff(5640,plain,
% 1.05/1.12 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
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% 1.05/1.12 tff(5641,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5642,plain,
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% 1.05/1.12 inference(monotonicity,[status(thm)],[5641])).
% 1.05/1.12 tff(5643,plain,
% 1.05/1.12 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | q(X) | p(s(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(transitivity,[status(thm)],[5642, 5640])).
% 1.05/1.12 tff(5644,plain,
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5644, 5643])).
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5645, 2249, 817])).
% 1.05/1.12 tff(5647,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5646, 5543, 5625, 5626])).
% 1.05/1.12 tff(5648,assumption,(ap(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5649,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[907, 25, 858, 5648])).
% 1.05/1.12 tff(5650,plain,(~ap(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5651,assumption,(pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5652,plain,
% 1.05/1.12 (^[X: $i] : refl((pp(X) | (~pqr2(X))) <=> (pp(X) | (~pqr2(X))))),
% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5653,plain,
% 1.05/1.12 (![X: $i] : (pp(X) | (~pqr2(X))) <=> ![X: $i] : (pp(X) | (~pqr2(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5652])).
% 1.05/1.12 tff(5654,plain,
% 1.05/1.12 (![X: $i] : (pp(X) | (~pqr2(X))) <=> ![X: $i] : (pp(X) | (~pqr2(X)))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5655,plain,
% 1.05/1.12 (^[X: $i] : rewrite(((~pqr2(X)) | pp(X)) <=> (pp(X) | (~pqr2(X))))),
% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5656,plain,
% 1.05/1.12 (![X: $i] : ((~pqr2(X)) | pp(X)) <=> ![X: $i] : (pp(X) | (~pqr2(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5655])).
% 1.05/1.12 tff(5657,axiom,(![X: $i] : ((~pqr2(X)) | pp(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c014')).
% 1.05/1.12 tff(5658,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5657, 5656])).
% 1.05/1.12 tff(5659,plain,
% 1.05/1.12 (![X: $i] : (pp(X) | (~pqr2(X)))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5658, 5654])).
% 1.05/1.12 tff(5660,plain,(
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% 1.05/1.12 inference(skolemize,[status(sab)],[5659])).
% 1.05/1.12 tff(5661,plain,
% 1.05/1.12 (![X: $i] : (pp(X) | (~pqr2(X)))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5660, 5653])).
% 1.05/1.12 tff(5662,plain,
% 1.05/1.12 (((~![X: $i] : (pp(X) | (~pqr2(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (pp(X) | (~pqr2(X)))) | pp(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5664,plain,
% 1.05/1.12 ((~![X: $i] : (pp(X) | (~pqr2(X)))) | pp(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5663, 5662])).
% 1.05/1.12 tff(5665,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5664, 5661, 909, 5651])).
% 1.05/1.12 tff(5666,plain,((~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5667,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5666, 5634])).
% 1.05/1.12 tff(5668,assumption,(pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5669,plain,
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% 1.05/1.12 tff(5670,plain,
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5670, 5669])).
% 1.05/1.12 tff(5672,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5671, 1601, 1082, 5668])).
% 1.05/1.12 tff(5673,plain,((~pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5674,plain,
% 1.05/1.12 (~pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5673, 5639])).
% 1.05/1.12 tff(5675,assumption,(pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5676,plain,
% 1.05/1.12 (^[X: $i] : refl(((~p(X)) | (~pqr1(X))) <=> ((~p(X)) | (~pqr1(X))))),
% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5677,plain,
% 1.05/1.12 (![X: $i] : ((~p(X)) | (~pqr1(X))) <=> ![X: $i] : ((~p(X)) | (~pqr1(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5676])).
% 1.05/1.12 tff(5678,plain,
% 1.05/1.12 (![X: $i] : ((~p(X)) | (~pqr1(X))) <=> ![X: $i] : ((~p(X)) | (~pqr1(X)))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5679,plain,
% 1.05/1.12 (^[X: $i] : rewrite(((~pqr1(X)) | (~p(X))) <=> ((~p(X)) | (~pqr1(X))))),
% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5680,plain,
% 1.05/1.12 (![X: $i] : ((~pqr1(X)) | (~p(X))) <=> ![X: $i] : ((~p(X)) | (~pqr1(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5679])).
% 1.05/1.12 tff(5681,axiom,(![X: $i] : ((~pqr1(X)) | (~p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c006')).
% 1.05/1.12 tff(5682,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5681, 5680])).
% 1.05/1.12 tff(5683,plain,
% 1.05/1.12 (![X: $i] : ((~p(X)) | (~pqr1(X)))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5682, 5678])).
% 1.05/1.12 tff(5684,plain,(
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% 1.05/1.12 inference(skolemize,[status(sab)],[5683])).
% 1.05/1.12 tff(5685,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5684, 5677])).
% 1.05/1.12 tff(5686,plain,
% 1.05/1.12 (((~![X: $i] : ((~p(X)) | (~pqr1(X)))) | ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~pqr1(X)))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5687,plain,
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5688,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5687, 5686])).
% 1.05/1.12 tff(5689,plain,
% 1.05/1.12 ($false),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5688, 5685, 4712, 5675])).
% 1.05/1.12 tff(5690,plain,((~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5691,plain,
% 1.05/1.12 (~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5690, 5647])).
% 1.05/1.12 tff(5692,plain,
% 1.05/1.12 (~pqr4(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1087, 5639])).
% 1.05/1.12 tff(5693,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5694,plain,
% 1.05/1.12 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5695,plain,
% 1.05/1.12 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(monotonicity,[status(thm)],[5694])).
% 1.05/1.12 tff(5696,plain,
% 1.05/1.12 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(transitivity,[status(thm)],[5695, 5693])).
% 1.05/1.12 tff(5697,plain,
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5698,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5697, 5696])).
% 1.05/1.12 tff(5699,plain,
% 1.05/1.12 ((~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5698, 3985, 673])).
% 1.05/1.12 tff(5700,plain,
% 1.05/1.12 (pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5699, 5502, 5480, 5509, 5506, 5504, 5508])).
% 1.05/1.12 tff(5701,plain,
% 1.05/1.12 (pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1532, 5700])).
% 1.05/1.12 tff(5702,plain,
% 1.05/1.12 (~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1151, 1145, 5543])).
% 1.05/1.12 tff(5703,assumption,(~pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5704,plain,
% 1.05/1.12 ($false),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1172, 1169, 1159, 1158, 4074, 4073, 4070, 5703])).
% 1.05/1.12 tff(5705,plain,(pr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr1(s(s(s(s(s(s(s(s(s(a)))))))))) | pqr2(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.12 tff(5706,plain,
% 1.05/1.12 (pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5705, 5702, 4064, 5701])).
% 1.05/1.12 tff(5707,plain,
% 1.05/1.12 (pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[1184, 5706, 5692, 5691, 5674, 5667])).
% 1.05/1.12 tff(5708,plain,
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% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5709,plain,
% 1.05/1.12 (![X: $i] : ((~qq(X)) | (~rpq2(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq2(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5708])).
% 1.05/1.12 tff(5710,plain,
% 1.05/1.12 (![X: $i] : ((~qq(X)) | (~rpq2(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq2(X)))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5711,plain,
% 1.05/1.12 (^[X: $i] : rewrite(((~rpq2(X)) | (~qq(X))) <=> ((~qq(X)) | (~rpq2(X))))),
% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5712,plain,
% 1.05/1.12 (![X: $i] : ((~rpq2(X)) | (~qq(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq2(X)))),
% 1.05/1.12 inference(quant_intro,[status(thm)],[5711])).
% 1.05/1.12 tff(5713,axiom,(![X: $i] : ((~rpq2(X)) | (~qq(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c074')).
% 1.05/1.12 tff(5714,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5713, 5712])).
% 1.05/1.12 tff(5715,plain,
% 1.05/1.12 (![X: $i] : ((~qq(X)) | (~rpq2(X)))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5714, 5710])).
% 1.05/1.12 tff(5716,plain,(
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% 1.05/1.12 inference(skolemize,[status(sab)],[5715])).
% 1.05/1.12 tff(5717,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5716, 5709])).
% 1.05/1.12 tff(5718,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
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% 1.05/1.12 ((~![X: $i] : ((~qq(X)) | (~rpq2(X)))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
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% 1.05/1.12 tff(5721,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5720, 5717, 1082])).
% 1.05/1.12 tff(5722,plain,
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% 1.05/1.12 inference(bind,[status(th)],[])).
% 1.05/1.12 tff(5723,plain,
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% 1.05/1.12 inference(quant_intro,[status(thm)],[5722])).
% 1.05/1.12 tff(5724,plain,
% 1.05/1.12 (![X: $i] : ((~p(X)) | (~rpq1(X))) <=> ![X: $i] : ((~p(X)) | (~rpq1(X)))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5725,plain,
% 1.05/1.12 (^[X: $i] : rewrite(((~rpq1(X)) | (~p(X))) <=> ((~p(X)) | (~rpq1(X))))),
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% 1.05/1.12 tff(5726,plain,
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% 1.05/1.12 inference(quant_intro,[status(thm)],[5725])).
% 1.05/1.12 tff(5727,axiom,(![X: $i] : ((~rpq1(X)) | (~p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c064')).
% 1.05/1.12 tff(5728,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5727, 5726])).
% 1.05/1.12 tff(5729,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5728, 5724])).
% 1.05/1.12 tff(5730,plain,(
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% 1.05/1.12 inference(skolemize,[status(sab)],[5729])).
% 1.05/1.12 tff(5731,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5730, 5723])).
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% 1.05/1.12 tff(5737,plain,
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% 1.05/1.12 inference(quant_intro,[status(thm)],[5736])).
% 1.05/1.12 tff(5738,plain,
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% 1.05/1.12 tff(5740,plain,
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% 1.05/1.12 inference(quant_intro,[status(thm)],[5739])).
% 1.05/1.12 tff(5741,axiom,(![X: $i] : ((~rpq3(X)) | (~p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c078')).
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5742, 5738])).
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5748, 5745, 4712])).
% 1.05/1.12 tff(5750,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5751,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
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% 1.05/1.12 inference(monotonicity,[status(thm)],[5751])).
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
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% 1.05/1.12 tff(5756,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[5755, 3111, 4712, 858, 1082])).
% 1.05/1.12 tff(5757,plain,
% 1.05/1.12 (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5756, 4579, 927, 4584])).
% 1.05/1.12 tff(5758,plain,
% 1.05/1.12 (((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5759,plain,
% 1.05/1.12 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | (ar(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5760,plain,
% 1.05/1.12 ((~![X: $i] : (ar(X) | rr(X) | (~rr(s(X))))) | ar(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(modus_ponens,[status(thm)],[5759, 5758])).
% 1.05/1.12 tff(5761,plain,
% 1.05/1.12 (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5760, 430, 933, 4579])).
% 1.05/1.12 tff(5762,assumption,(pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5763,plain,
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% 1.05/1.12 inference(rewrite,[status(thm)],[])).
% 1.05/1.12 tff(5764,plain,
% 1.05/1.12 (((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.12 inference(rewrite,[status(thm)],[])).
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% 1.05/1.12 inference(monotonicity,[status(thm)],[5764])).
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% 1.05/1.12 tff(5769,plain,
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% 1.05/1.12 tff(5770,plain,
% 1.05/1.12 (qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5769, 4579, 927, 4584])).
% 1.05/1.12 tff(5771,assumption,(~ap(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.05/1.12 tff(5772,plain,
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% 1.05/1.12 inference(unit_resolution,[status(thm)],[912, 281, 909, 5771])).
% 1.05/1.12 tff(5773,plain,
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% 1.05/1.12 inference(quant_inst,[status(thm)],[])).
% 1.05/1.12 tff(5775,plain,
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% 1.05/1.12 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 1.05/1.12 tff(5776,plain,
% 1.05/1.12 (p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.12 inference(unit_resolution,[status(thm)],[5775, 1671, 4712, 5771])).
% 1.05/1.12 tff(5777,plain,
% 1.05/1.12 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5778,plain,
% 1.05/1.13 ((pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5779,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(monotonicity,[status(thm)],[5778])).
% 1.05/1.13 tff(5780,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(transitivity,[status(thm)],[5779, 5777])).
% 1.05/1.13 tff(5781,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5782,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5781, 5780])).
% 1.05/1.13 tff(5783,plain,
% 1.05/1.13 (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5782, 3822, 863, 5761, 937])).
% 1.05/1.13 tff(5784,plain,
% 1.05/1.13 (qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5783, 5757, 5776, 5772, 5770])).
% 1.05/1.13 tff(5785,plain,
% 1.05/1.13 (~ap(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[1423, 156, 863])).
% 1.05/1.13 tff(5786,plain,
% 1.05/1.13 (((~![X: $i] : (ap(X) | (~rpq1(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5787,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq1(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5788,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq1(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5787, 5786])).
% 1.05/1.13 tff(5789,plain,
% 1.05/1.13 (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5788, 2415, 5785])).
% 1.05/1.13 tff(5790,plain,
% 1.05/1.13 (((~![X: $i] : (ap(X) | (~rpq2(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq2(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5791,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq2(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5792,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq2(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5791, 5790])).
% 1.05/1.13 tff(5793,plain,
% 1.05/1.13 (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5792, 2457, 5785])).
% 1.05/1.13 tff(5794,plain,
% 1.05/1.13 (((~![X: $i] : (ap(X) | (~rpq3(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq3(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5795,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq3(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5796,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq3(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5795, 5794])).
% 1.05/1.13 tff(5797,plain,
% 1.05/1.13 (~rpq3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5796, 2443, 5785])).
% 1.05/1.13 tff(5798,plain,
% 1.05/1.13 (((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5799,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5800,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5799, 5798])).
% 1.05/1.13 tff(5801,plain,
% 1.05/1.13 (~rpq4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5800, 2429, 5785])).
% 1.05/1.13 tff(5802,assumption,(rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.05/1.13 tff(5803,plain,
% 1.05/1.13 (((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5804,plain,
% 1.05/1.13 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | (rpq1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5805,plain,
% 1.05/1.13 ((~![X: $i] : (rpq1(X) | rpq2(X) | rpq3(X) | rpq4(X) | (~rq(X)) | rq(s(X)))) | rpq1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rpq4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5804, 5803])).
% 1.05/1.13 tff(5806,plain,
% 1.05/1.13 (rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5805, 4406, 5802, 5801, 5797, 5793, 5789])).
% 1.05/1.13 tff(5807,assumption,(~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.05/1.13 tff(5808,plain,
% 1.05/1.13 (((~![X: $i] : ((~pqr1(X)) | r(X))) | (r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~pqr1(X)) | r(X))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5809,plain,
% 1.05/1.13 (((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> (r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5810,plain,
% 1.05/1.13 (((~![X: $i] : ((~pqr1(X)) | r(X))) | ((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~pqr1(X)) | r(X))) | (r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(monotonicity,[status(thm)],[5809])).
% 1.05/1.13 tff(5811,plain,
% 1.05/1.13 (((~![X: $i] : ((~pqr1(X)) | r(X))) | ((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~pqr1(X)) | r(X))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(transitivity,[status(thm)],[5810, 5808])).
% 1.05/1.13 tff(5812,plain,
% 1.05/1.13 ((~![X: $i] : ((~pqr1(X)) | r(X))) | ((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5813,plain,
% 1.05/1.13 ((~![X: $i] : ((~pqr1(X)) | r(X))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5812, 5811])).
% 1.05/1.13 tff(5814,plain,
% 1.05/1.13 (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5813, 1145, 5807])).
% 1.05/1.13 tff(5815,assumption,(~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.05/1.13 tff(5816,plain,
% 1.05/1.13 (^[X: $i] : refl((rr(X) | (~pqr3(X))) <=> (rr(X) | (~pqr3(X))))),
% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5817,plain,
% 1.05/1.13 (![X: $i] : (rr(X) | (~pqr3(X))) <=> ![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5816])).
% 1.05/1.13 tff(5818,plain,
% 1.05/1.13 (![X: $i] : (rr(X) | (~pqr3(X))) <=> ![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5819,plain,
% 1.05/1.13 (^[X: $i] : rewrite(((~pqr3(X)) | rr(X)) <=> (rr(X) | (~pqr3(X))))),
% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5820,plain,
% 1.05/1.13 (![X: $i] : ((~pqr3(X)) | rr(X)) <=> ![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5819])).
% 1.05/1.13 tff(5821,axiom,(![X: $i] : ((~pqr3(X)) | rr(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c025')).
% 1.05/1.13 tff(5822,plain,
% 1.05/1.13 (![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5821, 5820])).
% 1.05/1.13 tff(5823,plain,
% 1.05/1.13 (![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5822, 5818])).
% 1.05/1.13 tff(5824,plain,(
% 1.05/1.13 ![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(skolemize,[status(sab)],[5823])).
% 1.05/1.13 tff(5825,plain,
% 1.05/1.13 (![X: $i] : (rr(X) | (~pqr3(X)))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5824, 5817])).
% 1.05/1.13 tff(5826,plain,
% 1.05/1.13 (((~![X: $i] : (rr(X) | (~pqr3(X)))) | (rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (rr(X) | (~pqr3(X)))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5827,plain,
% 1.05/1.13 ((~![X: $i] : (rr(X) | (~pqr3(X)))) | (rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5828,plain,
% 1.05/1.13 ((~![X: $i] : (rr(X) | (~pqr3(X)))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5827, 5826])).
% 1.05/1.13 tff(5829,plain,
% 1.05/1.13 (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5828, 5825, 5815])).
% 1.05/1.13 tff(5830,assumption,(~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.05/1.13 tff(5831,plain,
% 1.05/1.13 (((~![X: $i] : (q(X) | (~pqr2(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (q(X) | (~pqr2(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5832,plain,
% 1.05/1.13 ((~![X: $i] : (q(X) | (~pqr2(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5833,plain,
% 1.05/1.13 ((~![X: $i] : (q(X) | (~pqr2(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5832, 5831])).
% 1.05/1.13 tff(5834,plain,
% 1.05/1.13 (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5833, 3892, 5830])).
% 1.05/1.13 tff(5835,plain,
% 1.05/1.13 (((~![X: $i] : (q(X) | (~pqr4(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (q(X) | (~pqr4(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5836,plain,
% 1.05/1.13 ((~![X: $i] : (q(X) | (~pqr4(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5837,plain,
% 1.05/1.13 ((~![X: $i] : (q(X) | (~pqr4(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5836, 5835])).
% 1.05/1.13 tff(5838,plain,
% 1.05/1.13 (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5837, 3874, 5830])).
% 1.05/1.13 tff(5839,plain,
% 1.05/1.13 (pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[1188, 1169, 5762, 5838, 5834, 5829, 5814])).
% 1.05/1.13 tff(5840,assumption,(qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.05/1.13 tff(5841,plain,
% 1.05/1.13 (((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | ((~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5842,plain,
% 1.05/1.13 (((~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5843,plain,
% 1.05/1.13 (((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | ((~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | ((~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))))),
% 1.05/1.13 inference(monotonicity,[status(thm)],[5842])).
% 1.05/1.13 tff(5844,plain,
% 1.05/1.13 (((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | ((~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(transitivity,[status(thm)],[5843, 5841])).
% 1.05/1.13 tff(5845,plain,
% 1.05/1.13 ((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | ((~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5846,plain,
% 1.05/1.13 ((~![X: $i] : ((~pr(X)) | (~rq(X)) | (~qp(X)))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5845, 5844])).
% 1.05/1.13 tff(5847,plain,
% 1.05/1.13 ((~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5846, 1472, 5840])).
% 1.05/1.13 tff(5848,plain,
% 1.05/1.13 ($false),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5847, 5839, 5806])).
% 1.05/1.13 tff(5849,plain,((~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.13 tff(5850,plain,
% 1.05/1.13 (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5849, 5784, 5762, 937, 5761, 5757])).
% 1.05/1.13 tff(5851,plain,
% 1.05/1.13 (rpq1(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rpq2(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rpq3(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rpq4(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[4565, 4406, 4081])).
% 1.05/1.13 tff(5852,plain,
% 1.05/1.13 (rpq4(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5851, 5850, 5749, 5735, 5721])).
% 1.05/1.13 tff(5853,plain,
% 1.05/1.13 (((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5854,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5855,plain,
% 1.05/1.13 ((~![X: $i] : (ap(X) | (~rpq4(X)))) | ap(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rpq4(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5854, 5853])).
% 1.05/1.13 tff(5856,plain,
% 1.05/1.13 ($false),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5855, 2429, 5771, 5852])).
% 1.05/1.13 tff(5857,plain,(ap(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.13 tff(5858,plain,
% 1.05/1.13 (~rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5857, 5707, 5650, 5647, 5639, 5634, 5543, 5555, 5625])).
% 1.05/1.13 tff(5859,plain,
% 1.05/1.13 ($false),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[4450, 5858, 5624, 5572, 5570, 5556, 5547])).
% 1.05/1.13 tff(5860,plain,(r(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~q(s(s(s(a))))) | p(s(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.13 tff(5861,plain,
% 1.05/1.13 (r(s(s(s(a))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5860, 5463, 5448, 5447, 5049, 174])).
% 1.05/1.13 tff(5862,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a)))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5863,plain,
% 1.05/1.13 ((pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5864,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a))))))),
% 1.05/1.13 inference(monotonicity,[status(thm)],[5863])).
% 1.05/1.13 tff(5865,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.13 inference(transitivity,[status(thm)],[5864, 5862])).
% 1.05/1.13 tff(5866,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(s(a))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5867,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5866, 5865])).
% 1.05/1.13 tff(5868,plain,
% 1.05/1.13 ((~q(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5867, 983, 120])).
% 1.05/1.13 tff(5869,plain,
% 1.05/1.13 (~rr(s(s(a)))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5868, 5861, 4749, 44, 1844, 4895])).
% 1.05/1.13 tff(5870,plain,
% 1.05/1.13 (^[X: $i] : refl((pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X)))) <=> (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X)))))),
% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5871,plain,
% 1.05/1.13 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X)))) <=> ![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5870])).
% 1.05/1.13 tff(5872,plain,
% 1.05/1.13 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X)))) <=> ![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5873,plain,
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% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5874,plain,
% 1.05/1.13 (![X: $i] : (((((((~ar(X)) | (~q(X))) | r(X)) | rr(X)) | p(X)) | pp(X)) | (~r(s(X)))) <=> ![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5873])).
% 1.05/1.13 tff(5875,axiom,(![X: $i] : (((((((~ar(X)) | (~q(X))) | r(X)) | rr(X)) | p(X)) | pp(X)) | (~r(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c169')).
% 1.05/1.13 tff(5876,plain,
% 1.05/1.13 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5875, 5874])).
% 1.05/1.13 tff(5877,plain,
% 1.05/1.13 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5876, 5872])).
% 1.05/1.13 tff(5878,plain,(
% 1.05/1.13 ![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(skolemize,[status(sab)],[5877])).
% 1.05/1.13 tff(5879,plain,
% 1.05/1.13 (![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5878, 5871])).
% 1.05/1.13 tff(5880,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5881,plain,
% 1.05/1.13 ((pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | rr(s(s(a))) | (~r(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5882,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | rr(s(s(a))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a)))))))),
% 1.05/1.13 inference(monotonicity,[status(thm)],[5881])).
% 1.05/1.13 tff(5883,plain,
% 1.05/1.13 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | rr(s(s(a))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a))))))),
% 1.05/1.13 inference(transitivity,[status(thm)],[5882, 5880])).
% 1.05/1.13 tff(5884,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | rr(s(s(a))) | (~r(s(s(s(a))))))),
% 1.05/1.13 inference(quant_inst,[status(thm)],[])).
% 1.05/1.13 tff(5885,plain,
% 1.05/1.13 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | r(X) | (~q(X)) | rr(X) | (~r(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a)))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 1.05/1.13 tff(5886,plain,
% 1.05/1.13 ((~q(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | pp(s(s(a))) | (~r(s(s(s(a)))))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5885, 5879, 120])).
% 1.05/1.13 tff(5887,plain,
% 1.05/1.13 ($false),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5886, 5869, 5861, 4749, 44, 1844, 4895])).
% 1.05/1.13 tff(5888,plain,(r(s(a)) | pp(s(s(a))) | p(s(a))), inference(lemma,lemma(discharge,[]))).
% 1.05/1.13 tff(5889,plain,
% 1.05/1.13 (pp(s(s(a)))),
% 1.05/1.13 inference(unit_resolution,[status(thm)],[5888, 3901, 4])).
% 1.05/1.13 tff(5890,plain,
% 1.05/1.13 (^[X: $i] : refl(((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X)))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X)))))),
% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5891,plain,
% 1.05/1.13 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5890])).
% 1.05/1.13 tff(5892,plain,
% 1.05/1.13 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5893,plain,
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% 1.05/1.13 inference(bind,[status(th)],[])).
% 1.05/1.13 tff(5894,plain,
% 1.05/1.13 (![X: $i] : (((((((~ar(X)) | (~q(X))) | r(X)) | (~rr(X))) | p(X)) | (~pp(X))) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(quant_intro,[status(thm)],[5893])).
% 1.05/1.13 tff(5895,axiom,(![X: $i] : (((((((~ar(X)) | (~q(X))) | r(X)) | (~rr(X))) | p(X)) | (~pp(X))) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c172')).
% 1.05/1.13 tff(5896,plain,
% 1.05/1.13 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5895, 5894])).
% 1.05/1.13 tff(5897,plain,
% 1.05/1.13 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5896, 5892])).
% 1.05/1.13 tff(5898,plain,(
% 1.05/1.13 ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(skolemize,[status(sab)],[5897])).
% 1.05/1.13 tff(5899,plain,
% 1.05/1.13 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.13 inference(modus_ponens,[status(thm)],[5898, 5891])).
% 1.05/1.13 tff(5900,plain,
% 1.05/1.13 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5901,plain,
% 1.05/1.13 (((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.13 inference(rewrite,[status(thm)],[])).
% 1.05/1.13 tff(5902,plain,
% 1.05/1.13 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5901])).
% 1.05/1.14 tff(5903,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5902, 5900])).
% 1.05/1.14 tff(5904,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~rr(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5905,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~rr(X)) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 1.05/1.14 tff(5906,plain,
% 1.05/1.14 ((~q(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5905, 5899, 120])).
% 1.05/1.14 tff(5907,plain,
% 1.05/1.14 (~rr(s(s(a)))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5906, 5889, 4749, 44, 5447, 2])).
% 1.05/1.14 tff(5908,plain,
% 1.05/1.14 (^[X: $i] : refl(((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X)))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X)))))),
% 1.05/1.14 inference(bind,[status(th)],[])).
% 1.05/1.14 tff(5909,plain,
% 1.05/1.14 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(quant_intro,[status(thm)],[5908])).
% 1.05/1.14 tff(5910,plain,
% 1.05/1.14 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5911,plain,
% 1.05/1.14 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~ar(X)) | (~q(X))) | (~qq(X))) <=> ((~ar(X)) | (~q(X)) | (~qq(X)))), (((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) <=> (((~ar(X)) | (~q(X)) | (~qq(X))) | r(X)))), rewrite((((~ar(X)) | (~q(X)) | (~qq(X))) | r(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | (~qq(X)))), (((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | (~qq(X))))), ((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) <=> (((~ar(X)) | r(X) | (~q(X)) | (~qq(X))) | rr(X)))), rewrite((((~ar(X)) | r(X) | (~q(X)) | (~qq(X))) | rr(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X))), ((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) <=> ((~ar(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X)))), (((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) <=> (((~ar(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X)) | p(X)))), rewrite((((~ar(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X)) | p(X)) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X))), (((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X)))), ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) <=> (((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X)) | (~pp(X))))), rewrite((((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X)) | (~pp(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)))), ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X))))), (((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~rr(s(X)))) <=> (((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X))) | (~rr(s(X)))))), rewrite((((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X))) | (~rr(s(X)))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))), (((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~rr(s(X)))) <=> ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))))),
% 1.05/1.14 inference(bind,[status(th)],[])).
% 1.05/1.14 tff(5912,plain,
% 1.05/1.14 (![X: $i] : ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(quant_intro,[status(thm)],[5911])).
% 1.05/1.14 tff(5913,axiom,(![X: $i] : ((((((((~ar(X)) | (~q(X))) | (~qq(X))) | r(X)) | rr(X)) | p(X)) | (~pp(X))) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c188')).
% 1.05/1.14 tff(5914,plain,
% 1.05/1.14 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5913, 5912])).
% 1.05/1.14 tff(5915,plain,
% 1.05/1.14 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5914, 5910])).
% 1.05/1.14 tff(5916,plain,(
% 1.05/1.14 ![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(skolemize,[status(sab)],[5915])).
% 1.05/1.14 tff(5917,plain,
% 1.05/1.14 (![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5916, 5909])).
% 1.05/1.14 tff(5918,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5919,plain,
% 1.05/1.14 (((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5920,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5919])).
% 1.05/1.14 tff(5921,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5920, 5918])).
% 1.05/1.14 tff(5922,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5923,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5922, 5921])).
% 1.05/1.14 tff(5924,plain,
% 1.05/1.14 ((~q(s(s(a)))) | (~qq(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5923, 5917, 120])).
% 1.05/1.14 tff(5925,plain,
% 1.05/1.14 (~qq(s(s(a)))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5924, 5907, 4749, 44, 5447, 2, 5889])).
% 1.05/1.14 tff(5926,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5927,plain,
% 1.05/1.14 (((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a))))) <=> (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5928,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5927])).
% 1.05/1.14 tff(5929,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5928, 5926])).
% 1.05/1.14 tff(5930,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a)))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5931,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | r(s(X)))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5930, 5929])).
% 1.05/1.14 tff(5932,plain,
% 1.05/1.14 (qq(s(s(a))) | (~q(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | r(s(s(s(a))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5931, 2897, 120])).
% 1.05/1.14 tff(5933,plain,
% 1.05/1.14 (r(s(s(s(a))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5932, 5925, 4749, 2, 44, 5907, 5889])).
% 1.05/1.14 tff(5934,plain,
% 1.05/1.14 (~p(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5063, 5933, 5049])).
% 1.05/1.14 tff(5935,plain,
% 1.05/1.14 (r(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[164, 5933])).
% 1.05/1.14 tff(5936,plain,
% 1.05/1.14 (~pp(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5091, 5933, 5049, 174])).
% 1.05/1.14 tff(5937,plain,
% 1.05/1.14 (rr(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[2657, 5447])).
% 1.05/1.14 tff(5938,plain,
% 1.05/1.14 (~qq(s(s(s(a))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[194, 5925])).
% 1.05/1.14 tff(5939,plain,
% 1.05/1.14 (~qq(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[419, 5938])).
% 1.05/1.14 tff(5940,plain,
% 1.05/1.14 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5941,plain,
% 1.05/1.14 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a)))))))) <=> (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5942,plain,
% 1.05/1.14 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a)))))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5941])).
% 1.05/1.14 tff(5943,plain,
% 1.05/1.14 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5942, 5940])).
% 1.05/1.14 tff(5944,plain,
% 1.05/1.14 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5945,plain,
% 1.05/1.14 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~pr(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5944, 5943])).
% 1.05/1.14 tff(5946,plain,
% 1.05/1.14 (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pr(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5945, 5306, 450])).
% 1.05/1.14 tff(5947,plain,
% 1.05/1.14 (~pr(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5946, 5939, 5937, 5936, 5068, 5935, 5934])).
% 1.05/1.14 tff(5948,plain,
% 1.05/1.14 (~pr(s(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[3484, 5947])).
% 1.05/1.14 tff(5949,plain,
% 1.05/1.14 (~pr(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[3478, 5948])).
% 1.05/1.14 tff(5950,plain,
% 1.05/1.14 (rr(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[4204, 5937])).
% 1.05/1.14 tff(5951,plain,
% 1.05/1.14 (~qrp4(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[4606, 1233, 5950])).
% 1.05/1.14 tff(5952,plain,
% 1.05/1.14 (((~![X: $i] : ((~qrp3(X)) | (~rr(X)))) | ((~qrp3(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~qrp3(X)) | (~rr(X)))) | (~qrp3(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5953,plain,
% 1.05/1.14 ((~![X: $i] : ((~qrp3(X)) | (~rr(X)))) | ((~qrp3(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5954,plain,
% 1.05/1.14 ((~![X: $i] : ((~qrp3(X)) | (~rr(X)))) | (~qrp3(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5953, 5952])).
% 1.05/1.14 tff(5955,plain,
% 1.05/1.14 (~qrp3(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5954, 1222, 5950])).
% 1.05/1.14 tff(5956,plain,
% 1.05/1.14 (((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5957,plain,
% 1.05/1.14 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5958,plain,
% 1.05/1.14 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5957, 5956])).
% 1.05/1.14 tff(5959,plain,
% 1.05/1.14 (~qrp1(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5958, 1200, 5950])).
% 1.05/1.14 tff(5960,plain,
% 1.05/1.14 (~qrp2(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[4610, 1211, 5950])).
% 1.05/1.14 tff(5961,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5962,plain,
% 1.05/1.14 (((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a)))))) <=> (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5963,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a)))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5962])).
% 1.05/1.14 tff(5964,plain,
% 1.05/1.14 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5963, 5961])).
% 1.05/1.14 tff(5965,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | r(s(s(a))) | (~q(s(s(a)))) | qq(s(s(a))) | rr(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5966,plain,
% 1.05/1.14 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(a))) | (~q(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a)))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5965, 5964])).
% 1.05/1.14 tff(5967,plain,
% 1.05/1.14 (qq(s(s(a))) | (~q(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | r(s(s(a))) | (~pp(s(s(a)))) | (~qp(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5966, 3433, 120])).
% 1.05/1.14 tff(5968,plain,
% 1.05/1.14 (~qp(s(s(s(a))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5967, 5925, 4749, 2, 44, 5889, 5907])).
% 1.05/1.14 tff(5969,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5970,plain,
% 1.05/1.14 ((qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | qp(s(s(s(a)))) | (~qp(s(s(s(s(a))))))) <=> (qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5971,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | qp(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a))))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5970])).
% 1.05/1.14 tff(5972,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | qp(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5971, 5969])).
% 1.05/1.14 tff(5973,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | qp(s(s(s(a)))) | (~qp(s(s(s(s(a)))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5974,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5973, 5972])).
% 1.05/1.14 tff(5975,plain,
% 1.05/1.14 (qp(s(s(s(a)))) | qrp1(s(s(s(a)))) | qrp2(s(s(s(a)))) | qrp3(s(s(s(a)))) | qrp4(s(s(s(a)))) | (~qp(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5974, 2178])).
% 1.05/1.14 tff(5976,plain,
% 1.05/1.14 (qp(s(s(s(a)))) | (~qp(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5975, 4635, 4631, 4627, 4623])).
% 1.05/1.14 tff(5977,plain,
% 1.05/1.14 (~qp(s(s(s(s(a)))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5976, 5968])).
% 1.05/1.14 tff(5978,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5979,plain,
% 1.05/1.14 ((qrp1(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qp(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a)))))))) <=> (qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5980,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qp(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a)))))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5979])).
% 1.05/1.14 tff(5981,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qp(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5980, 5978])).
% 1.05/1.14 tff(5982,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qp(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5983,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | qp(s(s(s(s(a))))) | qrp4(s(s(s(s(a))))) | qrp3(s(s(s(s(a))))) | qrp2(s(s(s(s(a))))) | qrp1(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5982, 5981])).
% 1.05/1.14 tff(5984,plain,
% 1.05/1.14 (qp(s(s(s(s(a))))) | (~qp(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5983, 2178, 4657, 4653, 4649, 4645])).
% 1.05/1.14 tff(5985,plain,
% 1.05/1.14 (~qp(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5984, 5977])).
% 1.05/1.14 tff(5986,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | ((~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5987,plain,
% 1.05/1.14 ((qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))) | qp(s(s(s(s(s(a)))))) | (~qp(s(s(s(s(s(s(a))))))))) <=> ((~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(rewrite,[status(thm)],[])).
% 1.05/1.14 tff(5988,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))) | qp(s(s(s(s(s(a)))))) | (~qp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | ((~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(monotonicity,[status(thm)],[5987])).
% 1.05/1.14 tff(5989,plain,
% 1.05/1.14 (((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))) | qp(s(s(s(s(s(a)))))) | (~qp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(transitivity,[status(thm)],[5988, 5986])).
% 1.05/1.14 tff(5990,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a)))))) | qp(s(s(s(s(s(a)))))) | (~qp(s(s(s(s(s(s(a)))))))))),
% 1.05/1.14 inference(quant_inst,[status(thm)],[])).
% 1.05/1.14 tff(5991,plain,
% 1.05/1.14 ((~![X: $i] : (qrp1(X) | qrp2(X) | qrp3(X) | qrp4(X) | qp(X) | (~qp(s(X))))) | (~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(modus_ponens,[status(thm)],[5990, 5989])).
% 1.05/1.14 tff(5992,plain,
% 1.05/1.14 ((~qp(s(s(s(s(s(s(a)))))))) | qp(s(s(s(s(s(a)))))) | qrp1(s(s(s(s(s(a)))))) | qrp2(s(s(s(s(s(a)))))) | qrp3(s(s(s(s(s(a)))))) | qrp4(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5991, 2178])).
% 1.05/1.14 tff(5993,plain,
% 1.05/1.14 (~qp(s(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[5992, 5985, 5960, 5959, 5955, 5951])).
% 1.05/1.14 tff(5994,plain,
% 1.05/1.14 (~qp(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[2186, 5993])).
% 1.05/1.14 tff(5995,plain,
% 1.05/1.14 (~p(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[571, 5934])).
% 1.05/1.14 tff(5996,plain,
% 1.05/1.14 (~p(s(s(s(s(s(s(a)))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[650, 5995])).
% 1.05/1.14 tff(5997,plain,
% 1.05/1.14 (r(s(s(s(s(s(a))))))),
% 1.05/1.14 inference(unit_resolution,[status(thm)],[562, 5935])).
% 1.05/1.14 tff(5998,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(5999,plain,
% 1.05/1.15 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))) <=> (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6000,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(monotonicity,[status(thm)],[5999])).
% 1.05/1.15 tff(6001,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(transitivity,[status(thm)],[6000, 5998])).
% 1.05/1.15 tff(6002,plain,
% 1.05/1.15 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(quant_inst,[status(thm)],[])).
% 1.05/1.15 tff(6003,plain,
% 1.05/1.15 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6002, 6001])).
% 1.05/1.15 tff(6004,plain,
% 1.05/1.15 (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6003, 4883, 450])).
% 1.05/1.15 tff(6005,plain,
% 1.05/1.15 (~q(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6004, 5939, 5937, 5936, 5068, 5935, 5934])).
% 1.05/1.15 tff(6006,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6007,plain,
% 1.05/1.15 (((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))) <=> (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6008,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(monotonicity,[status(thm)],[6007])).
% 1.05/1.15 tff(6009,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(transitivity,[status(thm)],[6008, 6006])).
% 1.05/1.15 tff(6010,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(quant_inst,[status(thm)],[])).
% 1.05/1.15 tff(6011,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6010, 6009])).
% 1.05/1.15 tff(6012,plain,
% 1.05/1.15 (q(s(s(s(s(s(a)))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | r(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6011, 130, 472])).
% 1.05/1.15 tff(6013,plain,
% 1.05/1.15 (r(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6012, 6005, 5997, 5995])).
% 1.05/1.15 tff(6014,plain,
% 1.05/1.15 (~q(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[2238, 6005])).
% 1.05/1.15 tff(6015,plain,
% 1.05/1.15 (^[X: $i] : refl((pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X))) <=> (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X))))),
% 1.05/1.15 inference(bind,[status(th)],[])).
% 1.05/1.15 tff(6016,plain,
% 1.05/1.15 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(quant_intro,[status(thm)],[6015])).
% 1.05/1.15 tff(6017,plain,
% 1.05/1.15 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6018,plain,
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% 1.05/1.15 inference(bind,[status(th)],[])).
% 1.05/1.15 tff(6019,plain,
% 1.05/1.15 (![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | qq(s(X))) <=> ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(quant_intro,[status(thm)],[6018])).
% 1.05/1.15 tff(6020,axiom,(![X: $i] : ((((((((~aq(X)) | p(X)) | pp(X)) | (~q(X))) | qq(X)) | (~r(X))) | (~rr(X))) | qq(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c145')).
% 1.05/1.15 tff(6021,plain,
% 1.05/1.15 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6020, 6019])).
% 1.05/1.15 tff(6022,plain,
% 1.05/1.15 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6021, 6017])).
% 1.05/1.15 tff(6023,plain,(
% 1.05/1.15 ![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(skolemize,[status(sab)],[6022])).
% 1.05/1.15 tff(6024,plain,
% 1.05/1.15 (![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6023, 6016])).
% 1.05/1.15 tff(6025,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6026,plain,
% 1.05/1.15 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))) <=> (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6027,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(monotonicity,[status(thm)],[6026])).
% 1.05/1.15 tff(6028,plain,
% 1.05/1.15 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(transitivity,[status(thm)],[6027, 6025])).
% 1.05/1.15 tff(6029,plain,
% 1.05/1.15 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(quant_inst,[status(thm)],[])).
% 1.05/1.15 tff(6030,plain,
% 1.05/1.15 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6029, 6028])).
% 1.05/1.15 tff(6031,plain,
% 1.05/1.15 (pp(s(s(s(s(a))))) | p(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6030, 6024, 450])).
% 1.05/1.15 tff(6032,plain,
% 1.05/1.15 (qq(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6031, 5939, 5937, 5936, 5068, 5935, 5934])).
% 1.05/1.15 tff(6033,plain,
% 1.05/1.15 (qq(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[490, 6032])).
% 1.05/1.15 tff(6034,plain,
% 1.05/1.15 (~pp(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[2741, 5936])).
% 1.05/1.15 tff(6035,plain,
% 1.05/1.15 (~pp(s(s(s(s(s(s(a)))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[2746, 6034])).
% 1.05/1.15 tff(6036,assumption,(~q(s(s(s(s(s(a))))))), introduced(assumption)).
% 1.05/1.15 tff(6037,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6038,plain,
% 1.05/1.15 (((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))) <=> (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6039,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))))),
% 1.05/1.15 inference(monotonicity,[status(thm)],[6038])).
% 1.05/1.15 tff(6040,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(transitivity,[status(thm)],[6039, 6037])).
% 1.05/1.15 tff(6041,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(quant_inst,[status(thm)],[])).
% 1.05/1.15 tff(6042,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | q(X) | (~r(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6041, 6040])).
% 1.05/1.15 tff(6043,plain,
% 1.05/1.15 (q(s(s(s(s(s(a)))))) | p(s(s(s(s(s(a)))))) | (~r(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6042, 2553, 472])).
% 1.05/1.15 tff(6044,plain,
% 1.05/1.15 (~r(s(s(s(s(s(a))))))),
% 1.05/1.15 inference(unit_resolution,[status(thm)],[6043, 2817, 2749, 6036])).
% 1.05/1.15 tff(6045,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6046,plain,
% 1.05/1.15 (((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a))))))))) <=> (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(rewrite,[status(thm)],[])).
% 1.05/1.15 tff(6047,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a))))))))))),
% 1.05/1.15 inference(monotonicity,[status(thm)],[6046])).
% 1.05/1.15 tff(6048,plain,
% 1.05/1.15 (((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(transitivity,[status(thm)],[6047, 6045])).
% 1.05/1.15 tff(6049,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.05/1.15 inference(quant_inst,[status(thm)],[])).
% 1.05/1.15 tff(6050,plain,
% 1.05/1.15 ((~![X: $i] : ((~ar(X)) | p(X) | r(X) | q(X) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~ar(s(s(s(s(s(a))))))) | p(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 1.05/1.15 inference(modus_ponens,[status(thm)],[6049, 6048])).
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% 1.05/1.15 inference(bind,[status(th)],[])).
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% 1.05/1.15 inference(quant_intro,[status(thm)],[6090])).
% 1.05/1.15 tff(6092,plain,
% 1.05/1.15 (![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
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% 1.05/1.15 inference(bind,[status(th)],[])).
% 1.05/1.15 tff(6094,plain,
% 1.05/1.15 (![X: $i] : (((((((~ar(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | (~rr(X))) | p(X)) | (~rr(s(X)))) <=> ![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
% 1.05/1.15 inference(quant_intro,[status(thm)],[6093])).
% 1.05/1.15 tff(6095,axiom,(![X: $i] : (((((((~ar(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | (~rr(X))) | p(X)) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c168')).
% 1.05/1.15 tff(6096,plain,
% 1.05/1.16 (![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6095, 6094])).
% 1.05/1.16 tff(6097,plain,
% 1.05/1.16 (![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6096, 6092])).
% 1.05/1.16 tff(6098,plain,(
% 1.05/1.16 ![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
% 1.05/1.16 inference(skolemize,[status(sab)],[6097])).
% 1.05/1.16 tff(6099,plain,
% 1.05/1.16 (![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6098, 6091])).
% 1.05/1.16 tff(6100,plain,
% 1.05/1.16 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.16 inference(rewrite,[status(thm)],[])).
% 1.05/1.16 tff(6101,plain,
% 1.05/1.16 (((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(a)))) | (~rr(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.16 inference(rewrite,[status(thm)],[])).
% 1.05/1.16 tff(6102,plain,
% 1.05/1.16 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))))),
% 1.05/1.16 inference(monotonicity,[status(thm)],[6101])).
% 1.05/1.16 tff(6103,plain,
% 1.05/1.16 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a)))))),
% 1.05/1.16 inference(transitivity,[status(thm)],[6102, 6100])).
% 1.05/1.16 tff(6104,plain,
% 1.05/1.16 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~rr(s(s(a)))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.16 inference(quant_inst,[status(thm)],[])).
% 1.05/1.16 tff(6105,plain,
% 1.05/1.16 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6104, 6103])).
% 1.05/1.16 tff(6106,plain,
% 1.05/1.16 ((~q(s(s(a)))) | (~qq(s(s(a)))) | p(s(s(a))) | (~r(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6105, 6099, 120])).
% 1.05/1.16 tff(6107,plain,
% 1.05/1.16 (~rr(s(s(a)))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6106, 6089, 5358, 5362, 5357, 6071])).
% 1.05/1.16 tff(6108,plain,
% 1.05/1.16 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.16 inference(rewrite,[status(thm)],[])).
% 1.05/1.16 tff(6109,plain,
% 1.05/1.16 (((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.16 inference(rewrite,[status(thm)],[])).
% 1.05/1.16 tff(6110,plain,
% 1.05/1.16 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))))),
% 1.05/1.16 inference(monotonicity,[status(thm)],[6109])).
% 1.05/1.16 tff(6111,plain,
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% 1.05/1.16 inference(transitivity,[status(thm)],[6110, 6108])).
% 1.05/1.16 tff(6112,plain,
% 1.05/1.16 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.05/1.16 inference(quant_inst,[status(thm)],[])).
% 1.05/1.16 tff(6113,plain,
% 1.05/1.16 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6112, 6111])).
% 1.05/1.16 tff(6114,plain,
% 1.05/1.16 ((~q(s(s(a)))) | (~qq(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a)))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6113, 629, 120])).
% 1.05/1.16 tff(6115,plain,
% 1.05/1.16 (~pp(s(s(a)))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6114, 6107, 5358, 5362, 5357, 6071, 6089])).
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% 1.05/1.16 inference(rewrite,[status(thm)],[])).
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% 1.05/1.16 tff(6119,plain,
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% 1.05/1.16 inference(transitivity,[status(thm)],[6118, 6116])).
% 1.05/1.16 tff(6120,plain,
% 1.05/1.16 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | qp(s(s(s(a)))))),
% 1.05/1.16 inference(quant_inst,[status(thm)],[])).
% 1.05/1.16 tff(6121,plain,
% 1.05/1.16 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | qp(s(s(s(a))))),
% 1.05/1.16 inference(modus_ponens,[status(thm)],[6120, 6119])).
% 1.05/1.16 tff(6122,plain,
% 1.05/1.16 ((~q(s(s(a)))) | (~qq(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | qp(s(s(s(a))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6121, 845, 120])).
% 1.05/1.16 tff(6123,plain,
% 1.05/1.16 (qp(s(s(s(a))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[6122, 6115, 5358, 5362, 6107, 6071, 6089])).
% 1.05/1.16 tff(6124,plain,
% 1.05/1.16 (qp(s(s(s(s(a)))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[4640, 6123])).
% 1.05/1.16 tff(6125,plain,
% 1.05/1.16 (qp(s(s(s(s(s(a))))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[4661, 6124])).
% 1.05/1.16 tff(6126,plain,
% 1.05/1.16 (~qrp3(s(s(s(s(s(a))))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[5954, 1222, 5356])).
% 1.05/1.16 tff(6127,plain,
% 1.05/1.16 (qp(s(s(s(s(s(s(a)))))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[4670, 6126, 6125, 5445, 5441, 5437])).
% 1.05/1.16 tff(6128,plain,
% 1.05/1.16 (qp(s(s(s(s(s(s(s(a))))))))),
% 1.05/1.16 inference(unit_resolution,[status(thm)],[3835, 6127])).
% 1.05/1.16 tff(6129,plain,
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% 1.05/1.16 inference(unit_resolution,[status(thm)],[3753, 5384])).
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% 1.05/1.16 inference(unit_resolution,[status(thm)],[752, 5415])).
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% 1.05/1.16 inference(monotonicity,[status(thm)],[6145])).
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% 1.05/1.17 inference(unit_resolution,[status(thm)],[6209, 2415, 5650])).
% 1.05/1.17 tff(6211,assumption,(~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
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% 1.05/1.17 tff(6215,plain,
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% 1.05/1.17 inference(unit_resolution,[status(thm)],[6214, 6197])).
% 1.05/1.17 tff(6216,assumption,(qp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
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% 1.15/1.17 tff(6219,plain,
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[6218, 6215, 6177])).
% 1.15/1.17 tff(6220,assumption,(qp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.15/1.17 tff(6221,assumption,(~qp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.15/1.17 tff(6222,plain,
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% 1.15/1.17 tff(6223,plain,((~qp(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.17 tff(6224,plain,
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[6223, 6219])).
% 1.15/1.17 tff(6225,assumption,(~qp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
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% 1.15/1.17 tff(6231,plain,
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[5048, 215])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[2582, 6233])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[2657, 6241])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[194, 6240])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[1675, 6236])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[2662, 6231])).
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% 1.15/1.17 inference(modus_ponens,[status(thm)],[6255, 6251])).
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% 1.15/1.17 inference(skolemize,[status(sab)],[6256])).
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% 1.15/1.17 inference(modus_ponens,[status(thm)],[6257, 6250])).
% 1.15/1.17 tff(6259,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6260,plain,
% 1.15/1.17 (((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a)))))) <=> ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6261,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))))),
% 1.15/1.17 inference(monotonicity,[status(thm)],[6260])).
% 1.15/1.17 tff(6262,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a))))))),
% 1.15/1.17 inference(transitivity,[status(thm)],[6261, 6259])).
% 1.15/1.17 tff(6263,plain,
% 1.15/1.17 ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | (~pp(s(s(s(a))))) | p(s(s(s(s(a))))))),
% 1.15/1.17 inference(quant_inst,[status(thm)],[])).
% 1.15/1.17 tff(6264,plain,
% 1.15/1.17 ((~![X: $i] : ((~ap(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | p(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))),
% 1.15/1.17 inference(modus_ponens,[status(thm)],[6263, 6262])).
% 1.15/1.17 tff(6265,plain,
% 1.15/1.17 ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | p(s(s(s(s(a))))) | (~pp(s(s(s(a)))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6264, 6258, 149])).
% 1.15/1.17 tff(6266,plain,
% 1.15/1.17 (~pp(s(s(s(a))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6265, 6241, 6247, 446, 215, 6248])).
% 1.15/1.17 tff(6267,plain,
% 1.15/1.17 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6268,plain,
% 1.15/1.17 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | pp(s(s(s(s(a)))))) <=> ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6269,plain,
% 1.15/1.17 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a)))))))),
% 1.15/1.17 inference(monotonicity,[status(thm)],[6268])).
% 1.15/1.17 tff(6270,plain,
% 1.15/1.17 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | pp(s(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a))))))),
% 1.15/1.17 inference(transitivity,[status(thm)],[6269, 6267])).
% 1.15/1.17 tff(6271,plain,
% 1.15/1.17 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | (~rr(s(s(s(a))))) | (~r(s(s(s(a))))) | pp(s(s(s(s(a))))))),
% 1.15/1.17 inference(quant_inst,[status(thm)],[])).
% 1.15/1.17 tff(6272,plain,
% 1.15/1.17 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | pp(s(X)))) | (~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a)))))),
% 1.15/1.17 inference(modus_ponens,[status(thm)],[6271, 6270])).
% 1.15/1.17 tff(6273,plain,
% 1.15/1.17 ((~r(s(s(s(a))))) | (~rr(s(s(s(a))))) | pp(s(s(s(a)))) | (~p(s(s(s(a))))) | q(s(s(s(a)))) | qq(s(s(s(a)))) | pp(s(s(s(s(a)))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6272, 4271, 149])).
% 1.15/1.17 tff(6274,plain,
% 1.15/1.17 (pp(s(s(s(s(a)))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6273, 6266, 6248, 6247, 215, 6241, 6243])).
% 1.15/1.17 tff(6275,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6276,plain,
% 1.15/1.17 (((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))) <=> (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6277,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(monotonicity,[status(thm)],[6276])).
% 1.15/1.17 tff(6278,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(transitivity,[status(thm)],[6277, 6275])).
% 1.15/1.17 tff(6279,plain,
% 1.15/1.17 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(quant_inst,[status(thm)],[])).
% 1.15/1.17 tff(6280,plain,
% 1.15/1.17 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~q(s(X))))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(modus_ponens,[status(thm)],[6279, 6278])).
% 1.15/1.17 tff(6281,plain,
% 1.15/1.17 (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6280, 4298, 450])).
% 1.15/1.17 tff(6282,plain,
% 1.15/1.17 (~q(s(s(s(s(s(a))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6281, 6274, 6245, 6244, 6242, 446, 6231])).
% 1.15/1.17 tff(6283,plain,
% 1.15/1.17 (r(s(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6012, 6282, 572, 6232])).
% 1.15/1.17 tff(6284,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6285,plain,
% 1.15/1.17 (((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))) <=> (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6286,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | (p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(monotonicity,[status(thm)],[6285])).
% 1.15/1.17 tff(6287,plain,
% 1.15/1.17 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(a)))))) | p(s(s(s(s(a))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~qq(s(X))))) | p(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | q(s(s(s(s(a))))) | qq(s(s(s(s(a))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(transitivity,[status(thm)],[6286, 6284])).
% 1.15/1.17 tff(6288,plain,
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% 1.15/1.17 inference(quant_inst,[status(thm)],[])).
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% 1.15/1.17 inference(modus_ponens,[status(thm)],[6288, 6287])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[6289, 360, 450])).
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% 1.15/1.17 inference(unit_resolution,[status(thm)],[6290, 6274, 6245, 6244, 6242, 446, 6231])).
% 1.15/1.17 tff(6292,plain,
% 1.15/1.17 (~qq(s(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[2279, 6291])).
% 1.15/1.17 tff(6293,plain,
% 1.15/1.17 (pp(s(s(s(s(s(a))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[586, 6274])).
% 1.15/1.17 tff(6294,plain,
% 1.15/1.17 (pp(s(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[2344, 6293])).
% 1.15/1.17 tff(6295,plain,
% 1.15/1.17 (~q(s(s(s(s(s(s(a)))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[2238, 6282])).
% 1.15/1.17 tff(6296,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6297,plain,
% 1.15/1.17 (((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a)))))))))) <=> ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6298,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a))))))))))),
% 1.15/1.17 inference(monotonicity,[status(thm)],[6297])).
% 1.15/1.17 tff(6299,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~p(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | (~p(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(transitivity,[status(thm)],[6298, 6296])).
% 1.15/1.17 tff(6300,plain,
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% 1.15/1.17 inference(quant_inst,[status(thm)],[])).
% 1.15/1.17 tff(6301,plain,
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% 1.15/1.17 inference(modus_ponens,[status(thm)],[6300, 6299])).
% 1.15/1.17 tff(6302,plain,
% 1.15/1.17 ((~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6301, 1633, 495])).
% 1.15/1.17 tff(6303,plain,
% 1.15/1.17 (~p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[6302, 6295, 651, 6294, 6292, 6283])).
% 1.15/1.17 tff(6304,plain,
% 1.15/1.17 (~p(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[757, 6303])).
% 1.15/1.17 tff(6305,plain,
% 1.15/1.17 (~p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[762, 6304])).
% 1.15/1.17 tff(6306,plain,
% 1.15/1.17 (~q(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[2307, 6295])).
% 1.15/1.17 tff(6307,plain,
% 1.15/1.17 (~qq(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.17 inference(unit_resolution,[status(thm)],[2284, 6292])).
% 1.15/1.17 tff(6308,plain,
% 1.15/1.17 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.17 inference(rewrite,[status(thm)],[])).
% 1.15/1.17 tff(6309,plain,
% 1.15/1.17 (((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))) <=> ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6310,plain,
% 1.15/1.18 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(monotonicity,[status(thm)],[6309])).
% 1.15/1.18 tff(6311,plain,
% 1.15/1.18 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(transitivity,[status(thm)],[6310, 6308])).
% 1.15/1.18 tff(6312,plain,
% 1.15/1.18 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(quant_inst,[status(thm)],[])).
% 1.15/1.18 tff(6313,plain,
% 1.15/1.18 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | qq(X) | (~r(X)) | (~pp(X)) | pp(s(X)))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(modus_ponens,[status(thm)],[6312, 6311])).
% 1.15/1.18 tff(6314,plain,
% 1.15/1.18 ((~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | qq(s(s(s(s(s(s(a))))))) | pp(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6313, 225, 495])).
% 1.15/1.18 tff(6315,plain,
% 1.15/1.18 (pp(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6314, 6295, 651, 6294, 6292, 6283])).
% 1.15/1.18 tff(6316,plain,
% 1.15/1.18 (r(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[618, 6283])).
% 1.15/1.18 tff(6317,plain,
% 1.15/1.18 (~rr(s(s(s(s(s(s(a)))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6053, 6282, 572])).
% 1.15/1.18 tff(6318,plain,
% 1.15/1.18 (~rr(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[641, 6317])).
% 1.15/1.18 tff(6319,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6320,plain,
% 1.15/1.18 (((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))) <=> (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6321,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(monotonicity,[status(thm)],[6320])).
% 1.15/1.18 tff(6322,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(transitivity,[status(thm)],[6321, 6319])).
% 1.15/1.18 tff(6323,plain,
% 1.15/1.18 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(quant_inst,[status(thm)],[])).
% 1.15/1.18 tff(6324,plain,
% 1.15/1.18 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | qq(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(modus_ponens,[status(thm)],[6323, 6322])).
% 1.15/1.18 tff(6325,plain,
% 1.15/1.18 (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6324, 460, 673])).
% 1.15/1.18 tff(6326,plain,
% 1.15/1.18 (qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6325, 6318, 6316, 6315, 6307, 6306, 6303])).
% 1.15/1.18 tff(6327,plain,
% 1.15/1.18 (r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[771, 6316])).
% 1.15/1.18 tff(6328,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6329,plain,
% 1.15/1.18 (((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a)))))))))) <=> (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6330,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(monotonicity,[status(thm)],[6329])).
% 1.15/1.18 tff(6331,plain,
% 1.15/1.18 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(transitivity,[status(thm)],[6330, 6328])).
% 1.15/1.18 tff(6332,plain,
% 1.15/1.18 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(quant_inst,[status(thm)],[])).
% 1.15/1.18 tff(6333,plain,
% 1.15/1.18 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(modus_ponens,[status(thm)],[6332, 6331])).
% 1.15/1.18 tff(6334,plain,
% 1.15/1.18 (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6333, 342, 673])).
% 1.15/1.18 tff(6335,plain,
% 1.15/1.18 (q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6334, 6318, 6316, 6315, 6307, 6306, 6303])).
% 1.15/1.18 tff(6336,plain,
% 1.15/1.18 (pp(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[3422, 6315])).
% 1.15/1.18 tff(6337,plain,
% 1.15/1.18 (~rr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[776, 6318])).
% 1.15/1.18 tff(6338,plain,
% 1.15/1.18 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6339,plain,
% 1.15/1.18 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6340,plain,
% 1.15/1.18 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.18 inference(monotonicity,[status(thm)],[6339])).
% 1.15/1.18 tff(6341,plain,
% 1.15/1.18 (((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(transitivity,[status(thm)],[6340, 6338])).
% 1.15/1.18 tff(6342,plain,
% 1.15/1.18 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.18 inference(quant_inst,[status(thm)],[])).
% 1.15/1.18 tff(6343,plain,
% 1.15/1.18 ((~![X: $i] : ((~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~pp(X)) | r(s(X)))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(modus_ponens,[status(thm)],[6342, 6341])).
% 1.15/1.18 tff(6344,plain,
% 1.15/1.18 ((~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6343, 602, 695])).
% 1.15/1.18 tff(6345,plain,
% 1.15/1.18 (r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6344, 6337, 6336, 6335, 6327, 6326, 6304])).
% 1.15/1.18 tff(6346,plain,
% 1.15/1.18 (q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[752, 6335])).
% 1.15/1.18 tff(6347,plain,
% 1.15/1.18 (((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~p(s(X))))) | ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | (~q(X)) | (~r(X)) | (~p(s(X))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6348,plain,
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% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6406,plain,
% 1.15/1.18 ((pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))) <=> (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6407,plain,
% 1.15/1.18 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.18 inference(monotonicity,[status(thm)],[6406])).
% 1.15/1.18 tff(6408,plain,
% 1.15/1.18 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(transitivity,[status(thm)],[6407, 6405])).
% 1.15/1.18 tff(6409,plain,
% 1.15/1.18 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.18 inference(quant_inst,[status(thm)],[])).
% 1.15/1.18 tff(6410,plain,
% 1.15/1.18 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | pp(s(X)))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(modus_ponens,[status(thm)],[6409, 6408])).
% 1.15/1.18 tff(6411,plain,
% 1.15/1.18 (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6410, 263, 495])).
% 1.15/1.18 tff(6412,plain,
% 1.15/1.18 (pp(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.18 inference(unit_resolution,[status(thm)],[6411, 6404, 6402, 6401, 6399, 6398, 6391])).
% 1.15/1.18 tff(6413,plain,
% 1.15/1.18 (^[X: $i] : refl(((~pp(X)) | (~pqr4(X))) <=> ((~pp(X)) | (~pqr4(X))))),
% 1.15/1.18 inference(bind,[status(th)],[])).
% 1.15/1.18 tff(6414,plain,
% 1.15/1.18 (![X: $i] : ((~pp(X)) | (~pqr4(X))) <=> ![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.18 inference(quant_intro,[status(thm)],[6413])).
% 1.15/1.18 tff(6415,plain,
% 1.15/1.18 (![X: $i] : ((~pp(X)) | (~pqr4(X))) <=> ![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.18 inference(rewrite,[status(thm)],[])).
% 1.15/1.18 tff(6416,plain,
% 1.15/1.18 (^[X: $i] : rewrite(((~pqr4(X)) | (~pp(X))) <=> ((~pp(X)) | (~pqr4(X))))),
% 1.15/1.18 inference(bind,[status(th)],[])).
% 1.15/1.18 tff(6417,plain,
% 1.15/1.18 (![X: $i] : ((~pqr4(X)) | (~pp(X))) <=> ![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.19 inference(quant_intro,[status(thm)],[6416])).
% 1.15/1.19 tff(6418,axiom,(![X: $i] : ((~pqr4(X)) | (~pp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c028')).
% 1.15/1.19 tff(6419,plain,
% 1.15/1.19 (![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 1.15/1.19 tff(6420,plain,
% 1.15/1.19 (![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6419, 6415])).
% 1.15/1.19 tff(6421,plain,(
% 1.15/1.19 ![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.19 inference(skolemize,[status(sab)],[6420])).
% 1.15/1.19 tff(6422,plain,
% 1.15/1.19 (![X: $i] : ((~pp(X)) | (~pqr4(X)))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6421, 6414])).
% 1.15/1.19 tff(6423,plain,
% 1.15/1.19 (((~![X: $i] : ((~pp(X)) | (~pqr4(X)))) | ((~pp(s(s(s(s(s(s(s(a))))))))) | (~pqr4(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~pp(X)) | (~pqr4(X)))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pqr4(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6424,plain,
% 1.15/1.19 ((~![X: $i] : ((~pp(X)) | (~pqr4(X)))) | ((~pp(s(s(s(s(s(s(s(a))))))))) | (~pqr4(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
% 1.15/1.19 tff(6425,plain,
% 1.15/1.19 ((~![X: $i] : ((~pp(X)) | (~pqr4(X)))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pqr4(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6424, 6423])).
% 1.15/1.19 tff(6426,plain,
% 1.15/1.19 (~pqr4(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6425, 6422, 6412])).
% 1.15/1.19 tff(6427,plain,
% 1.15/1.19 (r(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[618, 6398])).
% 1.15/1.19 tff(6428,plain,
% 1.15/1.19 (~pqr3(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[1798, 1795, 6427])).
% 1.15/1.19 tff(6429,plain,
% 1.15/1.19 (~pr(s(s(s(s(s(a))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[5946, 1776, 3487, 6396, 6394, 6392, 6389])).
% 1.15/1.19 tff(6430,plain,
% 1.15/1.19 (~pr(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3484, 6429])).
% 1.15/1.19 tff(6431,plain,
% 1.15/1.19 (~pr(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3478, 6430])).
% 1.15/1.19 tff(6432,plain,
% 1.15/1.19 (~q(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2307, 6399])).
% 1.15/1.19 tff(6433,assumption,(r(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 1.15/1.19 tff(6434,assumption,(qq(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 1.15/1.19 tff(6435,assumption,(~p(s(s(s(s(s(s(a)))))))), introduced(assumption)).
% 1.15/1.19 tff(6436,assumption,(pp(s(s(s(s(s(s(s(a))))))))), introduced(assumption)).
% 1.15/1.19 tff(6437,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6438,plain,
% 1.15/1.19 (((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))) <=> ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6439,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(monotonicity,[status(thm)],[6438])).
% 1.15/1.19 tff(6440,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(transitivity,[status(thm)],[6439, 6437])).
% 1.15/1.19 tff(6441,plain,
% 1.15/1.19 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | ((~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
% 1.15/1.19 tff(6442,plain,
% 1.15/1.19 ((~![X: $i] : ((~ap(X)) | p(X) | q(X) | (~qq(X)) | (~r(X)) | (~pp(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(a)))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6441, 6440])).
% 1.15/1.19 tff(6443,plain,
% 1.15/1.19 ((~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6442, 2006, 495])).
% 1.15/1.19 tff(6444,plain,
% 1.15/1.19 (~pp(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6443, 6435, 6434, 2803, 6433, 6436])).
% 1.15/1.19 tff(6445,plain,
% 1.15/1.19 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6446,plain,
% 1.15/1.19 ((pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a))))))))) <=> (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6447,plain,
% 1.15/1.19 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(monotonicity,[status(thm)],[6446])).
% 1.15/1.19 tff(6448,plain,
% 1.15/1.19 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(transitivity,[status(thm)],[6447, 6445])).
% 1.15/1.19 tff(6449,plain,
% 1.15/1.19 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
% 1.15/1.19 tff(6450,plain,
% 1.15/1.19 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | (~ap(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6449, 6448])).
% 1.15/1.19 tff(6451,plain,
% 1.15/1.19 (rr(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | pp(s(s(s(s(s(s(a))))))) | p(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6450, 2064, 495])).
% 1.15/1.19 tff(6452,plain,
% 1.15/1.19 ($false),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6451, 6444, 6435, 6434, 2801, 2803, 6433, 2800])).
% 1.15/1.19 tff(6453,plain,(p(s(s(s(s(s(s(a))))))) | (~qq(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(a))))))) | q(s(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a)))))))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.19 tff(6454,plain,
% 1.15/1.19 (p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6453, 6399, 6391, 6404, 6398, 6402, 6412])).
% 1.15/1.19 tff(6455,plain,
% 1.15/1.19 (~qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3738, 6427, 6454, 6432])).
% 1.15/1.19 tff(6456,plain,
% 1.15/1.19 (~q(s(s(s(s(s(a))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6004, 6396, 3487, 1776, 6394, 6392, 6389])).
% 1.15/1.19 tff(6457,plain,
% 1.15/1.19 (~q(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2238, 6456])).
% 1.15/1.19 tff(6458,plain,
% 1.15/1.19 (~q(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2307, 6457])).
% 1.15/1.19 tff(6459,plain,
% 1.15/1.19 (r(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6012, 6456, 6393, 6390])).
% 1.15/1.19 tff(6460,plain,
% 1.15/1.19 (~rr(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6053, 6456, 6390])).
% 1.15/1.19 tff(6461,plain,
% 1.15/1.19 (qq(s(s(s(s(s(a))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6031, 6396, 3487, 1776, 6394, 6392, 6389])).
% 1.15/1.19 tff(6462,plain,
% 1.15/1.19 (qq(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[490, 6461])).
% 1.15/1.19 tff(6463,plain,
% 1.15/1.19 (pp(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6411, 6462, 6460, 6401, 6457, 6459, 6391])).
% 1.15/1.19 tff(6464,plain,
% 1.15/1.19 (p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6453, 6457, 6391, 6462, 6459, 6460, 6463])).
% 1.15/1.19 tff(6465,plain,
% 1.15/1.19 (r(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[618, 6459])).
% 1.15/1.19 tff(6466,plain,
% 1.15/1.19 (~q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3700, 6465, 6464, 6458])).
% 1.15/1.19 tff(6467,plain,
% 1.15/1.19 (pp(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3422, 6463])).
% 1.15/1.19 tff(6468,plain,
% 1.15/1.19 (r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[771, 6465])).
% 1.15/1.19 tff(6469,assumption,(~qq(s(s(s(s(s(s(s(s(a)))))))))), introduced(assumption)).
% 1.15/1.19 tff(6470,plain,
% 1.15/1.19 (p(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3691, 6464])).
% 1.15/1.19 tff(6471,plain,
% 1.15/1.19 (~rr(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[641, 6460])).
% 1.15/1.19 tff(6472,plain,
% 1.15/1.19 (~rr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[776, 6471])).
% 1.15/1.19 tff(6473,plain,
% 1.15/1.19 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6474,plain,
% 1.15/1.19 (((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6475,plain,
% 1.15/1.19 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | (qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.15/1.19 inference(monotonicity,[status(thm)],[6474])).
% 1.15/1.19 tff(6476,plain,
% 1.15/1.19 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(transitivity,[status(thm)],[6475, 6473])).
% 1.15/1.19 tff(6477,plain,
% 1.15/1.19 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | ((~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
% 1.15/1.19 tff(6478,plain,
% 1.15/1.19 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | (~qp(s(X))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.19 inference(modus_ponens,[status(thm)],[6477, 6476])).
% 1.15/1.19 tff(6479,plain,
% 1.15/1.19 (qq(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(a)))))))))) | (~qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6478, 2144, 695])).
% 1.15/1.19 tff(6480,plain,
% 1.15/1.19 (~qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6479, 6472, 6470, 6469, 6468, 6467, 6466])).
% 1.15/1.19 tff(6481,plain,
% 1.15/1.19 (~rq(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6061, 6460, 6401, 6462, 6457, 6459, 6391])).
% 1.15/1.19 tff(6482,plain,
% 1.15/1.19 (~rq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2538, 6481])).
% 1.15/1.19 tff(6483,plain,
% 1.15/1.19 (~rq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3385, 6482])).
% 1.15/1.19 tff(6484,plain,
% 1.15/1.19 ($false),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3452, 6483, 6480, 3442])).
% 1.15/1.19 tff(6485,plain,(qq(s(s(a))) | pr(s(s(s(s(s(s(s(s(s(a)))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(a)))) | p(s(s(a))) | (~q(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.19 tff(6486,plain,
% 1.15/1.19 (pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6485, 6455, 176, 3487, 1843, 2543, 3275])).
% 1.15/1.19 tff(6487,plain,
% 1.15/1.19 (pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3468, 6486])).
% 1.15/1.19 tff(6488,plain,
% 1.15/1.19 (~pqr2(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[1835, 1832, 6427])).
% 1.15/1.19 tff(6489,plain,
% 1.15/1.19 (qq(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[503, 6404])).
% 1.15/1.19 tff(6490,plain,
% 1.15/1.19 (~pqr1(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[514, 511, 6489])).
% 1.15/1.19 tff(6491,plain,
% 1.15/1.19 ($false),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3473, 6490, 6488, 6487, 6431, 6428, 6426])).
% 1.15/1.19 tff(6492,plain,(qq(s(s(a))) | (~rr(s(s(s(s(a)))))) | (~r(s(s(a)))) | p(s(s(a))) | (~q(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.19 tff(6493,plain,
% 1.15/1.19 (qq(s(s(a)))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6492, 6386, 6382, 6384, 6357])).
% 1.15/1.19 tff(6494,plain,
% 1.15/1.19 (~rr(s(s(a)))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6106, 6493, 6357, 6382, 6385, 6384])).
% 1.15/1.19 tff(6495,plain,
% 1.15/1.19 (~pp(s(s(a)))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6114, 6494, 6357, 6382, 6385, 6384, 6493])).
% 1.15/1.19 tff(6496,plain,
% 1.15/1.19 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))) | ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | (~r(s(s(s(a))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | (~r(s(X))))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | (~r(s(s(s(a))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6497,plain,
% 1.15/1.19 ((pp(s(s(a))) | (~ar(s(s(a)))) | p(s(s(a))) | (~q(s(s(a)))) | (~qq(s(s(a)))) | rr(s(s(a))) | (~r(s(s(a)))) | (~r(s(s(s(a)))))) <=> ((~q(s(s(a)))) | (~qq(s(s(a)))) | (~ar(s(s(a)))) | p(s(s(a))) | rr(s(s(a))) | (~r(s(s(a)))) | pp(s(s(a))) | (~r(s(s(s(a))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6498,plain,
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% 1.15/1.19 inference(monotonicity,[status(thm)],[6497])).
% 1.15/1.19 tff(6499,plain,
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% 1.15/1.19 inference(transitivity,[status(thm)],[6498, 6496])).
% 1.15/1.19 tff(6500,plain,
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% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
% 1.15/1.19 tff(6501,plain,
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% 1.15/1.19 inference(modus_ponens,[status(thm)],[6500, 6499])).
% 1.15/1.19 tff(6502,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6501, 805, 120])).
% 1.15/1.19 tff(6503,plain,
% 1.15/1.19 ($false),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6502, 6495, 6494, 6248, 6357, 6382, 6384, 6493])).
% 1.15/1.19 tff(6504,plain,(p(s(s(s(s(a))))) | (~p(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
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% 1.15/1.19 (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6504, 446])).
% 1.15/1.19 tff(6506,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6070, 4])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6492, 5937, 6506, 44, 4749])).
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% 1.15/1.19 (qq(s(s(s(a))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2045, 6507])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6106, 6507, 4749, 44, 5447, 6506])).
% 1.15/1.19 tff(6510,plain,
% 1.15/1.19 (~pp(s(s(a)))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6114, 6509, 4749, 44, 5447, 6506, 6507])).
% 1.15/1.19 tff(6511,plain,
% 1.15/1.19 (~pp(s(s(s(a))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[285, 6510])).
% 1.15/1.19 tff(6512,plain,
% 1.15/1.19 (~r(s(s(s(a))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6502, 6510, 4749, 44, 6509, 6506, 6507])).
% 1.15/1.19 tff(6513,plain,
% 1.15/1.19 (~p(s(s(s(s(a)))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3545, 6512, 5447, 5049, 6511, 174, 6508])).
% 1.15/1.19 tff(6514,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2662, 6512])).
% 1.15/1.19 tff(6515,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[4727, 6514, 5068, 6513])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2957, 6512, 6508, 5447, 5049, 174, 6511])).
% 1.15/1.19 tff(6517,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2741, 6516])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[571, 6513])).
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% 1.15/1.19 (~r(s(s(s(s(s(a))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2718, 6514])).
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% 1.15/1.19 (~r(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[5372, 6519, 5950, 6518, 6517, 6515])).
% 1.15/1.19 tff(6521,plain,
% 1.15/1.19 (~p(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[650, 6518])).
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% 1.15/1.19 (~qq(s(s(s(s(s(a))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3029, 6514, 6513])).
% 1.15/1.19 tff(6523,plain,
% 1.15/1.19 (~qq(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2279, 6522])).
% 1.15/1.19 tff(6524,plain,
% 1.15/1.19 (rr(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2884, 6519, 5950, 6518, 6517, 6515])).
% 1.15/1.19 tff(6525,plain,
% 1.15/1.19 (~pp(s(s(s(s(s(s(a)))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2746, 6517])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[548, 6515])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[5393, 6526, 6525, 6524, 6523, 6521, 6520])).
% 1.15/1.19 tff(6528,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[3422, 6527])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[4329, 6528])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2261, 6520])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[553, 6526])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2274, 6524])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2284, 6523])).
% 1.15/1.19 tff(6534,plain,
% 1.15/1.19 (p(s(s(s(s(s(s(s(a))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[5382, 6520, 6525, 6524, 6526, 6521, 6523])).
% 1.15/1.19 tff(6535,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[3743, 6535])).
% 1.15/1.19 tff(6537,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[3691, 6534])).
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% 1.15/1.19 (p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3753, 6537])).
% 1.15/1.19 tff(6539,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[5414, 6534, 6533, 6532, 6531, 6530, 6527])).
% 1.15/1.19 tff(6540,plain,
% 1.15/1.19 (~r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[3409, 6530])).
% 1.15/1.19 tff(6541,plain,
% 1.15/1.19 (~r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[5422, 6540, 6539, 6537])).
% 1.15/1.19 tff(6542,plain,
% 1.15/1.19 (q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[752, 6539])).
% 1.15/1.19 tff(6543,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6544,plain,
% 1.15/1.19 (((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(rewrite,[status(thm)],[])).
% 1.15/1.19 tff(6545,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.15/1.19 inference(monotonicity,[status(thm)],[6544])).
% 1.15/1.19 tff(6546,plain,
% 1.15/1.19 (((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(transitivity,[status(thm)],[6545, 6543])).
% 1.15/1.19 tff(6547,plain,
% 1.15/1.19 ((~![X: $i] : ((~ap(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | (~pp(X)) | p(s(X)))) | ((~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.15/1.19 inference(quant_inst,[status(thm)],[])).
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% 1.15/1.19 inference(modus_ponens,[status(thm)],[6547, 6546])).
% 1.15/1.19 tff(6549,plain,
% 1.15/1.19 (r(s(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(a))))))))))) | qq(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[6548, 2997, 817])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6549, 6542, 6541, 914, 6538, 6536, 6529])).
% 1.15/1.19 tff(6551,plain,(p(s(a)) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.15/1.19 tff(6552,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[6551, 6505])).
% 1.15/1.19 tff(6553,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[4703, 4678, 6552])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[378, 6553])).
% 1.15/1.19 tff(6555,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[3320, 6554, 6552, 4677])).
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% 1.15/1.19 (rr(s(s(s(a))))),
% 1.15/1.19 inference(unit_resolution,[status(thm)],[2040, 6555, 1])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2657, 6556])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[194, 6555])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[419, 6558])).
% 1.15/1.19 tff(6560,plain,
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[1675, 6552])).
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% 1.15/1.19 inference(unit_resolution,[status(thm)],[2667, 6560])).
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% 1.15/1.20 inference(unit_resolution,[status(thm)],[6590, 6583, 6582, 6581, 6580, 6579, 6572])).
% 1.15/1.20 tff(6592,assumption,(rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
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% 1.15/1.20 inference(unit_resolution,[status(thm)],[6594, 6591])).
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% 1.15/1.20 tff(6597,assumption,(~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
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% 1.15/1.20 (qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
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% 1.15/1.20 (q(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.15/1.20 inference(unit_resolution,[status(thm)],[6165, 6603])).
% 1.15/1.20 tff(6605,assumption,(~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.15/1.20 tff(6606,assumption,(~rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
% 1.15/1.20 tff(6607,assumption,(r(s(s(s(s(s(s(s(s(s(s(a)))))))))))), introduced(assumption)).
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% 1.15/1.20 inference(rewrite,[status(thm)],[])).
% 1.15/1.20 tff(6609,plain,
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% 1.15/1.20 inference(rewrite,[status(thm)],[])).
% 1.15/1.20 tff(6610,plain,
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% 1.15/1.20 inference(monotonicity,[status(thm)],[6609])).
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% 1.15/1.20 inference(bind,[status(th)],[])).
% 1.15/1.20 tff(6675,plain,
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% 1.15/1.20 inference(quant_intro,[status(thm)],[6674])).
% 1.15/1.20 tff(6676,axiom,(![X: $i] : (((((((~aq(X)) | p(X)) | (~q(X))) | (~qq(X))) | (~r(X))) | (~rr(X))) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c117')).
% 1.15/1.20 tff(6677,plain,
% 1.15/1.20 (![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | q(s(X)))),
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% 1.15/1.20 tff(6678,plain,
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% 1.15/1.20 inference(modus_ponens,[status(thm)],[6677, 6673])).
% 1.15/1.20 tff(6679,plain,(
% 1.15/1.20 ![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | q(s(X)))),
% 1.15/1.20 inference(skolemize,[status(sab)],[6678])).
% 1.15/1.20 tff(6680,plain,
% 1.15/1.20 (![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | q(s(X)))),
% 1.15/1.20 inference(modus_ponens,[status(thm)],[6679, 6672])).
% 1.15/1.20 tff(6681,plain,
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% 1.15/1.20 inference(rewrite,[status(thm)],[])).
% 1.15/1.20 tff(6682,plain,
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% 1.15/1.20 inference(rewrite,[status(thm)],[])).
% 1.15/1.20 tff(6683,plain,
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% 1.18/1.20 inference(monotonicity,[status(thm)],[6682])).
% 1.18/1.20 tff(6684,plain,
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% 1.18/1.20 inference(transitivity,[status(thm)],[6683, 6681])).
% 1.18/1.20 tff(6685,plain,
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% 1.18/1.20 inference(quant_inst,[status(thm)],[])).
% 1.18/1.20 tff(6686,plain,
% 1.18/1.20 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | (~rr(X)) | (~r(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.20 inference(modus_ponens,[status(thm)],[6685, 6684])).
% 1.18/1.20 tff(6687,plain,
% 1.18/1.20 ($false),
% 1.18/1.20 inference(unit_resolution,[status(thm)],[6686, 6680, 914, 858, 1082, 5830, 6167, 6607, 6592])).
% 1.18/1.20 tff(6688,plain,((~rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.20 tff(6689,plain,
% 1.18/1.20 (~rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.20 inference(unit_resolution,[status(thm)],[6688, 5830, 1082, 914, 6167, 6607])).
% 1.18/1.20 tff(6690,plain,
% 1.18/1.20 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | (p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.18/1.20 inference(rewrite,[status(thm)],[])).
% 1.18/1.20 tff(6691,plain,
% 1.18/1.20 (((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> (p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.18/1.20 inference(rewrite,[status(thm)],[])).
% 1.18/1.20 tff(6692,plain,
% 1.18/1.20 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | (p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.18/1.20 inference(monotonicity,[status(thm)],[6691])).
% 1.18/1.20 tff(6693,plain,
% 1.18/1.20 (((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.18/1.20 inference(transitivity,[status(thm)],[6692, 6690])).
% 1.18/1.20 tff(6694,plain,
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% 1.18/1.20 inference(quant_inst,[status(thm)],[])).
% 1.18/1.20 tff(6695,plain,
% 1.18/1.20 ((~![X: $i] : ((~aq(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | q(s(X)))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.20 inference(modus_ponens,[status(thm)],[6694, 6693])).
% 1.18/1.20 tff(6696,plain,
% 1.18/1.20 ($false),
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% 1.18/1.20 tff(6697,plain,(q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
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% 1.18/1.20 tff(6700,plain,
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% 1.18/1.20 tff(6701,plain,
% 1.18/1.20 (rr(s(s(s(s(a)))))),
% 1.18/1.20 inference(unit_resolution,[status(thm)],[2657, 6636])).
% 1.18/1.20 tff(6702,plain,
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% 1.18/1.20 inference(unit_resolution,[status(thm)],[419, 6638])).
% 1.18/1.20 tff(6703,plain,
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% 1.18/1.20 tff(6704,plain,
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% 1.18/1.20 inference(unit_resolution,[status(thm)],[2712, 6703, 445, 2073, 2748, 3487, 6245])).
% 1.18/1.20 tff(6705,plain,
% 1.18/1.20 (qq(s(s(s(s(s(a))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2693, 6703, 445, 2748, 2073, 3487, 6245])).
% 1.18/1.21 tff(6706,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[2797, 6705, 2748, 6704])).
% 1.18/1.21 tff(6707,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[2736, 6704, 3621, 2751])).
% 1.18/1.21 tff(6708,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[490, 6705])).
% 1.18/1.21 tff(6709,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[548, 6704])).
% 1.18/1.21 tff(6710,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[2741, 6703])).
% 1.18/1.21 tff(6711,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[2746, 6710])).
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% 1.18/1.21 tff(6715,plain,
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% 1.18/1.21 tff(6716,plain,
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% 1.18/1.21 tff(6721,plain,
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% 1.18/1.21 inference(modus_ponens,[status(thm)],[6721, 6720])).
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[6722, 1952, 149])).
% 1.18/1.21 tff(6724,plain,
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% 1.18/1.21 tff(6725,plain,
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% 1.18/1.21 inference(unit_resolution,[status(thm)],[285, 6724])).
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% 1.18/1.21 tff(6733,plain,
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% 1.18/1.21 tff(6734,plain,
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% 1.18/1.21 tff(6735,plain,
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% 1.18/1.21 inference(bind,[status(th)],[])).
% 1.18/1.21 tff(6738,plain,
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% 1.18/1.21 inference(quant_intro,[status(thm)],[6737])).
% 1.18/1.21 tff(6739,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | (~rr(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c176')).
% 1.18/1.21 tff(6740,plain,
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% 1.18/1.21 inference(modus_ponens,[status(thm)],[6739, 6738])).
% 1.18/1.21 tff(6741,plain,
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% 1.18/1.21 inference(modus_ponens,[status(thm)],[6740, 6736])).
% 1.18/1.21 tff(6742,plain,(
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% 1.18/1.21 inference(skolemize,[status(sab)],[6741])).
% 1.18/1.21 tff(6743,plain,
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% 1.18/1.21 inference(modus_ponens,[status(thm)],[6742, 6735])).
% 1.18/1.21 tff(6744,plain,
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% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6745,plain,
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% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6746,plain,
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% 1.18/1.21 inference(monotonicity,[status(thm)],[6745])).
% 1.18/1.21 tff(6747,plain,
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% 1.18/1.21 inference(transitivity,[status(thm)],[6746, 6744])).
% 1.18/1.21 tff(6748,plain,
% 1.18/1.21 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(a)))) | (~p(s(s(a)))) | q(s(s(a))) | (~rr(s(s(a)))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))))),
% 1.18/1.21 inference(quant_inst,[status(thm)],[])).
% 1.18/1.21 tff(6749,plain,
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% 1.18/1.21 inference(modus_ponens,[status(thm)],[6748, 6747])).
% 1.18/1.21 tff(6750,plain,
% 1.18/1.21 (q(s(s(a))) | (~p(s(s(a)))) | (~r(s(s(a)))) | (~pp(s(s(a)))) | (~rr(s(s(s(a))))) | (~rr(s(s(a))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6749, 6743, 120])).
% 1.18/1.21 tff(6751,plain,
% 1.18/1.21 ($false),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6750, 6733, 6725, 1, 6637, 4676, 6636])).
% 1.18/1.21 tff(6752,plain,(q(s(s(a))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.21 tff(6753,plain,
% 1.18/1.21 (q(s(s(a)))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6752, 914, 5830])).
% 1.18/1.21 tff(6754,plain,
% 1.18/1.21 (~r(s(s(s(a))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6381, 6637, 6753])).
% 1.18/1.21 tff(6755,plain,
% 1.18/1.21 (~r(s(s(s(s(a)))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2662, 6754])).
% 1.18/1.21 tff(6756,plain,
% 1.18/1.21 (q(s(s(s(a))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[5048, 6753])).
% 1.18/1.21 tff(6757,plain,
% 1.18/1.21 (~rr(s(s(s(a))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[5361, 6637, 6753])).
% 1.18/1.21 tff(6758,plain,
% 1.18/1.21 (q(s(s(s(s(s(a))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[4727, 2748, 5467, 446])).
% 1.18/1.21 tff(6759,plain,
% 1.18/1.21 (q(s(s(s(s(s(s(a)))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[548, 6758])).
% 1.18/1.21 tff(6760,plain,
% 1.18/1.21 (~qq(s(s(s(s(s(a))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2777, 2748, 5467, 446])).
% 1.18/1.21 tff(6761,assumption,(~rr(s(s(s(s(s(a))))))), introduced(assumption)).
% 1.18/1.21 tff(6762,plain,
% 1.18/1.21 (pp(s(s(s(s(a)))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[5262, 3123, 3125, 446, 6642, 175])).
% 1.18/1.21 tff(6763,plain,
% 1.18/1.21 (pp(s(s(s(s(s(a))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[586, 6762])).
% 1.18/1.21 tff(6764,plain,
% 1.18/1.21 (r(s(s(s(s(s(s(a)))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2904, 6763, 6761, 6760, 6758, 572, 2751])).
% 1.18/1.21 tff(6765,plain,
% 1.18/1.21 (~p(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[668, 6764, 651, 6759])).
% 1.18/1.21 tff(6766,plain,
% 1.18/1.21 (~p(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[757, 6765])).
% 1.18/1.21 tff(6767,plain,
% 1.18/1.21 (~p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[762, 6766])).
% 1.18/1.21 tff(6768,plain,
% 1.18/1.21 (r(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[618, 6764])).
% 1.18/1.21 tff(6769,plain,
% 1.18/1.21 (r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[771, 6768])).
% 1.18/1.21 tff(6770,plain,
% 1.18/1.21 (q(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[553, 6759])).
% 1.18/1.21 tff(6771,plain,
% 1.18/1.21 (rr(s(s(s(s(s(s(a)))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[5291, 6763, 6761, 6758, 6760, 572, 2751])).
% 1.18/1.21 tff(6772,plain,
% 1.18/1.21 (rr(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2274, 6771])).
% 1.18/1.21 tff(6773,plain,
% 1.18/1.21 (~qq(s(s(s(s(s(s(a)))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2279, 6760])).
% 1.18/1.21 tff(6774,plain,
% 1.18/1.21 (~qq(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2284, 6773])).
% 1.18/1.21 tff(6775,plain,
% 1.18/1.21 (~pp(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[711, 6764, 6759, 651])).
% 1.18/1.21 tff(6776,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6777,plain,
% 1.18/1.21 ((pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))) <=> (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6778,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.21 inference(monotonicity,[status(thm)],[6777])).
% 1.18/1.21 tff(6779,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.21 inference(transitivity,[status(thm)],[6778, 6776])).
% 1.18/1.21 tff(6780,plain,
% 1.18/1.21 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.21 inference(quant_inst,[status(thm)],[])).
% 1.18/1.21 tff(6781,plain,
% 1.18/1.21 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | (~q(s(X))))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(modus_ponens,[status(thm)],[6780, 6779])).
% 1.18/1.21 tff(6782,plain,
% 1.18/1.21 (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6781, 4883, 673])).
% 1.18/1.21 tff(6783,plain,
% 1.18/1.21 (~q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6782, 6775, 6774, 6772, 6765, 6770, 6768])).
% 1.18/1.21 tff(6784,plain,
% 1.18/1.21 (r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[4314, 6783, 6766, 6769])).
% 1.18/1.21 tff(6785,plain,
% 1.18/1.21 (~q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[3748, 6783])).
% 1.18/1.21 tff(6786,plain,
% 1.18/1.21 (~rr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[4355, 6783, 6766, 6769])).
% 1.18/1.21 tff(6787,assumption,(q(s(s(s(s(s(s(s(a))))))))), introduced(assumption)).
% 1.18/1.21 tff(6788,assumption,(rr(s(s(s(s(s(s(s(a))))))))), introduced(assumption)).
% 1.18/1.21 tff(6789,assumption,(~qq(s(s(s(s(s(s(s(a))))))))), introduced(assumption)).
% 1.18/1.21 tff(6790,plain,
% 1.18/1.21 (r(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[618, 6433])).
% 1.18/1.21 tff(6791,plain,
% 1.18/1.21 (q(s(s(s(s(s(s(a)))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[2307, 6787])).
% 1.18/1.21 tff(6792,plain,
% 1.18/1.21 (~pp(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[711, 6433, 6791, 6435])).
% 1.18/1.21 tff(6793,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6794,plain,
% 1.18/1.21 ((pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))) <=> (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6795,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.21 inference(monotonicity,[status(thm)],[6794])).
% 1.18/1.21 tff(6796,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(transitivity,[status(thm)],[6795, 6793])).
% 1.18/1.21 tff(6797,plain,
% 1.18/1.21 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | (pp(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(quant_inst,[status(thm)],[])).
% 1.18/1.21 tff(6798,plain,
% 1.18/1.21 ((~![X: $i] : (pp(X) | (~aq(X)) | p(X) | (~q(X)) | qq(X) | (~rr(X)) | (~r(X)) | qq(s(X)))) | pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(modus_ponens,[status(thm)],[6797, 6796])).
% 1.18/1.21 tff(6799,plain,
% 1.18/1.21 (pp(s(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6798, 6024, 673])).
% 1.18/1.21 tff(6800,plain,
% 1.18/1.21 ($false),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6799, 6792, 6790, 2800, 6789, 6788, 6787, 6469])).
% 1.18/1.21 tff(6801,plain,((~r(s(s(s(s(s(s(a)))))))) | p(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | (~rr(s(s(s(s(s(s(s(a))))))))) | (~q(s(s(s(s(s(s(s(a))))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(a)))))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.21 tff(6802,plain,
% 1.18/1.21 (qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[6801, 6772, 651, 6764, 6774, 6770, 6765])).
% 1.18/1.21 tff(6803,plain,
% 1.18/1.21 (qq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[703, 6802])).
% 1.18/1.21 tff(6804,plain,
% 1.18/1.21 (~pp(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[720, 6775])).
% 1.18/1.21 tff(6805,plain,
% 1.18/1.21 (~pp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.21 inference(unit_resolution,[status(thm)],[729, 6804])).
% 1.18/1.21 tff(6806,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6807,plain,
% 1.18/1.21 ((pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.21 inference(rewrite,[status(thm)],[])).
% 1.18/1.21 tff(6808,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.18/1.21 inference(monotonicity,[status(thm)],[6807])).
% 1.18/1.21 tff(6809,plain,
% 1.18/1.21 (((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.21 inference(transitivity,[status(thm)],[6808, 6806])).
% 1.18/1.21 tff(6810,plain,
% 1.18/1.21 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6811,plain,
% 1.18/1.22 ((~![X: $i] : (pp(X) | (~ap(X)) | p(X) | q(X) | (~qq(X)) | rr(X) | (~r(X)) | p(s(X)))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6810, 6809])).
% 1.18/1.22 tff(6812,plain,
% 1.18/1.22 (rr(s(s(s(s(s(s(s(s(s(a)))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | p(s(s(s(s(s(s(s(s(s(a)))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6811, 2064, 817])).
% 1.18/1.22 tff(6813,plain,
% 1.18/1.22 ($false),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6812, 6805, 6803, 914, 6786, 6785, 6784, 6767])).
% 1.18/1.22 tff(6814,plain,(r(s(s(s(s(a))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | rr(s(s(s(s(s(a)))))) | (~q(s(s(s(a))))) | p(s(s(s(s(a))))) | rr(s(s(s(a))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.22 tff(6815,plain,
% 1.18/1.22 (rr(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6814, 175, 2748, 3125, 914, 446])).
% 1.18/1.22 tff(6816,plain,
% 1.18/1.22 ($false),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[591, 6815, 435])).
% 1.18/1.22 tff(6817,plain,(rr(s(s(s(a)))) | r(s(s(s(s(a))))) | (~q(s(s(s(a))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.22 tff(6818,plain,
% 1.18/1.22 (p(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6817, 6757, 6756, 914, 6755])).
% 1.18/1.22 tff(6819,plain,
% 1.18/1.22 (~rr(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[434, 6757])).
% 1.18/1.22 tff(6820,plain,
% 1.18/1.22 (q(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[4719, 6756])).
% 1.18/1.22 tff(6821,assumption,(q(s(s(s(s(a)))))), introduced(assumption)).
% 1.18/1.22 tff(6822,plain,
% 1.18/1.22 (~q(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[3327, 212, 443, 2073, 2748])).
% 1.18/1.22 tff(6823,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6824,plain,
% 1.18/1.22 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))) <=> (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6825,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6824])).
% 1.18/1.22 tff(6826,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6825, 6823])).
% 1.18/1.22 tff(6827,plain,
% 1.18/1.22 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6828,plain,
% 1.18/1.22 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6827, 6826])).
% 1.18/1.22 tff(6829,plain,
% 1.18/1.22 (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6828, 3960, 450])).
% 1.18/1.22 tff(6830,plain,
% 1.18/1.22 (qq(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6829, 6822, 6821, 212, 2748, 2073])).
% 1.18/1.22 tff(6831,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6832,plain,
% 1.18/1.22 ((pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | q(s(s(s(s(s(a))))))) <=> (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6833,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6832])).
% 1.18/1.22 tff(6834,plain,
% 1.18/1.22 (((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6833, 6831])).
% 1.18/1.22 tff(6835,plain,
% 1.18/1.22 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | (pp(s(s(s(s(a))))) | (~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6836,plain,
% 1.18/1.22 ((~![X: $i] : (pp(X) | (~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | q(s(X)))) | pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6835, 6834])).
% 1.18/1.22 tff(6837,plain,
% 1.18/1.22 (pp(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6836, 3942, 450])).
% 1.18/1.22 tff(6838,plain,
% 1.18/1.22 ($false),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6837, 6830, 6822, 6821, 2073, 212, 2748])).
% 1.18/1.22 tff(6839,plain,(pp(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | rr(s(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 1.18/1.22 tff(6840,plain,
% 1.18/1.22 (pp(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6839, 6820, 6818, 6755, 6819])).
% 1.18/1.22 tff(6841,plain,
% 1.18/1.22 (~q(s(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[2238, 6036])).
% 1.18/1.22 tff(6842,plain,
% 1.18/1.22 (pp(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6839, 6821, 2073, 2748, 443])).
% 1.18/1.22 tff(6843,plain,
% 1.18/1.22 (pp(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[586, 6842])).
% 1.18/1.22 tff(6844,plain,
% 1.18/1.22 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X))) <=> ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X))))),
% 1.18/1.22 inference(bind,[status(th)],[])).
% 1.18/1.22 tff(6845,plain,
% 1.18/1.22 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(quant_intro,[status(thm)],[6844])).
% 1.18/1.22 tff(6846,plain,
% 1.18/1.22 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6847,plain,
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% 1.18/1.22 inference(bind,[status(th)],[])).
% 1.18/1.22 tff(6848,plain,
% 1.18/1.22 (![X: $i] : (((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | (~qq(X))) | r(X)) | q(s(X))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(quant_intro,[status(thm)],[6847])).
% 1.18/1.22 tff(6849,axiom,(![X: $i] : (((((((~aq(X)) | (~p(X))) | (~pp(X))) | (~q(X))) | (~qq(X))) | r(X)) | q(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c109')).
% 1.18/1.22 tff(6850,plain,
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% 1.18/1.22 inference(modus_ponens,[status(thm)],[6849, 6848])).
% 1.18/1.22 tff(6851,plain,
% 1.18/1.22 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6850, 6846])).
% 1.18/1.22 tff(6852,plain,(
% 1.18/1.22 ![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(skolemize,[status(sab)],[6851])).
% 1.18/1.22 tff(6853,plain,
% 1.18/1.22 (![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6852, 6845])).
% 1.18/1.22 tff(6854,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6855,plain,
% 1.18/1.22 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a))))))) <=> ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6856,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6855])).
% 1.18/1.22 tff(6857,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6856, 6854])).
% 1.18/1.22 tff(6858,plain,
% 1.18/1.22 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | (~qq(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6859,plain,
% 1.18/1.22 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | (~pp(X)) | q(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6858, 6857])).
% 1.18/1.22 tff(6860,plain,
% 1.18/1.22 ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6859, 6853, 450])).
% 1.18/1.22 tff(6861,plain,
% 1.18/1.22 (~qq(s(s(s(s(a)))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6860, 6036, 6821, 2073, 2748, 6842])).
% 1.18/1.22 tff(6862,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6863,plain,
% 1.18/1.22 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a))))))) <=> ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6864,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6863])).
% 1.18/1.22 tff(6865,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6864, 6862])).
% 1.18/1.22 tff(6866,plain,
% 1.18/1.22 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | qq(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6867,plain,
% 1.18/1.22 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | qq(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6866, 6865])).
% 1.18/1.22 tff(6868,plain,
% 1.18/1.22 ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | qq(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6867, 5519, 450])).
% 1.18/1.22 tff(6869,plain,
% 1.18/1.22 (qq(s(s(s(s(s(a))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6868, 6861, 6821, 443, 2073, 2748, 6842])).
% 1.18/1.22 tff(6870,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6871,plain,
% 1.18/1.22 (((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))) <=> (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6872,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6871])).
% 1.18/1.22 tff(6873,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6872, 6870])).
% 1.18/1.22 tff(6874,plain,
% 1.18/1.22 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6875,plain,
% 1.18/1.22 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~r(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6874, 6873])).
% 1.18/1.22 tff(6876,plain,
% 1.18/1.22 (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~r(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6875, 4169, 472])).
% 1.18/1.22 tff(6877,plain,
% 1.18/1.22 (~r(s(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6876, 6869, 592, 3621, 2751, 6843, 6036])).
% 1.18/1.22 tff(6878,plain,
% 1.18/1.22 (~pp(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[2302, 6877, 6841, 3667])).
% 1.18/1.22 tff(6879,plain,
% 1.18/1.22 (~pp(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[720, 6878])).
% 1.18/1.22 tff(6880,plain,
% 1.18/1.22 (~pp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[729, 6879])).
% 1.18/1.22 tff(6881,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6882,plain,
% 1.18/1.22 (((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))) <=> (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(rewrite,[status(thm)],[])).
% 1.18/1.22 tff(6883,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))))),
% 1.18/1.22 inference(monotonicity,[status(thm)],[6882])).
% 1.18/1.22 tff(6884,plain,
% 1.18/1.22 (((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(transitivity,[status(thm)],[6883, 6881])).
% 1.18/1.22 tff(6885,plain,
% 1.18/1.22 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | ((~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | r(s(s(s(s(s(a)))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a)))))))))),
% 1.18/1.22 inference(quant_inst,[status(thm)],[])).
% 1.18/1.22 tff(6886,plain,
% 1.18/1.22 ((~![X: $i] : ((~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~pp(X)) | (~rr(s(X))))) | q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~ar(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(modus_ponens,[status(thm)],[6885, 6884])).
% 1.18/1.22 tff(6887,plain,
% 1.18/1.22 (q(s(s(s(s(s(a)))))) | (~qq(s(s(s(s(s(a))))))) | (~p(s(s(s(s(s(a))))))) | rr(s(s(s(s(s(a)))))) | r(s(s(s(s(s(a)))))) | (~pp(s(s(s(s(s(a))))))) | (~rr(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6886, 4122, 472])).
% 1.18/1.22 tff(6888,plain,
% 1.18/1.22 (~rr(s(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[6887, 6869, 592, 3621, 2751, 6843, 6036])).
% 1.18/1.22 tff(6889,plain,
% 1.18/1.22 (~rr(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[641, 6888])).
% 1.18/1.22 tff(6890,plain,
% 1.18/1.22 (qq(s(s(s(s(s(s(a)))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[490, 6869])).
% 1.18/1.22 tff(6891,plain,
% 1.18/1.22 (qq(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[503, 6890])).
% 1.18/1.22 tff(6892,plain,
% 1.18/1.22 (p(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[3570, 6877, 6888])).
% 1.18/1.22 tff(6893,plain,
% 1.18/1.22 (~q(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[2307, 6841])).
% 1.18/1.22 tff(6894,plain,
% 1.18/1.22 (~r(s(s(s(s(s(s(s(a))))))))),
% 1.18/1.22 inference(unit_resolution,[status(thm)],[2261, 6877])).
% 1.18/1.22 tff(6895,plain,
% 1.18/1.22 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6896,plain,
% 1.18/1.23 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6897,plain,
% 1.18/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(monotonicity,[status(thm)],[6896])).
% 1.18/1.23 tff(6898,plain,
% 1.18/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(transitivity,[status(thm)],[6897, 6895])).
% 1.18/1.23 tff(6899,plain,
% 1.18/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(quant_inst,[status(thm)],[])).
% 1.18/1.23 tff(6900,plain,
% 1.18/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(modus_ponens,[status(thm)],[6899, 6898])).
% 1.18/1.23 tff(6901,plain,
% 1.18/1.23 ((~p(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | (~q(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6900, 3111, 673])).
% 1.18/1.23 tff(6902,plain,
% 1.18/1.23 (~q(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6901, 6894, 6893, 6892, 6891, 6889])).
% 1.18/1.23 tff(6903,plain,
% 1.18/1.23 (~q(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[3748, 6902])).
% 1.18/1.23 tff(6904,plain,
% 1.18/1.23 (p(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[3691, 6892])).
% 1.18/1.23 tff(6905,plain,
% 1.18/1.23 (p(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[3753, 6904])).
% 1.18/1.23 tff(6906,plain,
% 1.18/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6907,plain,
% 1.18/1.23 (((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a)))))))))) <=> ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6908,plain,
% 1.18/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(monotonicity,[status(thm)],[6907])).
% 1.18/1.23 tff(6909,plain,
% 1.18/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(transitivity,[status(thm)],[6908, 6906])).
% 1.18/1.23 tff(6910,plain,
% 1.18/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | (~p(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | (~qq(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(quant_inst,[status(thm)],[])).
% 1.18/1.23 tff(6911,plain,
% 1.18/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qq(s(X)))) | (~p(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(modus_ponens,[status(thm)],[6910, 6909])).
% 1.18/1.23 tff(6912,plain,
% 1.18/1.23 ((~p(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | r(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6911, 3611, 673])).
% 1.18/1.23 tff(6913,plain,
% 1.18/1.23 (qq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6912, 6894, 6893, 6892, 6891, 6889])).
% 1.18/1.23 tff(6914,plain,
% 1.18/1.23 (qq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[703, 6913])).
% 1.18/1.23 tff(6915,plain,
% 1.18/1.23 (~rr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[776, 6889])).
% 1.18/1.23 tff(6916,plain,
% 1.18/1.23 (~r(s(s(s(s(s(s(s(s(a)))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[3409, 6894])).
% 1.18/1.23 tff(6917,plain,
% 1.18/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6918,plain,
% 1.18/1.23 ((pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6919,plain,
% 1.18/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.18/1.23 inference(monotonicity,[status(thm)],[6918])).
% 1.18/1.23 tff(6920,plain,
% 1.18/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(transitivity,[status(thm)],[6919, 6917])).
% 1.18/1.23 tff(6921,plain,
% 1.18/1.23 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(quant_inst,[status(thm)],[])).
% 1.18/1.23 tff(6922,plain,
% 1.18/1.23 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(modus_ponens,[status(thm)],[6921, 6920])).
% 1.18/1.23 tff(6923,plain,
% 1.18/1.23 (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6922, 3631, 695])).
% 1.18/1.23 tff(6924,plain,
% 1.18/1.23 (rr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.18/1.23 inference(unit_resolution,[status(thm)],[6923, 6879, 6902, 6913, 6916, 6904, 6915])).
% 1.18/1.23 tff(6925,plain,
% 1.18/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.18/1.23 inference(rewrite,[status(thm)],[])).
% 1.18/1.23 tff(6926,plain,
% 1.18/1.23 ((pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6927,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.23 inference(monotonicity,[status(thm)],[6926])).
% 1.21/1.23 tff(6928,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.23 inference(transitivity,[status(thm)],[6927, 6925])).
% 1.21/1.23 tff(6929,plain,
% 1.21/1.23 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(6930,plain,
% 1.21/1.23 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | r(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[6929, 6928])).
% 1.21/1.23 tff(6931,plain,
% 1.21/1.23 (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6930, 3655, 695])).
% 1.21/1.23 tff(6932,plain,
% 1.21/1.23 (r(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6931, 6879, 6902, 6913, 6916, 6904, 6915])).
% 1.21/1.23 tff(6933,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6934,plain,
% 1.21/1.23 ((pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6935,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.23 inference(monotonicity,[status(thm)],[6934])).
% 1.21/1.23 tff(6936,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.23 inference(transitivity,[status(thm)],[6935, 6933])).
% 1.21/1.23 tff(6937,plain,
% 1.21/1.23 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(6938,plain,
% 1.21/1.23 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | p(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[6937, 6936])).
% 1.21/1.23 tff(6939,plain,
% 1.21/1.23 ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6938, 3679, 817])).
% 1.21/1.23 tff(6940,plain,
% 1.21/1.23 ($false),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6939, 6932, 6924, 6914, 6905, 6903, 6880, 914])).
% 1.21/1.23 tff(6941,plain,(q(s(s(s(s(s(a)))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~q(s(s(s(s(a)))))) | rr(s(s(s(s(a))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a)))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.23 tff(6942,plain,
% 1.21/1.23 (q(s(s(s(s(s(a))))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6941, 914, 6820, 6819, 6818, 6755])).
% 1.21/1.23 tff(6943,plain,
% 1.21/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6944,plain,
% 1.21/1.23 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a)))))))) <=> ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6945,plain,
% 1.21/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))))),
% 1.21/1.23 inference(monotonicity,[status(thm)],[6944])).
% 1.21/1.23 tff(6946,plain,
% 1.21/1.23 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a))))))))),
% 1.21/1.23 inference(transitivity,[status(thm)],[6945, 6943])).
% 1.21/1.23 tff(6947,plain,
% 1.21/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(s(a))))))))),
% 1.21/1.23 inference(quant_inst,[status(thm)],[])).
% 1.21/1.23 tff(6948,plain,
% 1.21/1.23 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | (~q(s(X))))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))),
% 1.21/1.23 inference(modus_ponens,[status(thm)],[6947, 6946])).
% 1.21/1.23 tff(6949,plain,
% 1.21/1.23 ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(s(a)))))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6948, 3285, 450])).
% 1.21/1.23 tff(6950,plain,
% 1.21/1.23 (qq(s(s(s(s(a)))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[6949, 6942, 6820, 6819, 6818, 6755, 6840])).
% 1.21/1.23 tff(6951,plain,
% 1.21/1.23 (qq(s(s(s(a))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[419, 6950])).
% 1.21/1.23 tff(6952,plain,
% 1.21/1.23 (~pp(s(s(s(a))))),
% 1.21/1.23 inference(unit_resolution,[status(thm)],[5344, 6951, 6642, 6756, 6754, 6840])).
% 1.21/1.23 tff(6953,plain,
% 1.21/1.23 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a)))))))),
% 1.21/1.23 inference(rewrite,[status(thm)],[])).
% 1.21/1.23 tff(6954,plain,
% 1.21/1.23 ((pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~p(s(s(s(s(a))))))) <=> (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a)))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(6955,plain,
% 1.21/1.24 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~p(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a))))))))),
% 1.21/1.24 inference(monotonicity,[status(thm)],[6954])).
% 1.21/1.24 tff(6956,plain,
% 1.21/1.24 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~p(s(s(s(s(a)))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a)))))))),
% 1.21/1.24 inference(transitivity,[status(thm)],[6955, 6953])).
% 1.21/1.24 tff(6957,plain,
% 1.21/1.24 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | (pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | r(s(s(s(a)))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | rr(s(s(s(a)))) | (~p(s(s(s(s(a)))))))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(6958,plain,
% 1.21/1.24 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | r(X) | (~q(X)) | (~qq(X)) | rr(X) | (~p(s(X))))) | rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~ap(s(s(s(a))))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a))))))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[6957, 6956])).
% 1.21/1.24 tff(6959,plain,
% 1.21/1.24 (rr(s(s(s(a)))) | r(s(s(s(a)))) | pp(s(s(s(a)))) | (~p(s(s(s(a))))) | (~q(s(s(s(a))))) | (~qq(s(s(s(a))))) | (~p(s(s(s(s(a))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6958, 3581, 149])).
% 1.21/1.24 tff(6960,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6959, 6952, 6951, 6756, 6757, 6754, 6642, 6818])).
% 1.21/1.24 tff(6961,plain,(p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.24 tff(6962,plain,
% 1.21/1.24 (q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6961, 6505])).
% 1.21/1.24 tff(6963,plain,
% 1.21/1.24 (~pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5673, 6602])).
% 1.21/1.24 tff(6964,plain,
% 1.21/1.24 (~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5666, 6625])).
% 1.21/1.24 tff(6965,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[1101, 1098, 909, 5675])).
% 1.21/1.24 tff(6966,plain,((~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.24 tff(6967,plain,
% 1.21/1.24 (~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6966, 6625])).
% 1.21/1.24 tff(6968,assumption,(pqr1(s(s(s(s(s(s(s(s(s(a))))))))))), introduced(assumption)).
% 1.21/1.24 tff(6969,plain,
% 1.21/1.24 (((~![X: $i] : (aq(X) | (~pqr1(X)))) | (aq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~![X: $i] : (aq(X) | (~pqr1(X)))) | aq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(6970,plain,
% 1.21/1.24 ((~![X: $i] : (aq(X) | (~pqr1(X)))) | (aq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(6971,plain,
% 1.21/1.24 ((~![X: $i] : (aq(X) | (~pqr1(X)))) | aq(s(s(s(s(s(s(s(s(s(a)))))))))) | (~pqr1(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[6970, 6969])).
% 1.21/1.24 tff(6972,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6971, 1491, 960, 6968])).
% 1.21/1.24 tff(6973,plain,(~pqr1(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.24 tff(6974,plain,
% 1.21/1.24 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(6975,plain,
% 1.21/1.24 (((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))) <=> (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(6976,plain,
% 1.21/1.24 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(monotonicity,[status(thm)],[6975])).
% 1.21/1.24 tff(6977,plain,
% 1.21/1.24 (((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))) <=> ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(transitivity,[status(thm)],[6976, 6974])).
% 1.21/1.24 tff(6978,plain,
% 1.21/1.24 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(s(s(s(a))))))))) | p(s(s(s(s(s(s(s(a)))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(6979,plain,
% 1.21/1.24 ((~![X: $i] : ((~aq(X)) | p(X) | q(X) | qq(X) | rr(X) | (~r(X)) | (~pp(X)) | pr(s(X)))) | p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | (~aq(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[6978, 6977])).
% 1.21/1.24 tff(6980,plain,
% 1.21/1.24 (p(s(s(s(s(s(s(s(a)))))))) | (~pp(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(a)))))))) | qq(s(s(s(s(s(s(s(a)))))))) | rr(s(s(s(s(s(s(s(a)))))))) | (~r(s(s(s(s(s(s(s(a))))))))) | pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6979, 1543, 673])).
% 1.21/1.24 tff(6981,plain,
% 1.21/1.24 (pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6980, 6571, 6577, 6573, 6574, 6575, 6578])).
% 1.21/1.24 tff(6982,plain,
% 1.21/1.24 (pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[1532, 6981])).
% 1.21/1.24 tff(6983,plain,
% 1.21/1.24 (pr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(a))))))))))) | pqr1(s(s(s(s(s(s(s(s(s(a))))))))))),
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% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[7009, 3782, 149])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[5607, 7011])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[5612, 7012])).
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% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[7016, 4530, 6569])).
% 1.21/1.24 tff(7018,plain,
% 1.21/1.24 (rq(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5621, 7017, 7013, 5270, 7003, 4733])).
% 1.21/1.24 tff(7019,plain,
% 1.21/1.24 (rq(s(s(s(s(s(s(s(s(a)))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[4411, 7018])).
% 1.21/1.24 tff(7020,plain,
% 1.21/1.24 (rq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[4416, 7019])).
% 1.21/1.24 tff(7021,plain,
% 1.21/1.24 (rq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[4450, 7020, 6999, 6998, 6997, 6995])).
% 1.21/1.24 tff(7022,plain,
% 1.21/1.24 (rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[6214, 7021])).
% 1.21/1.24 tff(7023,assumption,(r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.24 tff(7024,plain,
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% 1.21/1.24 tff(7025,plain,
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% 1.21/1.24 tff(7026,plain,
% 1.21/1.24 (![X: $i] : ((~r(X)) | (~rpq4(X))) <=> ![X: $i] : ((~r(X)) | (~rpq4(X)))),
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% 1.21/1.24 inference(quant_intro,[status(thm)],[7027])).
% 1.21/1.24 tff(7029,axiom,(![X: $i] : ((~rpq4(X)) | (~r(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c083')).
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7029, 7028])).
% 1.21/1.24 tff(7031,plain,
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7030, 7026])).
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7032, 7025])).
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7035, 7034])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[7036, 7033, 7023])).
% 1.21/1.24 tff(7038,assumption,(qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7040, 7039])).
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% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7044, 7043])).
% 1.21/1.24 tff(7046,plain,
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[7045, 522, 7038])).
% 1.21/1.24 tff(7047,plain,
% 1.21/1.24 (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[1063, 1060, 6988])).
% 1.21/1.24 tff(7048,plain,
% 1.21/1.24 (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[1074, 1071, 6988])).
% 1.21/1.24 tff(7049,plain,
% 1.21/1.24 (pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[1188, 1169, 5762, 7048, 7047, 7046, 7042])).
% 1.21/1.24 tff(7050,plain,
% 1.21/1.24 (~rq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5846, 1472, 5840, 7049])).
% 1.21/1.24 tff(7051,plain,
% 1.21/1.24 (^[X: $i] : refl(((~qq(X)) | (~rpq1(X))) <=> ((~qq(X)) | (~rpq1(X))))),
% 1.21/1.24 inference(bind,[status(th)],[])).
% 1.21/1.24 tff(7052,plain,
% 1.21/1.24 (![X: $i] : ((~qq(X)) | (~rpq1(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(quant_intro,[status(thm)],[7051])).
% 1.21/1.24 tff(7053,plain,
% 1.21/1.24 (![X: $i] : ((~qq(X)) | (~rpq1(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7054,plain,
% 1.21/1.24 (^[X: $i] : rewrite(((~rpq1(X)) | (~qq(X))) <=> ((~qq(X)) | (~rpq1(X))))),
% 1.21/1.24 inference(bind,[status(th)],[])).
% 1.21/1.24 tff(7055,plain,
% 1.21/1.24 (![X: $i] : ((~rpq1(X)) | (~qq(X))) <=> ![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(quant_intro,[status(thm)],[7054])).
% 1.21/1.24 tff(7056,axiom,(![X: $i] : ((~rpq1(X)) | (~qq(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c067')).
% 1.21/1.24 tff(7057,plain,
% 1.21/1.24 (![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7056, 7055])).
% 1.21/1.24 tff(7058,plain,
% 1.21/1.24 (![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7057, 7053])).
% 1.21/1.24 tff(7059,plain,(
% 1.21/1.24 ![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(skolemize,[status(sab)],[7058])).
% 1.21/1.24 tff(7060,plain,
% 1.21/1.24 (![X: $i] : ((~qq(X)) | (~rpq1(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7059, 7052])).
% 1.21/1.24 tff(7061,plain,
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% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7062,plain,
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% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(7063,plain,
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% 1.21/1.24 inference(modus_ponens,[status(thm)],[7062, 7061])).
% 1.21/1.24 tff(7064,plain,
% 1.21/1.24 (~rpq1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7063, 7060, 7038])).
% 1.21/1.24 tff(7065,plain,
% 1.21/1.24 (^[X: $i] : refl(((~q(X)) | (~rpq2(X))) <=> ((~q(X)) | (~rpq2(X))))),
% 1.21/1.24 inference(bind,[status(th)],[])).
% 1.21/1.24 tff(7066,plain,
% 1.21/1.24 (![X: $i] : ((~q(X)) | (~rpq2(X))) <=> ![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(quant_intro,[status(thm)],[7065])).
% 1.21/1.24 tff(7067,plain,
% 1.21/1.24 (![X: $i] : ((~q(X)) | (~rpq2(X))) <=> ![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7068,plain,
% 1.21/1.24 (^[X: $i] : rewrite(((~rpq2(X)) | (~q(X))) <=> ((~q(X)) | (~rpq2(X))))),
% 1.21/1.24 inference(bind,[status(th)],[])).
% 1.21/1.24 tff(7069,plain,
% 1.21/1.24 (![X: $i] : ((~rpq2(X)) | (~q(X))) <=> ![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(quant_intro,[status(thm)],[7068])).
% 1.21/1.24 tff(7070,axiom,(![X: $i] : ((~rpq2(X)) | (~q(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c073')).
% 1.21/1.24 tff(7071,plain,
% 1.21/1.24 (![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7070, 7069])).
% 1.21/1.24 tff(7072,plain,
% 1.21/1.24 (![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7071, 7067])).
% 1.21/1.24 tff(7073,plain,(
% 1.21/1.24 ![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(skolemize,[status(sab)],[7072])).
% 1.21/1.24 tff(7074,plain,
% 1.21/1.24 (![X: $i] : ((~q(X)) | (~rpq2(X)))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7073, 7066])).
% 1.21/1.24 tff(7075,plain,
% 1.21/1.24 (((~![X: $i] : ((~q(X)) | (~rpq2(X)))) | ((~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~q(X)) | (~rpq2(X)))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7076,plain,
% 1.21/1.24 ((~![X: $i] : ((~q(X)) | (~rpq2(X)))) | ((~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(7077,plain,
% 1.21/1.24 ((~![X: $i] : ((~q(X)) | (~rpq2(X)))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7076, 7075])).
% 1.21/1.24 tff(7078,plain,
% 1.21/1.24 (~rpq2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7077, 7074, 6988])).
% 1.21/1.24 tff(7079,assumption,(~rpq3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.24 tff(7080,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5805, 4406, 5802, 7079, 7078, 7064, 7050, 7037])).
% 1.21/1.24 tff(7081,plain,(rpq3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.24 tff(7082,plain,
% 1.21/1.24 (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7081, 7022, 6962, 6994, 6631, 6616, 6986])).
% 1.21/1.24 tff(7083,plain,
% 1.21/1.24 (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[912, 281, 909, 5650])).
% 1.21/1.24 tff(7084,plain,
% 1.21/1.24 (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[917, 39, 914, 5650])).
% 1.21/1.24 tff(7085,assumption,(~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.24 tff(7086,plain,
% 1.21/1.24 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | ((~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7087,plain,
% 1.21/1.24 ((pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(rewrite,[status(thm)],[])).
% 1.21/1.24 tff(7088,plain,
% 1.21/1.24 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | ((~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.24 inference(monotonicity,[status(thm)],[7087])).
% 1.21/1.24 tff(7089,plain,
% 1.21/1.24 (((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(transitivity,[status(thm)],[7088, 7086])).
% 1.21/1.24 tff(7090,plain,
% 1.21/1.24 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.24 inference(quant_inst,[status(thm)],[])).
% 1.21/1.24 tff(7091,plain,
% 1.21/1.24 ((~![X: $i] : (pp(X) | (~ar(X)) | p(X) | (~q(X)) | (~qq(X)) | rr(X) | (~r(X)) | qp(s(X)))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.24 inference(modus_ponens,[status(thm)],[7090, 7089])).
% 1.21/1.24 tff(7092,plain,
% 1.21/1.24 (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7091, 845, 863, 7085, 7023, 5815, 6988, 7038])).
% 1.21/1.24 tff(7093,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7092, 7084, 7083])).
% 1.21/1.24 tff(7094,plain,((~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.24 tff(7095,plain,
% 1.21/1.24 (rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[7094, 7082, 6962, 6631, 6625, 6505, 6616])).
% 1.21/1.24 tff(7096,plain,
% 1.21/1.24 ($false),
% 1.21/1.24 inference(unit_resolution,[status(thm)],[5760, 430, 933, 7095, 6595])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[591, 7126])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[776, 7141])).
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% 1.21/1.24 inference(unit_resolution,[status(thm)],[3409, 7146])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[490, 7139])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[503, 7148])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6599, 7157])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6630, 7158])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6941, 7134, 7116, 7126, 7104, 7118])).
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% 1.21/1.25 tff(7163,plain,(p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[7163, 7160])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[641, 7167])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6876, 7166, 7138, 7137, 7136, 7135, 7165])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[3570, 7170, 7167])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[3691, 7171])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[2238, 7165])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[720, 7174])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[490, 7166])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[503, 7176])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[2307, 7173])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[2261, 7170])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6912, 7179, 7178, 7171, 7177, 7168])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[3409, 7179])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[6901, 7179, 7178, 7171, 7177, 7168])).
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% 1.21/1.25 tff(7184,plain,(qq(s(s(s(s(a))))) | rr(s(s(s(s(s(s(s(s(s(a))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7185,plain,
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[7184, 7133])).
% 1.21/1.25 tff(7186,plain,
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[729, 7156])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[3748, 7153])).
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% 1.21/1.25 inference(unit_resolution,[status(thm)],[3753, 7145])).
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% 1.21/1.25 (qq(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[703, 7152])).
% 1.21/1.25 tff(7190,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7191,plain,
% 1.21/1.25 ((pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))) <=> ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7192,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[7191])).
% 1.21/1.25 tff(7193,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(transitivity,[status(thm)],[7192, 7190])).
% 1.21/1.25 tff(7194,plain,
% 1.21/1.25 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7195,plain,
% 1.21/1.25 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | (~qq(X)) | (~rr(X)) | (~r(X)) | (~pp(s(X))))) | (~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~ap(s(s(s(s(s(s(s(s(s(a))))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7194, 7193])).
% 1.21/1.25 tff(7196,plain,
% 1.21/1.25 ((~r(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a))))))))))) | pp(s(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(s(a))))))))))) | q(s(s(s(s(s(s(s(s(s(a)))))))))) | (~qq(s(s(s(s(s(s(s(s(s(a))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7195, 2026, 817])).
% 1.21/1.25 tff(7197,plain,
% 1.21/1.25 (~pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7196, 7189, 7188, 7157, 7187, 7186, 7185])).
% 1.21/1.25 tff(7198,assumption,(pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7199,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[912, 281, 909, 5650, 7198])).
% 1.21/1.25 tff(7200,plain,((~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7201,plain,
% 1.21/1.25 (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7200, 7197])).
% 1.21/1.25 tff(7202,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[951, 948, 938, 922, 6606])).
% 1.21/1.25 tff(7203,plain,(rr(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7204,plain,
% 1.21/1.25 (rr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7203, 7185])).
% 1.21/1.25 tff(7205,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[955, 948, 933, 5815, 6592])).
% 1.21/1.25 tff(7206,plain,(rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7207,plain,
% 1.21/1.25 (rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7206, 7204])).
% 1.21/1.25 tff(7208,assumption,(~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7209,assumption,(p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7210,assumption,(~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7211,assumption,(rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7212,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7213,plain,
% 1.21/1.25 ((pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7214,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[7213])).
% 1.21/1.25 tff(7215,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(transitivity,[status(thm)],[7214, 7212])).
% 1.21/1.25 tff(7216,plain,
% 1.21/1.25 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7217,plain,
% 1.21/1.25 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | rr(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7216, 7215])).
% 1.21/1.25 tff(7218,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7217, 1854, 863, 7023, 7211, 5830, 7210, 7209, 7208])).
% 1.21/1.25 tff(7219,plain,(rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7220,plain,
% 1.21/1.25 (rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7219, 5830, 7207, 7201, 7164, 7159])).
% 1.21/1.25 tff(7221,assumption,(pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7222,assumption,(rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7223,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[1044, 1041, 7222, 7221])).
% 1.21/1.25 tff(7224,plain,((~pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7225,plain,
% 1.21/1.25 (~pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7224, 7220])).
% 1.21/1.25 tff(7226,assumption,(~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7227,plain,
% 1.21/1.25 (^[X: $i] : refl(((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X))))),
% 1.21/1.25 inference(bind,[status(th)],[])).
% 1.21/1.25 tff(7228,plain,
% 1.21/1.25 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(quant_intro,[status(thm)],[7227])).
% 1.21/1.25 tff(7229,plain,
% 1.21/1.25 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7230,plain,
% 1.21/1.25 (^[X: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~ar(X)) | q(X)) <=> ((~ar(X)) | q(X))), ((((~ar(X)) | q(X)) | (~r(X))) <=> (((~ar(X)) | q(X)) | (~r(X))))), rewrite((((~ar(X)) | q(X)) | (~r(X))) <=> ((~ar(X)) | q(X) | (~r(X)))), ((((~ar(X)) | q(X)) | (~r(X))) <=> ((~ar(X)) | q(X) | (~r(X))))), (((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) <=> (((~ar(X)) | q(X) | (~r(X))) | (~rr(X))))), rewrite((((~ar(X)) | q(X) | (~r(X))) | (~rr(X))) <=> ((~ar(X)) | q(X) | (~rr(X)) | (~r(X)))), (((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) <=> ((~ar(X)) | q(X) | (~rr(X)) | (~r(X))))), ((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> (((~ar(X)) | q(X) | (~rr(X)) | (~r(X))) | (~p(X))))), rewrite((((~ar(X)) | q(X) | (~rr(X)) | (~r(X))) | (~p(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)))), ((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))))), (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) <=> (((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))) | (~pp(X))))), rewrite((((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X))) | (~pp(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)))), (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))))), ((((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | r(s(X))) <=> (((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))) | r(s(X))))), rewrite((((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X))) | r(s(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))), ((((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | r(s(X))) <=> ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))))),
% 1.21/1.25 inference(bind,[status(th)],[])).
% 1.21/1.25 tff(7231,plain,
% 1.21/1.25 (![X: $i] : (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | r(s(X))) <=> ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(quant_intro,[status(thm)],[7230])).
% 1.21/1.25 tff(7232,axiom,(![X: $i] : (((((((~ar(X)) | q(X)) | (~r(X))) | (~rr(X))) | (~p(X))) | (~pp(X))) | r(s(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c175')).
% 1.21/1.25 tff(7233,plain,
% 1.21/1.25 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7232, 7231])).
% 1.21/1.25 tff(7234,plain,
% 1.21/1.25 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7233, 7229])).
% 1.21/1.25 tff(7235,plain,(
% 1.21/1.25 ![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(skolemize,[status(sab)],[7234])).
% 1.21/1.25 tff(7236,plain,
% 1.21/1.25 (![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7235, 7228])).
% 1.21/1.25 tff(7237,plain,
% 1.21/1.25 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7238,plain,
% 1.21/1.25 (((~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7239,plain,
% 1.21/1.25 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[7238])).
% 1.21/1.25 tff(7240,plain,
% 1.21/1.25 (((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(transitivity,[status(thm)],[7239, 7237])).
% 1.21/1.25 tff(7241,plain,
% 1.21/1.25 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | ((~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7242,plain,
% 1.21/1.25 ((~![X: $i] : ((~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | (~pp(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7241, 7240])).
% 1.21/1.25 tff(7243,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7242, 7236, 863, 7023, 7211, 5830, 7226, 7209, 7198])).
% 1.21/1.25 tff(7244,plain,((~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7245,plain,
% 1.21/1.25 (~pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7244, 7226, 7211, 5830, 7023, 7209])).
% 1.21/1.25 tff(7246,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7247,plain,
% 1.21/1.25 ((pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7248,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.25 inference(monotonicity,[status(thm)],[7247])).
% 1.21/1.25 tff(7249,plain,
% 1.21/1.25 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(transitivity,[status(thm)],[7248, 7246])).
% 1.21/1.25 tff(7250,plain,
% 1.21/1.25 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | q(X) | (~rr(X)) | (~r(X)) | r(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~ar(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7251,plain,
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% 1.21/1.25 inference(modus_ponens,[status(thm)],[7250, 7249])).
% 1.21/1.25 tff(7252,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7251, 3764, 863, 7023, 7211, 5830, 7226, 7209, 7245])).
% 1.21/1.25 tff(7253,plain,(r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7254,plain,
% 1.21/1.25 (r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7253, 5830, 7164, 7207, 7159])).
% 1.21/1.25 tff(7255,assumption,(pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7256,assumption,(r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7257,plain,
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% 1.21/1.25 tff(7258,plain,
% 1.21/1.25 ((~![X: $i] : ((~pqr3(X)) | (~r(X)))) | ((~pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7259,plain,
% 1.21/1.25 ((~![X: $i] : ((~pqr3(X)) | (~r(X)))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7258, 7257])).
% 1.21/1.25 tff(7260,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7259, 1795, 7256, 7255])).
% 1.21/1.25 tff(7261,plain,((~pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7262,plain,
% 1.21/1.25 (~pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7261, 7254])).
% 1.21/1.25 tff(7263,assumption,(pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.25 tff(7264,plain,
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% 1.21/1.25 inference(rewrite,[status(thm)],[])).
% 1.21/1.25 tff(7265,plain,
% 1.21/1.25 ((~![X: $i] : ((~pqr3(X)) | (~r(X)))) | ((~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.25 inference(quant_inst,[status(thm)],[])).
% 1.21/1.25 tff(7266,plain,
% 1.21/1.25 ((~![X: $i] : ((~pqr3(X)) | (~r(X)))) | (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.25 inference(modus_ponens,[status(thm)],[7265, 7264])).
% 1.21/1.25 tff(7267,plain,
% 1.21/1.25 ($false),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7266, 1795, 7023, 7263])).
% 1.21/1.25 tff(7268,plain,((~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.25 tff(7269,plain,
% 1.21/1.25 (~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[7268, 7159])).
% 1.21/1.25 tff(7270,plain,
% 1.21/1.25 (qq(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[5638, 7189])).
% 1.21/1.25 tff(7271,plain,
% 1.21/1.25 (~pqr3(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[5673, 7270])).
% 1.21/1.25 tff(7272,plain,
% 1.21/1.25 (~pqr2(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[5666, 7197])).
% 1.21/1.25 tff(7273,plain,
% 1.21/1.25 (~pqr1(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[5690, 7160])).
% 1.21/1.25 tff(7274,plain,
% 1.21/1.25 (~pqr4(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.25 inference(unit_resolution,[status(thm)],[1087, 7270])).
% 1.21/1.26 tff(7275,plain,
% 1.21/1.26 (~pqr1(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[514, 511, 7149])).
% 1.21/1.26 tff(7276,plain,
% 1.21/1.26 (~pqr2(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1615, 1612, 7149])).
% 1.21/1.26 tff(7277,plain,
% 1.21/1.26 (~pqr3(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1604, 1601, 7149])).
% 1.21/1.26 tff(7278,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a)))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7279,plain,
% 1.21/1.26 (((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | pr(s(s(s(s(s(a))))))) <=> ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a)))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7280,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(monotonicity,[status(thm)],[7279])).
% 1.21/1.26 tff(7281,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a)))))))),
% 1.21/1.26 inference(transitivity,[status(thm)],[7280, 7278])).
% 1.21/1.26 tff(7282,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | ((~aq(s(s(s(s(a)))))) | (~p(s(s(s(s(a)))))) | r(s(s(s(s(a))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | (~pp(s(s(s(s(a)))))) | pr(s(s(s(s(s(a)))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7283,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | r(X) | (~q(X)) | qq(X) | rr(X) | (~pp(X)) | pr(s(X)))) | (~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~aq(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7282, 7281])).
% 1.21/1.26 tff(7284,plain,
% 1.21/1.26 ((~p(s(s(s(s(a)))))) | (~pp(s(s(s(s(a)))))) | (~q(s(s(s(s(a)))))) | qq(s(s(s(s(a))))) | rr(s(s(s(s(a))))) | r(s(s(s(s(a))))) | pr(s(s(s(s(s(a))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7283, 3985, 450])).
% 1.21/1.26 tff(7285,plain,
% 1.21/1.26 (pr(s(s(s(s(s(a))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7284, 7133, 7104, 7116, 7126, 7118, 7127])).
% 1.21/1.26 tff(7286,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(a)))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1572, 7285])).
% 1.21/1.26 tff(7287,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1593, 7286])).
% 1.21/1.26 tff(7288,plain,
% 1.21/1.26 (~pqr4(s(s(s(s(s(s(s(a))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[525, 522, 7149])).
% 1.21/1.26 tff(7289,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(s(a)))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1620, 7288, 7287, 7277, 7276, 7275])).
% 1.21/1.26 tff(7290,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1532, 7289])).
% 1.21/1.26 tff(7291,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[6983, 7290, 6973])).
% 1.21/1.26 tff(7292,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1184, 7291, 7274, 7273, 7272, 7271])).
% 1.21/1.26 tff(7293,plain,
% 1.21/1.26 (((~![X: $i] : ((~pqr1(X)) | (~rr(X)))) | ((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~pqr1(X)) | (~rr(X)))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7294,plain,
% 1.21/1.26 ((~![X: $i] : ((~pqr1(X)) | (~rr(X)))) | ((~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7295,plain,
% 1.21/1.26 ((~![X: $i] : ((~pqr1(X)) | (~rr(X)))) | (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7294, 7293])).
% 1.21/1.26 tff(7296,plain,
% 1.21/1.26 (~pqr1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7295, 1041, 7211])).
% 1.21/1.26 tff(7297,plain,
% 1.21/1.26 (^[X: $i] : refl(((~p(X)) | (~pqr4(X))) <=> ((~p(X)) | (~pqr4(X))))),
% 1.21/1.26 inference(bind,[status(th)],[])).
% 1.21/1.26 tff(7298,plain,
% 1.21/1.26 (![X: $i] : ((~p(X)) | (~pqr4(X))) <=> ![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(quant_intro,[status(thm)],[7297])).
% 1.21/1.26 tff(7299,plain,
% 1.21/1.26 (![X: $i] : ((~p(X)) | (~pqr4(X))) <=> ![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7300,plain,
% 1.21/1.26 (^[X: $i] : rewrite(((~pqr4(X)) | (~p(X))) <=> ((~p(X)) | (~pqr4(X))))),
% 1.21/1.26 inference(bind,[status(th)],[])).
% 1.21/1.26 tff(7301,plain,
% 1.21/1.26 (![X: $i] : ((~pqr4(X)) | (~p(X))) <=> ![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(quant_intro,[status(thm)],[7300])).
% 1.21/1.26 tff(7302,axiom,(![X: $i] : ((~pqr4(X)) | (~p(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c027')).
% 1.21/1.26 tff(7303,plain,
% 1.21/1.26 (![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7302, 7301])).
% 1.21/1.26 tff(7304,plain,
% 1.21/1.26 (![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7303, 7299])).
% 1.21/1.26 tff(7305,plain,(
% 1.21/1.26 ![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(skolemize,[status(sab)],[7304])).
% 1.21/1.26 tff(7306,plain,
% 1.21/1.26 (![X: $i] : ((~p(X)) | (~pqr4(X)))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7305, 7298])).
% 1.21/1.26 tff(7307,plain,
% 1.21/1.26 (((~![X: $i] : ((~p(X)) | (~pqr4(X)))) | ((~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~p(X)) | (~pqr4(X)))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7308,plain,
% 1.21/1.26 ((~![X: $i] : ((~p(X)) | (~pqr4(X)))) | ((~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7309,plain,
% 1.21/1.26 ((~![X: $i] : ((~p(X)) | (~pqr4(X)))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7308, 7307])).
% 1.21/1.26 tff(7310,plain,
% 1.21/1.26 (~pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7309, 7306, 7209])).
% 1.21/1.26 tff(7311,assumption,(~pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7312,assumption,(~pqr3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7313,assumption,(pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7314,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1052, 1030, 7211, 7313])).
% 1.21/1.26 tff(7315,plain,((~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7316,plain,
% 1.21/1.26 (~pqr2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7315, 7211])).
% 1.21/1.26 tff(7317,plain,
% 1.21/1.26 (pqr1(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | pqr4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1188, 1169, 5762, 7316, 7312, 7311])).
% 1.21/1.26 tff(7318,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7317, 7310, 7296])).
% 1.21/1.26 tff(7319,plain,(pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7320,plain,
% 1.21/1.26 (pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7319, 7292, 7207, 7164, 7269])).
% 1.21/1.26 tff(7321,assumption,(~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7322,plain,
% 1.21/1.26 (((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7323,plain,
% 1.21/1.26 ((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | (ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7324,plain,
% 1.21/1.26 ((~![X: $i] : (ap(X) | (~p(X)) | p(s(X)))) | ap(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7323, 7322])).
% 1.21/1.26 tff(7325,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7324, 1671, 7321, 7209, 5785])).
% 1.21/1.26 tff(7326,plain,((~p(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7327,plain,
% 1.21/1.26 (p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7326, 7164])).
% 1.21/1.26 tff(7328,assumption,(aq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7329,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1431, 90, 863, 7328])).
% 1.21/1.26 tff(7330,plain,(~aq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7331,plain,
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% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7332,plain,
% 1.21/1.26 (((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7333,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(monotonicity,[status(thm)],[7332])).
% 1.21/1.26 tff(7334,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(transitivity,[status(thm)],[7333, 7331])).
% 1.21/1.26 tff(7335,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7336,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~qq(s(X))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7335, 7334])).
% 1.21/1.26 tff(7337,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7336, 2084, 7160, 858, 6163, 7158, 7038])).
% 1.21/1.26 tff(7338,plain,(q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7339,plain,
% 1.21/1.26 (q(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7338, 7038])).
% 1.21/1.26 tff(7340,plain,
% 1.21/1.26 (((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7341,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7342,plain,
% 1.21/1.26 ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~qq(s(X))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7341, 7340])).
% 1.21/1.26 tff(7343,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7342, 2102, 7160, 858, 7339, 7158, 7038])).
% 1.21/1.26 tff(7344,plain,(~qq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7345,assumption,(~aq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7346,assumption,(qq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7347,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1435, 190, 6605, 7346, 7345])).
% 1.21/1.26 tff(7348,plain,(aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7349,plain,
% 1.21/1.26 (~qq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7348, 7344, 7330])).
% 1.21/1.26 tff(7350,assumption,(qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7351,plain,
% 1.21/1.26 (((~![X: $i] : ((~qrp4(X)) | (~rr(X)))) | ((~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~qrp4(X)) | (~rr(X)))) | (~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7352,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp4(X)) | (~rr(X)))) | ((~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7353,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp4(X)) | (~rr(X)))) | (~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7352, 7351])).
% 1.21/1.26 tff(7354,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7353, 1233, 7211, 7350])).
% 1.21/1.26 tff(7355,plain,((~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7356,plain,
% 1.21/1.26 (~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7355, 7207])).
% 1.21/1.26 tff(7357,plain,
% 1.21/1.26 (~qrp4(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3725, 1233, 7185])).
% 1.21/1.26 tff(7358,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7359,plain,
% 1.21/1.26 ((pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))) <=> (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7360,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(monotonicity,[status(thm)],[7359])).
% 1.21/1.26 tff(7361,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))) <=> ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(transitivity,[status(thm)],[7360, 7358])).
% 1.21/1.26 tff(7362,plain,
% 1.21/1.26 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | (pp(s(s(s(s(s(s(s(s(a))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7363,plain,
% 1.21/1.26 ((~![X: $i] : (pp(X) | (~ar(X)) | (~p(X)) | r(X) | q(X) | (~qq(X)) | rr(X) | qp(s(X)))) | q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~ar(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7362, 7361])).
% 1.21/1.26 tff(7364,plain,
% 1.21/1.26 (q(s(s(s(s(s(s(s(s(a))))))))) | (~qq(s(s(s(s(s(s(s(s(a)))))))))) | (~p(s(s(s(s(s(s(s(s(a)))))))))) | rr(s(s(s(s(s(s(s(s(a))))))))) | r(s(s(s(s(s(s(s(s(a))))))))) | pp(s(s(s(s(s(s(s(s(a))))))))) | qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7363, 3822, 695])).
% 1.21/1.26 tff(7365,plain,
% 1.21/1.26 (qp(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7364, 7153, 7147, 7152, 7156, 7145, 7142])).
% 1.21/1.26 tff(7366,plain,
% 1.21/1.26 (~qrp2(s(s(s(s(s(s(s(s(s(a))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[3721, 1211, 7185])).
% 1.21/1.26 tff(7367,plain,
% 1.21/1.26 (qp(s(s(s(s(s(s(s(s(s(s(a)))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[6228, 7366, 7365, 7357])).
% 1.21/1.26 tff(7368,plain,
% 1.21/1.26 (qp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[6223, 7367])).
% 1.21/1.26 tff(7369,plain,
% 1.21/1.26 (((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7370,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | ((~qrp1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7371,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp1(X)) | (~rr(X)))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7370, 7369])).
% 1.21/1.26 tff(7372,plain,
% 1.21/1.26 (~qrp1(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7371, 1200, 7211])).
% 1.21/1.26 tff(7373,plain,
% 1.21/1.26 (((~![X: $i] : ((~qrp2(X)) | (~rr(X)))) | ((~qrp2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~qrp2(X)) | (~rr(X)))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7374,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp2(X)) | (~rr(X)))) | ((~qrp2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7375,plain,
% 1.21/1.26 ((~![X: $i] : ((~qrp2(X)) | (~rr(X)))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7374, 7373])).
% 1.21/1.26 tff(7376,plain,
% 1.21/1.26 (~qrp2(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7375, 1211, 7211])).
% 1.21/1.26 tff(7377,plain,
% 1.21/1.26 (~qrp3(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1240, 1222, 7211])).
% 1.21/1.26 tff(7378,assumption,(~qrp4(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7379,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1415, 1404, 7085, 6216, 7378, 7377, 7376, 7372])).
% 1.21/1.26 tff(7380,plain,(qrp4(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7381,plain,
% 1.21/1.26 (qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7380, 7368, 7207, 7356])).
% 1.21/1.26 tff(7382,assumption,(pp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7383,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1427, 281, 7382, 7208, 5785])).
% 1.21/1.26 tff(7384,plain,((~pp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7385,plain,
% 1.21/1.26 (~pp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7384, 7201])).
% 1.21/1.26 tff(7386,plain,
% 1.21/1.26 (~aq(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1431, 90, 863])).
% 1.21/1.26 tff(7387,assumption,(q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7388,plain,
% 1.21/1.26 (((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7389,plain,
% 1.21/1.26 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | (aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7390,plain,
% 1.21/1.26 ((~![X: $i] : (aq(X) | q(X) | (~q(s(X))))) | aq(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7389, 7388])).
% 1.21/1.26 tff(7391,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7390, 206, 5830, 7387, 7386])).
% 1.21/1.26 tff(7392,plain,((~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7393,plain,
% 1.21/1.26 (~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7392, 5830])).
% 1.21/1.26 tff(7394,assumption,(~q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7395,assumption,(~pp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7396,assumption,(p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7397,assumption,(~qq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7398,assumption,(pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7399,assumption,(rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7400,plain,
% 1.21/1.26 (~qp(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1478, 1472, 7398, 7399])).
% 1.21/1.26 tff(7401,plain,
% 1.21/1.26 (~qrp3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1225, 1222, 7222])).
% 1.21/1.26 tff(7402,plain,
% 1.21/1.26 (~qrp4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1236, 1233, 7222])).
% 1.21/1.26 tff(7403,plain,
% 1.21/1.26 (((~![X: $i] : (qq(X) | (~qrp1(X)))) | (qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (qq(X) | (~qrp1(X)))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7404,plain,
% 1.21/1.26 ((~![X: $i] : (qq(X) | (~qrp1(X)))) | (qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7405,plain,
% 1.21/1.26 ((~![X: $i] : (qq(X) | (~qrp1(X)))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7404, 7403])).
% 1.21/1.26 tff(7406,plain,
% 1.21/1.26 (~qrp1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7405, 1283, 7397])).
% 1.21/1.26 tff(7407,plain,
% 1.21/1.26 (((~![X: $i] : (qq(X) | (~qrp2(X)))) | (qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (qq(X) | (~qrp2(X)))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7408,plain,
% 1.21/1.26 ((~![X: $i] : (qq(X) | (~qrp2(X)))) | (qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7409,plain,
% 1.21/1.26 ((~![X: $i] : (qq(X) | (~qrp2(X)))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~qrp2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7408, 7407])).
% 1.21/1.26 tff(7410,plain,
% 1.21/1.26 (~qrp2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7409, 1297, 7397])).
% 1.21/1.26 tff(7411,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1419, 1404, 5840, 7410, 7406, 7402, 7401, 7400])).
% 1.21/1.26 tff(7412,plain,((~rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7413,plain,
% 1.21/1.26 (~rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7412, 7397, 7398, 7222, 5840])).
% 1.21/1.26 tff(7414,assumption,(~rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7415,plain,
% 1.21/1.26 (ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[885, 145, 863])).
% 1.21/1.26 tff(7416,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | ((~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7417,plain,
% 1.21/1.26 ((pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(rewrite,[status(thm)],[])).
% 1.21/1.26 tff(7418,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | ((~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))))),
% 1.21/1.26 inference(monotonicity,[status(thm)],[7417])).
% 1.21/1.26 tff(7419,plain,
% 1.21/1.26 (((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(transitivity,[status(thm)],[7418, 7416])).
% 1.21/1.26 tff(7420,plain,
% 1.21/1.26 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.26 inference(quant_inst,[status(thm)],[])).
% 1.21/1.26 tff(7421,plain,
% 1.21/1.26 ((~![X: $i] : (pp(X) | (~ap(X)) | (~p(X)) | q(X) | qq(X) | (~rr(X)) | (~r(X)) | rq(s(X)))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~ap(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(modus_ponens,[status(thm)],[7420, 7419])).
% 1.21/1.26 tff(7422,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7421, 3782, 7222, 7256, 7415, 7395, 7396, 7397, 7394, 7414])).
% 1.21/1.26 tff(7423,plain,(rq(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7424,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7423, 7413, 7397, 7396, 7395, 7222, 7394, 7256])).
% 1.21/1.26 tff(7425,plain,(qq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | q(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) | (~qp(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7426,plain,
% 1.21/1.26 (~pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7425, 7393, 7385, 7381, 7349, 7254, 7220, 7327])).
% 1.21/1.26 tff(7427,assumption,(pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7428,plain,
% 1.21/1.26 ($false),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[1033, 1030, 7222, 7427])).
% 1.21/1.26 tff(7429,plain,((~pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | (~rr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.26 tff(7430,plain,
% 1.21/1.26 (~pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.26 inference(unit_resolution,[status(thm)],[7429, 7220])).
% 1.21/1.26 tff(7431,assumption,(pr(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7432,assumption,(~pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7433,assumption,(~pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7434,assumption,(~pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), introduced(assumption)).
% 1.21/1.26 tff(7435,assumption,(~pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.27 tff(7436,assumption,(pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), introduced(assumption)).
% 1.21/1.27 tff(7437,plain,
% 1.21/1.27 (~aq(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.27 inference(unit_resolution,[status(thm)],[889, 25, 7415])).
% 1.21/1.27 tff(7438,plain,
% 1.21/1.27 (((~![X: $i] : (aq(X) | (~pqr4(X)))) | (aq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))) <=> ((~![X: $i] : (aq(X) | (~pqr4(X)))) | aq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.27 inference(rewrite,[status(thm)],[])).
% 1.21/1.27 tff(7439,plain,
% 1.21/1.27 ((~![X: $i] : (aq(X) | (~pqr4(X)))) | (aq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.27 inference(quant_inst,[status(thm)],[])).
% 1.21/1.27 tff(7440,plain,
% 1.21/1.27 ((~![X: $i] : (aq(X) | (~pqr4(X)))) | aq(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(modus_ponens,[status(thm)],[7439, 7438])).
% 1.21/1.27 tff(7441,plain,
% 1.21/1.27 ($false),
% 1.21/1.27 inference(unit_resolution,[status(thm)],[7440, 1505, 7437, 7436])).
% 1.21/1.27 tff(7442,plain,(~pqr4(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.27 tff(7443,plain,
% 1.21/1.27 ($false),
% 1.21/1.27 inference(unit_resolution,[status(thm)],[1192, 1169, 7442, 7435, 7434, 7433, 7432, 7431])).
% 1.21/1.27 tff(7444,plain,(pr(s(s(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) | pqr1(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr2(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | pqr3(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))) | (~pr(s(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.27 tff(7445,plain,
% 1.21/1.27 ($false),
% 1.21/1.27 inference(unit_resolution,[status(thm)],[7444, 7430, 7426, 7320, 7262, 7225])).
% 1.21/1.27 tff(7446,plain,(q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.27 tff(7447,plain,
% 1.21/1.27 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(rewrite,[status(thm)],[])).
% 1.21/1.27 tff(7448,plain,
% 1.21/1.27 (((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))) <=> ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(rewrite,[status(thm)],[])).
% 1.21/1.27 tff(7449,plain,
% 1.21/1.27 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | ((~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))))),
% 1.21/1.27 inference(monotonicity,[status(thm)],[7448])).
% 1.21/1.27 tff(7450,plain,
% 1.21/1.27 (((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(transitivity,[status(thm)],[7449, 7447])).
% 1.21/1.27 tff(7451,plain,
% 1.21/1.27 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(quant_inst,[status(thm)],[])).
% 1.21/1.27 tff(7452,plain,
% 1.21/1.27 ((~![X: $i] : ((~aq(X)) | (~p(X)) | q(X) | (~r(X)) | (~q(s(X))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | q(s(s(s(s(s(s(s(s(s(s(a))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.27 inference(modus_ponens,[status(thm)],[7451, 7450])).
% 1.21/1.27 tff(7453,plain,
% 1.21/1.27 ($false),
% 1.21/1.27 inference(unit_resolution,[status(thm)],[7452, 2126, 7160, 858, 7446, 6163, 7158])).
% 1.21/1.27 tff(7454,plain,(q(s(s(s(s(s(s(s(s(s(s(a)))))))))))), inference(lemma,lemma(discharge,[]))).
% 1.21/1.27 tff(7455,plain,
% 1.21/1.27 (^[X: $i] : refl(((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X)))))),
% 1.21/1.27 inference(bind,[status(th)],[])).
% 1.21/1.27 tff(7456,plain,
% 1.21/1.27 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(quant_intro,[status(thm)],[7455])).
% 1.21/1.27 tff(7457,plain,
% 1.21/1.27 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(rewrite,[status(thm)],[])).
% 1.21/1.27 tff(7458,plain,
% 1.21/1.27 (^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~aq(X)) | (~p(X))) | (~q(X))) <=> ((~aq(X)) | (~p(X)) | (~q(X)))), (((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) <=> (((~aq(X)) | (~p(X)) | (~q(X))) | (~r(X))))), rewrite((((~aq(X)) | (~p(X)) | (~q(X))) | (~r(X))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)))), (((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X))))), ((((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) | (~q(s(X)))) <=> (((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X))) | (~q(s(X)))))), rewrite((((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X))) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))), ((((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) | (~q(s(X)))) <=> ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))))),
% 1.21/1.27 inference(bind,[status(th)],[])).
% 1.21/1.27 tff(7459,plain,
% 1.21/1.27 (![X: $i] : (((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) | (~q(s(X)))) <=> ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(quant_intro,[status(thm)],[7458])).
% 1.21/1.27 tff(7460,axiom,(![X: $i] : (((((~aq(X)) | (~p(X))) | (~q(X))) | (~r(X))) | (~q(s(X))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','c099')).
% 1.21/1.27 tff(7461,plain,
% 1.21/1.27 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(modus_ponens,[status(thm)],[7460, 7459])).
% 1.21/1.27 tff(7462,plain,
% 1.21/1.27 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(modus_ponens,[status(thm)],[7461, 7457])).
% 1.21/1.27 tff(7463,plain,(
% 1.21/1.27 ![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(skolemize,[status(sab)],[7462])).
% 1.21/1.27 tff(7464,plain,
% 1.21/1.27 (![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))),
% 1.21/1.27 inference(modus_ponens,[status(thm)],[7463, 7456])).
% 1.21/1.27 tff(7465,plain,
% 1.21/1.27 (((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))) <=> ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.27 inference(rewrite,[status(thm)],[])).
% 1.21/1.27 tff(7466,plain,
% 1.21/1.27 ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))) | ((~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a))))))))))))))),
% 1.21/1.28 inference(quant_inst,[status(thm)],[])).
% 1.21/1.28 tff(7467,plain,
% 1.21/1.28 ((~![X: $i] : ((~aq(X)) | (~p(X)) | (~q(X)) | (~r(X)) | (~q(s(X))))) | (~aq(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~p(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~r(s(s(s(s(s(s(s(s(s(s(a)))))))))))) | (~q(s(s(s(s(s(s(s(s(s(s(s(a)))))))))))))),
% 1.21/1.28 inference(modus_ponens,[status(thm)],[7466, 7465])).
% 1.21/1.28 tff(7468,plain,
% 1.21/1.28 ($false),
% 1.21/1.28 inference(unit_resolution,[status(thm)],[7467, 7464, 7160, 858, 7446, 7454, 7158])).
% 1.21/1.28 % SZS output end Proof
%------------------------------------------------------------------------------