TSTP Solution File: KRS010-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sat Sep 17 17:44:21 EDT 2022
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS010-1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 09:30:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(c_type, type, (
% 0.12/0.40 c: $i > $o)).
% 0.12/0.40 tff(u2r2_type, type, (
% 0.12/0.40 u2r2: $i > $i)).
% 0.12/0.40 tff(exist_type, type, (
% 0.12/0.40 exist: $i)).
% 0.12/0.40 tff(d_type, type, (
% 0.12/0.40 d: $i > $o)).
% 0.12/0.40 tff(u2r3_type, type, (
% 0.12/0.40 u2r3: $i > $i)).
% 0.12/0.40 tff(equalish_type, type, (
% 0.12/0.40 equalish: ( $i * $i ) > $o)).
% 0.12/0.40 tff(r3least_type, type, (
% 0.12/0.40 r3least: $i > $o)).
% 0.12/0.40 tff(e_type, type, (
% 0.12/0.40 e: $i > $o)).
% 0.12/0.40 tff(r_type, type, (
% 0.12/0.40 r: ( $i * $i ) > $o)).
% 0.12/0.40 tff(a_type, type, (
% 0.12/0.40 a: $i > $o)).
% 0.12/0.40 tff(u2r1_type, type, (
% 0.12/0.40 u2r1: $i > $i)).
% 0.12/0.40 tff(f_type, type, (
% 0.12/0.40 f: $i > $o)).
% 0.12/0.40 tff(1,assumption,(c(u2r3(exist))), introduced(assumption)).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 (^[X1: $i] : refl((r3least(X1) | (~e(X1))) <=> (r3least(X1) | (~e(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (![X1: $i] : (r3least(X1) | (~e(X1))) <=> ![X1: $i] : (r3least(X1) | (~e(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[2])).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (![X1: $i] : (r3least(X1) | (~e(X1))) <=> ![X1: $i] : (r3least(X1) | (~e(X1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(5,axiom,(![X1: $i] : (r3least(X1) | (~e(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_7')).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (![X1: $i] : (r3least(X1) | (~e(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.12/0.40 tff(7,plain,(
% 0.12/0.40 ![X1: $i] : (r3least(X1) | (~e(X1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[6])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (![X1: $i] : (r3least(X1) | (~e(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (e(exist) <=> e(exist)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(10,axiom,(e(exist)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_1')).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (e(exist)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (((~![X1: $i] : (r3least(X1) | (~e(X1)))) | (r3least(exist) | (~e(exist)))) <=> ((~![X1: $i] : (r3least(X1) | (~e(X1)))) | r3least(exist) | (~e(exist)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 ((~![X1: $i] : (r3least(X1) | (~e(X1)))) | (r3least(exist) | (~e(exist)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 ((~![X1: $i] : (r3least(X1) | (~e(X1)))) | r3least(exist) | (~e(exist))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (r3least(exist)),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[14, 11, 8])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (^[X1: $i] : refl(((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1)))) <=> ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1)))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1)))) <=> ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1)))) <=> ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(19,axiom,(![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_21')).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.12/0.40 tff(21,plain,(
% 0.12/0.40 ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))),
% 0.12/0.40 inference(skolemize,[status(sab)],[20])).
% 0.12/0.40 tff(22,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.12/0.40 tff(23,plain,
% 0.12/0.40 (((~![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))) | ((~r3least(exist)) | (~equalish(u2r3(exist), u2r2(exist))))) <=> ((~![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))) | (~r3least(exist)) | (~equalish(u2r3(exist), u2r2(exist))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(24,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))) | ((~r3least(exist)) | (~equalish(u2r3(exist), u2r2(exist))))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(25,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r2(X1))))) | (~r3least(exist)) | (~equalish(u2r3(exist), u2r2(exist)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.12/0.40 tff(26,plain,
% 0.12/0.40 (~equalish(u2r3(exist), u2r2(exist))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[25, 22, 15])).
% 0.12/0.40 tff(27,plain,
% 0.12/0.40 (^[X1: $i] : refl(((~r3least(X1)) | r(X1, u2r2(X1))) <=> ((~r3least(X1)) | r(X1, u2r2(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(28,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[27])).
% 0.12/0.40 tff(29,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(30,plain,
% 0.12/0.40 (^[X1: $i] : rewrite((r(X1, u2r2(X1)) | (~r3least(X1))) <=> ((~r3least(X1)) | r(X1, u2r2(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(31,plain,
% 0.12/0.40 (![X1: $i] : (r(X1, u2r2(X1)) | (~r3least(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[30])).
% 0.12/0.40 tff(32,axiom,(![X1: $i] : (r(X1, u2r2(X1)) | (~r3least(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_23')).
% 0.12/0.40 tff(33,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.12/0.40 tff(34,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.12/0.40 tff(35,plain,(
% 0.12/0.40 ![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[34])).
% 0.12/0.40 tff(36,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[35, 28])).
% 0.12/0.40 tff(37,plain,
% 0.12/0.40 (((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))) | ((~r3least(exist)) | r(exist, u2r2(exist)))) <=> ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))) | (~r3least(exist)) | r(exist, u2r2(exist)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(38,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))) | ((~r3least(exist)) | r(exist, u2r2(exist)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(39,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r2(X1)))) | (~r3least(exist)) | r(exist, u2r2(exist))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.12/0.40 tff(40,plain,
% 0.12/0.40 (r(exist, u2r2(exist))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[39, 36, 15])).
% 0.12/0.40 tff(41,plain,
% 0.12/0.40 (^[X1: $i] : refl(((~r3least(X1)) | r(X1, u2r3(X1))) <=> ((~r3least(X1)) | r(X1, u2r3(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(42,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[41])).
% 0.12/0.40 tff(43,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(44,plain,
% 0.12/0.40 (^[X1: $i] : rewrite((r(X1, u2r3(X1)) | (~r3least(X1))) <=> ((~r3least(X1)) | r(X1, u2r3(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(45,plain,
% 0.12/0.40 (![X1: $i] : (r(X1, u2r3(X1)) | (~r3least(X1))) <=> ![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.12/0.40 tff(46,axiom,(![X1: $i] : (r(X1, u2r3(X1)) | (~r3least(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_24')).
% 0.12/0.40 tff(47,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.12/0.40 tff(48,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.12/0.40 tff(49,plain,(
% 0.12/0.40 ![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[48])).
% 0.12/0.40 tff(50,plain,
% 0.12/0.40 (![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.12/0.40 tff(51,plain,
% 0.12/0.40 (((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))) | ((~r3least(exist)) | r(exist, u2r3(exist)))) <=> ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))) | (~r3least(exist)) | r(exist, u2r3(exist)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(52,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))) | ((~r3least(exist)) | r(exist, u2r3(exist)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(53,plain,
% 0.12/0.40 ((~![X1: $i] : ((~r3least(X1)) | r(X1, u2r3(X1)))) | (~r3least(exist)) | r(exist, u2r3(exist))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.40 tff(54,plain,
% 0.12/0.40 (r(exist, u2r3(exist))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[53, 50, 15])).
% 0.12/0.40 tff(55,plain,
% 0.12/0.40 (^[X4: $i, X3: $i, X1: $i] : refl(((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) <=> ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(56,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) <=> ![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.12/0.40 tff(57,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) <=> ![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(58,plain,
% 0.12/0.40 (^[X4: $i, X3: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((equalish(X4, X3) | (~e(X1))) <=> ((~e(X1)) | equalish(X4, X3))), (((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) <=> (((~e(X1)) | equalish(X4, X3)) | (~r(X1, X4))))), rewrite((((~e(X1)) | equalish(X4, X3)) | (~r(X1, X4))) <=> ((~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))), (((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) <=> ((~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)))), ((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) <=> (((~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~r(X1, X3))))), rewrite((((~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))), ((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)))), (((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) <=> (((~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~c(X4))))), rewrite((((~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~c(X4))) <=> ((~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))), (((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) <=> ((~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)))), ((((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) | (~c(X3))) <=> (((~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~c(X3))))), rewrite((((~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3)) | (~c(X3))) <=> ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))), ((((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) | (~c(X3))) <=> ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(59,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : (((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) | (~c(X3))) <=> ![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[58])).
% 0.12/0.40 tff(60,axiom,(![X4: $i, X3: $i, X1: $i] : (((((equalish(X4, X3) | (~e(X1))) | (~r(X1, X4))) | (~r(X1, X3))) | (~c(X4))) | (~c(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_6')).
% 0.12/0.40 tff(61,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.40 tff(62,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.12/0.40 tff(63,plain,(
% 0.12/0.40 ![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(skolemize,[status(sab)],[62])).
% 0.12/0.40 tff(64,plain,
% 0.12/0.40 (![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.12/0.40 tff(65,plain,
% 0.12/0.40 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist))))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(66,plain,
% 0.12/0.40 (((~c(u2r2(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist))) <=> ((~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(67,plain,
% 0.12/0.40 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r2(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist)))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[66])).
% 0.12/0.40 tff(68,plain,
% 0.12/0.40 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r2(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[67, 65])).
% 0.12/0.40 tff(69,plain,
% 0.12/0.40 ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r2(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(70,plain,
% 0.12/0.40 ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r2(exist))) | (~c(u2r3(exist))) | (~c(u2r2(exist)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.40 tff(71,plain,
% 0.12/0.40 ((~c(u2r3(exist))) | (~c(u2r2(exist)))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[70, 11, 64, 54, 40, 26])).
% 0.12/0.40 tff(72,plain,
% 0.12/0.40 (~c(u2r2(exist))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[71, 1])).
% 0.12/0.40 tff(73,plain,
% 0.12/0.40 (^[X2: $i, X1: $i] : refl((a(X2) | (~r(X1, X2)) | (~e(X1))) <=> (a(X2) | (~r(X1, X2)) | (~e(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(74,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1))) <=> ![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.40 tff(75,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1))) <=> ![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(76,plain,
% 0.12/0.40 (^[X2: $i, X1: $i] : rewrite(((a(X2) | (~e(X1))) | (~r(X1, X2))) <=> (a(X2) | (~r(X1, X2)) | (~e(X1))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(77,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : ((a(X2) | (~e(X1))) | (~r(X1, X2))) <=> ![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[76])).
% 0.12/0.40 tff(78,axiom,(![X2: $i, X1: $i] : ((a(X2) | (~e(X1))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_8')).
% 0.12/0.40 tff(79,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.40 tff(80,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.12/0.40 tff(81,plain,(
% 0.12/0.40 ![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(skolemize,[status(sab)],[80])).
% 0.12/0.40 tff(82,plain,
% 0.12/0.40 (![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.12/0.40 tff(83,plain,
% 0.12/0.40 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | ((~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(84,plain,
% 0.12/0.40 ((a(u2r2(exist)) | (~r(exist, u2r2(exist))) | (~e(exist))) <=> ((~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(85,plain,
% 0.12/0.40 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r2(exist)) | (~r(exist, u2r2(exist))) | (~e(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | ((~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist))))),
% 0.12/0.40 inference(monotonicity,[status(thm)],[84])).
% 0.12/0.40 tff(86,plain,
% 0.12/0.40 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r2(exist)) | (~r(exist, u2r2(exist))) | (~e(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist)))),
% 0.12/0.40 inference(transitivity,[status(thm)],[85, 83])).
% 0.12/0.40 tff(87,plain,
% 0.12/0.40 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r2(exist)) | (~r(exist, u2r2(exist))) | (~e(exist)))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(88,plain,
% 0.12/0.40 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r2(exist))) | a(u2r2(exist))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.12/0.40 tff(89,plain,
% 0.12/0.40 (a(u2r2(exist))),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[88, 11, 82, 40])).
% 0.12/0.40 tff(90,plain,
% 0.12/0.40 (^[X1: $i] : refl(((~a(X1)) | d(X1) | c(X1)) <=> ((~a(X1)) | d(X1) | c(X1)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(91,plain,
% 0.12/0.40 (![X1: $i] : ((~a(X1)) | d(X1) | c(X1)) <=> ![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[90])).
% 0.12/0.40 tff(92,plain,
% 0.12/0.40 (![X1: $i] : ((~a(X1)) | d(X1) | c(X1)) <=> ![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(93,plain,
% 0.12/0.40 (^[X1: $i] : rewrite(((c(X1) | d(X1)) | (~a(X1))) <=> ((~a(X1)) | d(X1) | c(X1)))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(94,plain,
% 0.12/0.40 (![X1: $i] : ((c(X1) | d(X1)) | (~a(X1))) <=> ![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[93])).
% 0.12/0.40 tff(95,axiom,(![X1: $i] : ((c(X1) | d(X1)) | (~a(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_3')).
% 0.12/0.40 tff(96,plain,
% 0.12/0.40 (![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.12/0.40 tff(97,plain,
% 0.12/0.40 (![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.12/0.40 tff(98,plain,(
% 0.12/0.40 ![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(skolemize,[status(sab)],[97])).
% 0.12/0.40 tff(99,plain,
% 0.12/0.40 (![X1: $i] : ((~a(X1)) | d(X1) | c(X1))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.12/0.40 tff(100,plain,
% 0.12/0.40 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | (d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist))))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(101,plain,
% 0.12/0.40 (((~a(u2r2(exist))) | d(u2r2(exist)) | c(u2r2(exist))) <=> (d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(102,plain,
% 0.12/0.40 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r2(exist))) | d(u2r2(exist)) | c(u2r2(exist)))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | (d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist)))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[101])).
% 0.12/0.41 tff(103,plain,
% 0.12/0.41 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r2(exist))) | d(u2r2(exist)) | c(u2r2(exist)))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[102, 100])).
% 0.12/0.41 tff(104,plain,
% 0.12/0.41 ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r2(exist))) | d(u2r2(exist)) | c(u2r2(exist)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(105,plain,
% 0.12/0.41 ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r2(exist)) | c(u2r2(exist)) | (~a(u2r2(exist)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.12/0.41 tff(106,plain,
% 0.12/0.41 (d(u2r2(exist)) | c(u2r2(exist))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[105, 99, 89])).
% 0.12/0.41 tff(107,plain,
% 0.12/0.41 (d(u2r2(exist))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[106, 72])).
% 0.12/0.41 tff(108,plain,
% 0.12/0.41 (^[X1: $i] : refl(((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1)))) <=> ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(109,plain,
% 0.12/0.41 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1)))) <=> ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[108])).
% 0.12/0.41 tff(110,plain,
% 0.12/0.41 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1)))) <=> ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(111,axiom,(![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_20')).
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% 0.12/0.41 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.12/0.41 tff(113,plain,(
% 0.12/0.41 ![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))),
% 0.12/0.41 inference(skolemize,[status(sab)],[112])).
% 0.12/0.41 tff(114,plain,
% 0.12/0.41 (![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[113, 109])).
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% 0.12/0.41 inference(rewrite,[status(thm)],[])).
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% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(117,plain,
% 0.12/0.41 ((~![X1: $i] : ((~r3least(X1)) | (~equalish(u2r3(X1), u2r1(X1))))) | (~r3least(exist)) | (~equalish(u2r3(exist), u2r1(exist)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.12/0.41 tff(118,plain,
% 0.12/0.41 (~equalish(u2r3(exist), u2r1(exist))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[117, 114, 15])).
% 0.12/0.41 tff(119,plain,
% 0.12/0.41 (^[X1: $i] : refl((r(X1, u2r1(X1)) | (~r3least(X1))) <=> (r(X1, u2r1(X1)) | (~r3least(X1))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(120,plain,
% 0.12/0.41 (![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1))) <=> ![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[119])).
% 0.12/0.41 tff(121,plain,
% 0.12/0.41 (![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1))) <=> ![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(122,axiom,(![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_22')).
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% 0.12/0.41 (![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.12/0.41 tff(124,plain,(
% 0.12/0.41 ![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[123])).
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% 0.12/0.41 inference(modus_ponens,[status(thm)],[124, 120])).
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% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(127,plain,
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% 0.19/0.41 inference(rewrite,[status(thm)],[])).
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% 0.19/0.41 inference(monotonicity,[status(thm)],[127])).
% 0.19/0.41 tff(129,plain,
% 0.19/0.41 (((~![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))) | (r(exist, u2r1(exist)) | (~r3least(exist)))) <=> ((~![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))) | (~r3least(exist)) | r(exist, u2r1(exist)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[128, 126])).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 ((~![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))) | (r(exist, u2r1(exist)) | (~r3least(exist)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(131,plain,
% 0.19/0.41 ((~![X1: $i] : (r(X1, u2r1(X1)) | (~r3least(X1)))) | (~r3least(exist)) | r(exist, u2r1(exist))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.19/0.41 tff(132,plain,
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[131, 125, 15])).
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% 0.19/0.41 inference(rewrite,[status(thm)],[])).
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% 0.19/0.41 (((~c(u2r1(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r1(exist))) <=> ((~e(exist)) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r3(exist))) | (~c(u2r1(exist))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(135,plain,
% 0.19/0.41 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r1(exist))) | (~c(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | (~e(exist)) | equalish(u2r3(exist), u2r1(exist)))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~e(exist)) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r3(exist))) | (~c(u2r1(exist)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.41 tff(136,plain,
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% 0.19/0.41 inference(transitivity,[status(thm)],[135, 133])).
% 0.19/0.41 tff(137,plain,
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% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r3(exist))) | (~c(u2r1(exist)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.41 tff(139,plain,
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[138, 11, 64, 54, 132, 118])).
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[139, 1])).
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% 0.19/0.41 inference(rewrite,[status(thm)],[])).
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% 0.19/0.41 ((a(u2r1(exist)) | (~r(exist, u2r1(exist))) | (~e(exist))) <=> ((~e(exist)) | (~r(exist, u2r1(exist))) | a(u2r1(exist)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
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% 0.19/0.41 inference(monotonicity,[status(thm)],[142])).
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% 0.19/0.41 inference(transitivity,[status(thm)],[143, 141])).
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% 0.19/0.41 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r1(exist)) | (~r(exist, u2r1(exist))) | (~e(exist)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
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% 0.19/0.41 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r1(exist))) | a(u2r1(exist))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
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% 0.19/0.41 ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r1(exist)) | c(u2r1(exist)) | (~a(u2r1(exist)))),
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% 0.19/0.41 inference(unit_resolution,[status(thm)],[154, 140])).
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% 0.19/0.41 inference(quant_intro,[status(thm)],[156])).
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% 0.19/0.41 tff(159,axiom,(![X1: $i] : ((~r3least(X1)) | (~equalish(u2r2(X1), u2r1(X1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_19')).
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% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(168,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[167])).
% 0.19/0.41 tff(169,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3))) <=> ![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(170,plain,
% 0.19/0.41 (^[X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) <=> ((~r(X1, X3)) | equalish(X3, X2) | f(X1))), ((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) <=> (((~r(X1, X3)) | equalish(X3, X2) | f(X1)) | (~r(X1, X2))))), rewrite((((~r(X1, X3)) | equalish(X3, X2) | f(X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1))), ((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1)))), (((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) <=> (((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1)) | (~d(X3))))), rewrite((((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1)) | (~d(X3))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X3)))), (((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X3))))), ((((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) | (~d(X2))) <=> (((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X3))) | (~d(X2))))), rewrite((((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X3))) | (~d(X2))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))), ((((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) | (~d(X2))) <=> ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(171,plain,
% 0.19/0.41 (![X3: $i, X2: $i, X1: $i] : (((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) | (~d(X2))) <=> ![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[170])).
% 0.19/0.41 tff(172,axiom,(![X3: $i, X2: $i, X1: $i] : (((((f(X1) | equalish(X3, X2)) | (~r(X1, X3))) | (~r(X1, X2))) | (~d(X3))) | (~d(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_31')).
% 0.19/0.42 tff(173,plain,
% 0.19/0.42 (![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.19/0.42 tff(174,plain,
% 0.19/0.42 (![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[173, 169])).
% 0.19/0.42 tff(175,plain,(
% 0.19/0.42 ![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[174])).
% 0.19/0.42 tff(176,plain,
% 0.19/0.42 (![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[175, 168])).
% 0.19/0.42 tff(177,plain,
% 0.19/0.42 ((~f(exist)) <=> (~f(exist))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(178,axiom,(~f(exist)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','clause_2')).
% 0.19/0.42 tff(179,plain,
% 0.19/0.42 (~f(exist)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.19/0.42 tff(180,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(181,plain,
% 0.19/0.42 (((~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | equalish(u2r2(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r2(exist)))) <=> (f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(182,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | equalish(u2r2(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r2(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[181])).
% 0.19/0.42 tff(183,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | equalish(u2r2(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r2(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[182, 180])).
% 0.19/0.42 tff(184,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | equalish(u2r2(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r2(exist))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(185,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.19/0.42 tff(186,plain,
% 0.19/0.42 ((~d(u2r2(exist))) | (~d(u2r1(exist)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[185, 179, 176, 40, 132, 166])).
% 0.19/0.42 tff(187,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[186, 155, 107])).
% 0.19/0.42 tff(188,plain,(~c(u2r3(exist))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.42 tff(189,plain,
% 0.19/0.42 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | ((~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(190,plain,
% 0.19/0.42 ((a(u2r3(exist)) | (~r(exist, u2r3(exist))) | (~e(exist))) <=> ((~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(191,plain,
% 0.19/0.42 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r3(exist)) | (~r(exist, u2r3(exist))) | (~e(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | ((~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[190])).
% 0.19/0.42 tff(192,plain,
% 0.19/0.42 (((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r3(exist)) | (~r(exist, u2r3(exist))) | (~e(exist)))) <=> ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[191, 189])).
% 0.19/0.42 tff(193,plain,
% 0.19/0.42 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (a(u2r3(exist)) | (~r(exist, u2r3(exist))) | (~e(exist)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(194,plain,
% 0.19/0.42 ((~![X2: $i, X1: $i] : (a(X2) | (~r(X1, X2)) | (~e(X1)))) | (~e(exist)) | (~r(exist, u2r3(exist))) | a(u2r3(exist))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.42 tff(195,plain,
% 0.19/0.42 (a(u2r3(exist))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[194, 11, 82, 54])).
% 0.19/0.42 tff(196,plain,
% 0.19/0.42 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | (d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist))))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(197,plain,
% 0.19/0.42 (((~a(u2r3(exist))) | d(u2r3(exist)) | c(u2r3(exist))) <=> (d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(198,plain,
% 0.19/0.42 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r3(exist))) | d(u2r3(exist)) | c(u2r3(exist)))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | (d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[197])).
% 0.19/0.42 tff(199,plain,
% 0.19/0.42 (((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r3(exist))) | d(u2r3(exist)) | c(u2r3(exist)))) <=> ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[198, 196])).
% 0.19/0.42 tff(200,plain,
% 0.19/0.42 ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | ((~a(u2r3(exist))) | d(u2r3(exist)) | c(u2r3(exist)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(201,plain,
% 0.19/0.42 ((~![X1: $i] : ((~a(X1)) | d(X1) | c(X1))) | d(u2r3(exist)) | c(u2r3(exist)) | (~a(u2r3(exist)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.19/0.42 tff(202,plain,
% 0.19/0.42 (d(u2r3(exist)) | c(u2r3(exist))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[201, 99, 195])).
% 0.19/0.42 tff(203,plain,
% 0.19/0.42 (d(u2r3(exist))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[202, 188])).
% 0.19/0.42 tff(204,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(205,plain,
% 0.19/0.42 (((~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r2(exist)) | f(exist) | (~d(u2r2(exist))) | (~d(u2r3(exist)))) <=> (f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(206,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r2(exist)) | f(exist) | (~d(u2r2(exist))) | (~d(u2r3(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[205])).
% 0.19/0.42 tff(207,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r2(exist)) | f(exist) | (~d(u2r2(exist))) | (~d(u2r3(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[206, 204])).
% 0.19/0.42 tff(208,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r2(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r2(exist)) | f(exist) | (~d(u2r2(exist))) | (~d(u2r3(exist))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(209,plain,
% 0.19/0.42 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r2(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r2(exist))) | (~d(u2r2(exist)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.19/0.42 tff(210,plain,
% 0.19/0.42 ((~d(u2r3(exist))) | (~d(u2r2(exist)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[209, 179, 176, 54, 40, 26])).
% 0.19/0.42 tff(211,plain,
% 0.19/0.42 (~d(u2r2(exist))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[210, 203])).
% 0.19/0.42 tff(212,plain,
% 0.19/0.42 (c(u2r2(exist))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[106, 211])).
% 0.19/0.42 tff(213,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(214,plain,
% 0.19/0.42 (((~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r3(exist)))) <=> (f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(215,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r3(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | (f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist)))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[214])).
% 0.19/0.42 tff(216,plain,
% 0.19/0.42 (((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r3(exist))))) <=> ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[215, 213])).
% 0.19/0.43 tff(217,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | ((~r(exist, u2r1(exist))) | (~r(exist, u2r3(exist))) | equalish(u2r3(exist), u2r1(exist)) | f(exist) | (~d(u2r1(exist))) | (~d(u2r3(exist))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(218,plain,
% 0.19/0.43 ((~![X3: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X1, X3)) | equalish(X3, X2) | f(X1) | (~d(X2)) | (~d(X3)))) | f(exist) | equalish(u2r3(exist), u2r1(exist)) | (~r(exist, u2r3(exist))) | (~d(u2r3(exist))) | (~r(exist, u2r1(exist))) | (~d(u2r1(exist)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.19/0.43 tff(219,plain,
% 0.19/0.43 ((~d(u2r3(exist))) | (~d(u2r1(exist)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[218, 179, 176, 54, 132, 118])).
% 0.19/0.43 tff(220,plain,
% 0.19/0.43 (~d(u2r1(exist))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[219, 203])).
% 0.19/0.43 tff(221,plain,
% 0.19/0.43 (c(u2r1(exist))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[154, 220])).
% 0.19/0.43 tff(222,plain,
% 0.19/0.43 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist))))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(223,plain,
% 0.19/0.43 (((~c(u2r1(exist))) | (~c(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist))) <=> ((~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(224,plain,
% 0.19/0.43 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r1(exist))) | (~c(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[223])).
% 0.19/0.43 tff(225,plain,
% 0.19/0.43 (((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r1(exist))) | (~c(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)))) <=> ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[224, 222])).
% 0.19/0.43 tff(226,plain,
% 0.19/0.43 ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | ((~c(u2r1(exist))) | (~c(u2r2(exist))) | (~r(exist, u2r1(exist))) | (~r(exist, u2r2(exist))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(227,plain,
% 0.19/0.43 ((~![X4: $i, X3: $i, X1: $i] : ((~c(X3)) | (~c(X4)) | (~r(X1, X3)) | (~r(X1, X4)) | (~e(X1)) | equalish(X4, X3))) | (~e(exist)) | equalish(u2r2(exist), u2r1(exist)) | (~r(exist, u2r2(exist))) | (~r(exist, u2r1(exist))) | (~c(u2r2(exist))) | (~c(u2r1(exist)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.19/0.43 tff(228,plain,
% 0.19/0.43 ((~c(u2r2(exist))) | (~c(u2r1(exist)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[227, 11, 64, 40, 132, 166])).
% 0.19/0.43 tff(229,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[228, 221, 212])).
% 0.19/0.43 % SZS output end Proof
%------------------------------------------------------------------------------