TSTP Solution File: COL094-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL094-2 : TPTP v8.1.0. Released v2.7.0.
% 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 : Tue Sep 6 17:48:32 EDT 2022
% Result : Unsatisfiable 0.21s 0.57s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : COL094-2 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 12:20:36 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.57 % SZS status Unsatisfiable
% 0.21/0.57 % SZS output start Proof
% 0.21/0.57 tff(comb_app_type, type, (
% 0.21/0.57 comb_app: ( $i * $i ) > $i)).
% 0.21/0.57 tff(ap_parcontractE_sk2q_type, type, (
% 0.21/0.57 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.21/0.57 tff(r_type, type, (
% 0.21/0.57 r: $i)).
% 0.21/0.57 tff(q_type, type, (
% 0.21/0.57 q: $i)).
% 0.21/0.57 tff(p_type, type, (
% 0.21/0.57 p: $i)).
% 0.21/0.57 tff(combS_type, type, (
% 0.21/0.57 combS: $i)).
% 0.21/0.57 tff(combK_type, type, (
% 0.21/0.57 combK: $i)).
% 0.21/0.57 tff(ap_parcontractE_c2_type, type, (
% 0.21/0.57 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(ap_parcontractE_c4_type, type, (
% 0.21/0.57 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(member_type, type, (
% 0.21/0.57 member: ( $i * $i ) > $o)).
% 0.21/0.57 tff(parcontract_type, type, (
% 0.21/0.57 parcontract: $i)).
% 0.21/0.57 tff(pair_type, type, (
% 0.21/0.57 pair: ( $i * $i ) > $i)).
% 0.21/0.57 tff(comb_type, type, (
% 0.21/0.57 comb: $i)).
% 0.21/0.57 tff(ap_parcontractE_c1_type, type, (
% 0.21/0.57 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(ap_parcontractE_c3_type, type, (
% 0.21/0.57 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.21/0.57 tff(ap_parcontractE_sk1q_type, type, (
% 0.21/0.57 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.21/0.57 tff(ap_parcontractE_sk1p_type, type, (
% 0.21/0.57 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.21/0.57 tff(ap_parcontractE_sk2s_type, type, (
% 0.21/0.57 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.21/0.57 tff(1,assumption,(~ap_parcontractE_c4(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.57 tff(2,assumption,(~member(q, comb)), introduced(assumption)).
% 0.21/0.57 tff(3,plain,
% 0.21/0.57 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(4,plain,
% 0.21/0.57 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.57 tff(5,plain,
% 0.21/0.57 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(6,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E2')).
% 0.21/0.57 tff(7,plain,
% 0.21/0.57 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.57 tff(8,plain,(
% 0.21/0.57 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.57 inference(skolemize,[status(sab)],[7])).
% 0.21/0.57 tff(9,plain,
% 0.21/0.57 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.57 tff(10,plain,
% 0.21/0.57 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(11,plain,
% 0.21/0.57 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(12,plain,
% 0.21/0.57 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.21/0.57 tff(13,plain,
% 0.21/0.57 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(q, comb)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[12, 9])).
% 0.21/0.57 tff(14,plain,
% 0.21/0.57 (~member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[13, 2])).
% 0.21/0.57 tff(15,assumption,(~ap_parcontractE_c1(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.57 tff(16,assumption,(ap_parcontractE_c2(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.57 tff(17,plain,
% 0.21/0.57 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(18,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[17])).
% 0.21/0.57 tff(19,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(20,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.21/0.57 tff(21,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.21/0.57 tff(22,plain,(
% 0.21/0.57 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(skolemize,[status(sab)],[21])).
% 0.21/0.57 tff(23,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.21/0.57 tff(24,plain,
% 0.21/0.57 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | member(q, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | member(q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(25,plain,
% 0.21/0.57 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | member(q, comb))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(26,plain,
% 0.21/0.57 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | member(q, comb)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.57 tff(27,plain,
% 0.21/0.57 ($false),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[26, 23, 16, 2])).
% 0.21/0.57 tff(28,plain,((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | member(q, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.57 tff(29,plain,
% 0.21/0.57 (~ap_parcontractE_c2(comb_app(combS, p), q, r)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[28, 2])).
% 0.21/0.57 tff(30,assumption,(ap_parcontractE_c3(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.57 tff(31,plain,
% 0.21/0.57 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(32,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[31])).
% 0.21/0.57 tff(33,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(34,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.21/0.57 tff(35,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.21/0.57 tff(36,plain,(
% 0.21/0.57 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(skolemize,[status(sab)],[35])).
% 0.21/0.57 tff(37,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.21/0.57 tff(38,plain,
% 0.21/0.57 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | member(q, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | member(q, comb))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(39,plain,
% 0.21/0.57 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | member(q, comb))),
% 0.21/0.57 inference(quant_inst,[status(thm)],[])).
% 0.21/0.57 tff(40,plain,
% 0.21/0.57 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | member(q, comb)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.21/0.57 tff(41,plain,
% 0.21/0.57 ($false),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[40, 37, 30, 2])).
% 0.21/0.57 tff(42,plain,((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | member(q, comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.57 tff(43,plain,
% 0.21/0.57 (~ap_parcontractE_c3(comb_app(combS, p), q, r)),
% 0.21/0.57 inference(unit_resolution,[status(thm)],[42, 2])).
% 0.21/0.57 tff(44,plain,
% 0.21/0.57 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract) <=> member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(45,axiom,(member(pair(comb_app(comb_app(combS, p), q), r), parcontract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s2_parcontractD_h1')).
% 0.21/0.57 tff(46,plain,
% 0.21/0.57 (member(pair(comb_app(comb_app(combS, p), q), r), parcontract)),
% 0.21/0.57 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.21/0.57 tff(47,plain,
% 0.21/0.57 (^[R: $i, Q: $i, P: $i] : refl((ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))),
% 0.21/0.57 inference(bind,[status(th)],[])).
% 0.21/0.57 tff(48,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.57 inference(quant_intro,[status(thm)],[47])).
% 0.21/0.57 tff(49,plain,
% 0.21/0.57 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.57 inference(rewrite,[status(thm)],[])).
% 0.21/0.57 tff(50,plain,
% 0.21/0.57 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) <=> (ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> ((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)))), rewrite(((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)))), rewrite(((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(51,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[50])).
% 0.21/0.58 tff(52,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.21/0.58 tff(53,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.58 tff(54,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.21/0.58 tff(55,plain,(
% 0.21/0.58 ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.58 inference(skolemize,[status(sab)],[54])).
% 0.21/0.58 tff(56,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.21/0.58 tff(57,plain,
% 0.21/0.58 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(58,plain,
% 0.21/0.58 ((ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract))) <=> ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(59,plain,
% 0.21/0.58 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)))),
% 0.21/0.58 inference(monotonicity,[status(thm)],[58])).
% 0.21/0.58 tff(60,plain,
% 0.21/0.58 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r))),
% 0.21/0.58 inference(transitivity,[status(thm)],[59, 57])).
% 0.21/0.58 tff(61,plain,
% 0.21/0.58 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)))),
% 0.21/0.58 inference(quant_inst,[status(thm)],[])).
% 0.21/0.58 tff(62,plain,
% 0.21/0.58 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(comb_app(combS, p), q), r), parcontract)) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.58 tff(63,plain,
% 0.21/0.58 (ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c3(comb_app(combS, p), q, r) | ap_parcontractE_c2(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[62, 56, 46])).
% 0.21/0.58 tff(64,plain,
% 0.21/0.58 ($false),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[63, 43, 29, 1, 15])).
% 0.21/0.58 tff(65,plain,(member(q, comb) | ap_parcontractE_c4(comb_app(combS, p), q, r) | ap_parcontractE_c1(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.58 tff(66,plain,
% 0.21/0.58 (ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.58 inference(unit_resolution,[status(thm)],[65, 2, 1])).
% 0.21/0.58 tff(67,assumption,(~member(comb_app(comb_app(combS, p), q), comb)), introduced(assumption)).
% 0.21/0.58 tff(68,assumption,(ap_parcontractE_c1(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.21/0.58 tff(69,plain,
% 0.21/0.58 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)))),
% 0.21/0.58 inference(bind,[status(th)],[])).
% 0.21/0.58 tff(70,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.58 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.58 tff(71,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.58 inference(rewrite,[status(thm)],[])).
% 0.21/0.58 tff(72,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.21/0.58 tff(73,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.21/0.58 tff(74,plain,(
% 0.21/0.58 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.58 inference(skolemize,[status(sab)],[73])).
% 0.21/0.58 tff(75,plain,
% 0.21/0.58 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.21/0.58 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.58 tff(76,plain,
% 0.21/0.58 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(77,plain,
% 0.21/0.59 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(78,plain,
% 0.21/0.59 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.21/0.59 tff(79,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[78, 75, 68, 67])).
% 0.21/0.59 tff(80,plain,((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | member(comb_app(comb_app(combS, p), q), comb)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.59 tff(81,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[80, 66, 14])).
% 0.21/0.59 tff(82,plain,(member(q, comb) | ap_parcontractE_c4(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.59 tff(83,plain,
% 0.21/0.59 (member(q, comb)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[82, 1])).
% 0.21/0.59 tff(84,plain,
% 0.21/0.59 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(85,plain,
% 0.21/0.59 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[84])).
% 0.21/0.59 tff(86,plain,
% 0.21/0.59 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(87,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.21/0.59 tff(88,plain,
% 0.21/0.59 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.21/0.59 tff(89,plain,(
% 0.21/0.59 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.59 inference(skolemize,[status(sab)],[88])).
% 0.21/0.59 tff(90,plain,
% 0.21/0.59 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.21/0.59 tff(91,plain,
% 0.21/0.59 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(92,plain,
% 0.21/0.59 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(q, comb)) | member(pair(q, q), parcontract))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(93,plain,
% 0.21/0.59 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(q, comb)) | member(pair(q, q), parcontract)),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.59 tff(94,plain,
% 0.21/0.59 (member(pair(q, q), parcontract)),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[93, 90, 83])).
% 0.21/0.59 tff(95,assumption,(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.59 tff(96,assumption,(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.21/0.59 tff(97,plain,
% 0.21/0.59 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(98,plain,
% 0.21/0.59 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[97])).
% 0.21/0.59 tff(99,plain,
% 0.21/0.59 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(100,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_app')).
% 0.21/0.59 tff(101,plain,
% 0.21/0.59 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.21/0.59 tff(102,plain,(
% 0.21/0.59 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.59 inference(skolemize,[status(sab)],[101])).
% 0.21/0.59 tff(103,plain,
% 0.21/0.59 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.59 tff(104,plain,
% 0.21/0.59 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(105,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[104, 103, 96])).
% 0.21/0.59 tff(106,plain,(~(combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.59 tff(107,plain,
% 0.21/0.59 (^[P2: $i, Q2: $i, Q1: $i, P1: $i] : refl(((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(108,plain,
% 0.21/0.59 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[107])).
% 0.21/0.59 tff(109,plain,
% 0.21/0.59 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(110,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_app1')).
% 0.21/0.59 tff(111,plain,
% 0.21/0.59 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.21/0.59 tff(112,plain,(
% 0.21/0.59 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.59 inference(skolemize,[status(sab)],[111])).
% 0.21/0.59 tff(113,plain,
% 0.21/0.59 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.21/0.59 tff(114,plain,
% 0.21/0.59 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(115,plain,
% 0.21/0.59 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r))))),
% 0.21/0.59 inference(quant_inst,[status(thm)],[])).
% 0.21/0.59 tff(116,plain,
% 0.21/0.59 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))) | (combS = comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.21/0.59 tff(117,plain,
% 0.21/0.59 ($false),
% 0.21/0.59 inference(unit_resolution,[status(thm)],[116, 113, 106, 95])).
% 0.21/0.59 tff(118,plain,(~(comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.59 tff(119,plain,
% 0.21/0.59 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))))),
% 0.21/0.59 inference(bind,[status(th)],[])).
% 0.21/0.59 tff(120,plain,
% 0.21/0.59 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.59 inference(quant_intro,[status(thm)],[119])).
% 0.21/0.59 tff(121,plain,
% 0.21/0.59 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(122,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.21/0.59 tff(123,plain,
% 0.21/0.59 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.21/0.59 tff(124,plain,(
% 0.21/0.59 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.59 inference(skolemize,[status(sab)],[123])).
% 0.21/0.59 tff(125,plain,
% 0.21/0.59 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.21/0.59 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.21/0.59 tff(126,plain,
% 0.21/0.59 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.21/0.59 inference(rewrite,[status(thm)],[])).
% 0.21/0.59 tff(127,plain,
% 0.21/0.59 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r))))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(128,plain,
% 0.21/0.60 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.21/0.60 tff(129,plain,
% 0.21/0.60 ((~ap_parcontractE_c3(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combS, p), q, r)), ap_parcontractE_sk1q(comb_app(combS, p), q, r)))),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.21/0.60 tff(130,plain,
% 0.21/0.60 (~ap_parcontractE_c3(comb_app(combS, p), q, r)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[129, 118])).
% 0.21/0.60 tff(131,assumption,(comb_app(combS, p) = comb_app(combK, r)), introduced(assumption)).
% 0.21/0.60 tff(132,plain,
% 0.21/0.60 ((combS = combK) <=> (combK = combS)),
% 0.21/0.60 inference(commutativity,[status(thm)],[])).
% 0.21/0.60 tff(133,plain,
% 0.21/0.60 ((combK = combS) <=> (combS = combK)),
% 0.21/0.60 inference(symmetry,[status(thm)],[132])).
% 0.21/0.60 tff(134,plain,
% 0.21/0.60 ((~(combK = combS)) <=> (~(combS = combK))),
% 0.21/0.60 inference(monotonicity,[status(thm)],[133])).
% 0.21/0.60 tff(135,plain,
% 0.21/0.60 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(136,axiom,(~(combK = combS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_s')).
% 0.21/0.60 tff(137,plain,
% 0.21/0.60 (~(combK = combS)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.21/0.60 tff(138,plain,
% 0.21/0.60 (~(combS = combK)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[137, 134])).
% 0.21/0.60 tff(139,plain,
% 0.21/0.60 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(140,plain,
% 0.21/0.60 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(141,plain,
% 0.21/0.60 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, p) = comb_app(combK, r))) | (combS = combK)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.60 tff(142,plain,
% 0.21/0.60 ($false),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[141, 113, 138, 131])).
% 0.21/0.60 tff(143,plain,(~(comb_app(combS, p) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.60 tff(144,plain,
% 0.21/0.60 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(145,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.60 tff(146,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(147,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.21/0.60 tff(148,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.21/0.60 tff(149,plain,(
% 0.21/0.60 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.60 inference(skolemize,[status(sab)],[148])).
% 0.21/0.60 tff(150,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.21/0.60 tff(151,plain,
% 0.21/0.60 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(152,plain,
% 0.21/0.60 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r)))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(153,plain,
% 0.21/0.60 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combS, p), q, r)) | (comb_app(combS, p) = comb_app(combK, r))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.60 tff(154,plain,
% 0.21/0.60 ($false),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[153, 150, 16, 143])).
% 0.21/0.60 tff(155,plain,(~ap_parcontractE_c2(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.60 tff(156,plain,
% 0.21/0.60 (ap_parcontractE_c1(comb_app(combS, p), q, r)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[63, 1, 155, 130])).
% 0.21/0.60 tff(157,plain,
% 0.21/0.60 (member(comb_app(comb_app(combS, p), q), comb)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[80, 156])).
% 0.21/0.60 tff(158,plain,
% 0.21/0.60 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(P, comb)))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(159,plain,
% 0.21/0.60 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[158])).
% 0.21/0.60 tff(160,plain,
% 0.21/0.60 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(161,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E1')).
% 0.21/0.60 tff(162,plain,
% 0.21/0.60 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.21/0.60 tff(163,plain,(
% 0.21/0.60 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.60 inference(skolemize,[status(sab)],[162])).
% 0.21/0.60 tff(164,plain,
% 0.21/0.60 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.21/0.60 tff(165,plain,
% 0.21/0.60 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(166,plain,
% 0.21/0.60 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(167,plain,
% 0.21/0.60 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(P, comb))) | (~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.21/0.60 tff(168,plain,
% 0.21/0.60 ((~member(comb_app(comb_app(combS, p), q), comb)) | member(comb_app(combS, p), comb)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[167, 164])).
% 0.21/0.60 tff(169,plain,
% 0.21/0.60 (member(comb_app(combS, p), comb)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[168, 157])).
% 0.21/0.60 tff(170,plain,
% 0.21/0.60 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(171,plain,
% 0.21/0.60 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(172,plain,
% 0.21/0.60 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.21/0.60 tff(173,plain,
% 0.21/0.60 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[172, 9])).
% 0.21/0.60 tff(174,plain,
% 0.21/0.60 (member(p, comb)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[173, 169])).
% 0.21/0.60 tff(175,plain,
% 0.21/0.60 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(176,plain,
% 0.21/0.60 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(177,plain,
% 0.21/0.60 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.60 tff(178,plain,
% 0.21/0.60 (member(pair(p, p), parcontract)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[177, 90, 174])).
% 0.21/0.60 tff(179,plain,
% 0.21/0.60 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))))),
% 0.21/0.60 inference(bind,[status(th)],[])).
% 0.21/0.60 tff(180,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.60 inference(quant_intro,[status(thm)],[179])).
% 0.21/0.60 tff(181,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(182,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.21/0.60 tff(183,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.21/0.60 tff(184,plain,(
% 0.21/0.60 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.60 inference(skolemize,[status(sab)],[183])).
% 0.21/0.60 tff(185,plain,
% 0.21/0.60 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[184, 180])).
% 0.21/0.60 tff(186,plain,
% 0.21/0.60 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.60 inference(rewrite,[status(thm)],[])).
% 0.21/0.60 tff(187,plain,
% 0.21/0.60 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q)))),
% 0.21/0.60 inference(quant_inst,[status(thm)],[])).
% 0.21/0.60 tff(188,plain,
% 0.21/0.60 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combS, p), q, r)) | (r = comb_app(comb_app(combS, p), q))),
% 0.21/0.60 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.21/0.60 tff(189,plain,
% 0.21/0.60 (r = comb_app(comb_app(combS, p), q)),
% 0.21/0.60 inference(unit_resolution,[status(thm)],[188, 185, 156])).
% 0.21/0.60 tff(190,plain,
% 0.21/0.60 (^[QP: $i, PP: $i] : refl(((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))))),
% 0.21/0.61 inference(bind,[status(th)],[])).
% 0.21/0.61 tff(191,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(quant_intro,[status(thm)],[190])).
% 0.21/0.61 tff(192,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(rewrite,[status(thm)],[])).
% 0.21/0.61 tff(193,plain,
% 0.21/0.61 (^[QP: $i, PP: $i] : trans(monotonicity(rewrite(((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) <=> ((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> (((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))))), rewrite((((~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP)))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))), ((((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))))),
% 0.21/0.61 inference(bind,[status(th)],[])).
% 0.21/0.61 tff(194,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract))) <=> ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(quant_intro,[status(thm)],[193])).
% 0.21/0.61 tff(195,axiom,(![QP: $i, PP: $i] : (((~(r = comb_app(comb_app(combS, PP), QP))) | (~member(pair(p, PP), parcontract))) | (~member(pair(q, QP), parcontract)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s2_parcontractD_c1')).
% 0.21/0.61 tff(196,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(modus_ponens,[status(thm)],[195, 194])).
% 0.21/0.61 tff(197,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(modus_ponens,[status(thm)],[196, 192])).
% 0.21/0.61 tff(198,plain,(
% 0.21/0.61 ![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(skolemize,[status(sab)],[197])).
% 0.21/0.61 tff(199,plain,
% 0.21/0.61 (![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))),
% 0.21/0.61 inference(modus_ponens,[status(thm)],[198, 191])).
% 0.21/0.61 tff(200,plain,
% 0.21/0.61 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.21/0.61 inference(rewrite,[status(thm)],[])).
% 0.21/0.61 tff(201,plain,
% 0.21/0.61 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(202,plain,
% 0.57/0.61 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.57/0.61 tff(203,plain,
% 0.57/0.61 ((~member(pair(q, q), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), q)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.57/0.61 tff(204,plain,
% 0.57/0.61 ($false),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[203, 189, 178, 94])).
% 0.57/0.61 tff(205,plain,(ap_parcontractE_c4(comb_app(combS, p), q, r)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.61 tff(206,plain,
% 0.57/0.61 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(207,plain,
% 0.57/0.61 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[206])).
% 0.57/0.61 tff(208,plain,
% 0.57/0.61 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(209,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.57/0.61 tff(210,plain,
% 0.57/0.61 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.57/0.61 tff(211,plain,(
% 0.57/0.61 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.57/0.61 inference(skolemize,[status(sab)],[210])).
% 0.57/0.61 tff(212,plain,
% 0.57/0.61 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.57/0.61 tff(213,plain,
% 0.57/0.61 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(214,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(215,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.57/0.61 tff(216,plain,
% 0.57/0.61 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[215, 212])).
% 0.57/0.61 tff(217,plain,
% 0.57/0.61 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[216, 205])).
% 0.57/0.61 tff(218,assumption,(~member(p, comb)), introduced(assumption)).
% 0.57/0.61 tff(219,assumption,(ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.57/0.61 tff(220,plain,
% 0.57/0.61 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(221,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(222,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.57/0.61 tff(223,plain,
% 0.57/0.61 ($false),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[222, 23, 218, 219])).
% 0.57/0.61 tff(224,plain,((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.61 tff(225,plain,
% 0.57/0.61 (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[224, 218])).
% 0.57/0.61 tff(226,assumption,(ap_parcontractE_c4(comb_app(combS, p), q, r)), introduced(assumption)).
% 0.57/0.61 tff(227,assumption,(ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.57/0.61 tff(228,plain,
% 0.57/0.61 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(229,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(230,plain,
% 0.57/0.61 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.57/0.61 tff(231,plain,
% 0.57/0.61 ($false),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[230, 37, 218, 227])).
% 0.57/0.61 tff(232,plain,((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.61 tff(233,plain,
% 0.57/0.61 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[232, 218])).
% 0.57/0.61 tff(234,plain,
% 0.57/0.61 (~member(comb_app(combS, p), comb)),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[173, 218])).
% 0.57/0.61 tff(235,assumption,(ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.57/0.61 tff(236,assumption,(~member(comb_app(combS, p), comb)), introduced(assumption)).
% 0.57/0.61 tff(237,plain,
% 0.57/0.61 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(238,plain,
% 0.57/0.62 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(239,plain,
% 0.57/0.62 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.57/0.62 tff(240,plain,
% 0.57/0.62 ($false),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[239, 75, 236, 235])).
% 0.57/0.62 tff(241,plain,((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(comb_app(combS, p), comb)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.62 tff(242,plain,
% 0.57/0.62 (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[241, 234])).
% 0.57/0.62 tff(243,plain,
% 0.57/0.62 (r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[216, 226])).
% 0.57/0.62 tff(244,plain,
% 0.57/0.62 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.57/0.62 inference(symmetry,[status(thm)],[243])).
% 0.57/0.62 tff(245,plain,
% 0.57/0.62 (ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) = ap_parcontractE_sk2s(comb_app(combS, p), q, r)),
% 0.57/0.62 inference(monotonicity,[status(thm)],[244])).
% 0.57/0.62 tff(246,plain,
% 0.57/0.62 (ap_parcontractE_sk2s(comb_app(combS, p), q, r) = ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.57/0.62 inference(symmetry,[status(thm)],[245])).
% 0.57/0.62 tff(247,plain,
% 0.57/0.62 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[246])).
% 0.57/0.62 tff(248,plain,
% 0.57/0.62 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.57/0.62 inference(monotonicity,[status(thm)],[247])).
% 0.57/0.62 tff(249,plain,
% 0.57/0.62 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.57/0.62 inference(symmetry,[status(thm)],[248])).
% 0.57/0.62 tff(250,plain,
% 0.57/0.62 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) <=> ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.57/0.62 inference(monotonicity,[status(thm)],[244])).
% 0.57/0.62 tff(251,plain,
% 0.57/0.62 (ap_parcontractE_c4(comb_app(combS, p), q, r) <=> ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.57/0.62 inference(symmetry,[status(thm)],[250])).
% 0.57/0.62 tff(252,plain,
% 0.57/0.62 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[226, 251])).
% 0.57/0.62 tff(253,plain,
% 0.57/0.62 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(254,plain,
% 0.57/0.62 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[253])).
% 0.57/0.62 tff(255,plain,
% 0.57/0.62 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(256,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.57/0.62 tff(257,plain,
% 0.57/0.62 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.57/0.62 tff(258,plain,(
% 0.57/0.62 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.57/0.62 inference(skolemize,[status(sab)],[257])).
% 0.57/0.62 tff(259,plain,
% 0.57/0.62 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.57/0.62 tff(260,plain,
% 0.57/0.62 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(261,plain,
% 0.57/0.62 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(262,plain,
% 0.57/0.62 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.57/0.62 tff(263,plain,
% 0.57/0.62 ((~ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[262, 259])).
% 0.57/0.63 tff(264,plain,
% 0.57/0.63 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[263, 252])).
% 0.57/0.63 tff(265,plain,
% 0.57/0.63 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[264, 249])).
% 0.57/0.63 tff(266,assumption,(~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.57/0.63 tff(267,assumption,(~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.57/0.63 tff(268,plain,
% 0.57/0.63 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(269,plain,
% 0.57/0.63 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[268])).
% 0.57/0.63 tff(270,plain,
% 0.57/0.63 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(271,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.57/0.63 tff(272,plain,
% 0.57/0.63 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.57/0.63 tff(273,plain,(
% 0.57/0.63 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.57/0.63 inference(skolemize,[status(sab)],[272])).
% 0.57/0.63 tff(274,plain,
% 0.57/0.63 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[273, 269])).
% 0.57/0.63 tff(275,plain,
% 0.57/0.63 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(276,plain,
% 0.57/0.63 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))),
% 0.57/0.63 inference(quant_inst,[status(thm)],[])).
% 0.57/0.63 tff(277,plain,
% 0.57/0.63 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.57/0.63 tff(278,plain,
% 0.57/0.63 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[277, 274])).
% 0.57/0.63 tff(279,plain,
% 0.57/0.63 (member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[278, 226])).
% 0.59/0.63 tff(280,assumption,(~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.59/0.63 tff(281,plain,
% 0.59/0.63 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(282,plain,
% 0.59/0.63 ((ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract))) <=> ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.59/0.63 inference(rewrite,[status(thm)],[])).
% 0.59/0.63 tff(283,plain,
% 0.59/0.63 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.59/0.63 inference(monotonicity,[status(thm)],[282])).
% 0.59/0.63 tff(284,plain,
% 0.59/0.63 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.60/0.64 inference(transitivity,[status(thm)],[283, 281])).
% 0.60/0.64 tff(285,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(286,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.60/0.64 tff(287,plain,
% 0.60/0.64 ((~member(pair(comb_app(combS, p), ap_parcontractE_sk2q(comb_app(combS, p), q, r)), parcontract)) | ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[286, 56, 280])).
% 0.60/0.64 tff(288,plain,
% 0.60/0.64 (ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[287, 279, 267, 266])).
% 0.60/0.64 tff(289,plain,
% 0.60/0.64 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(290,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(291,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.60/0.64 tff(292,plain,
% 0.60/0.64 (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[291, 212, 288])).
% 0.60/0.64 tff(293,plain,
% 0.60/0.64 (comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.60/0.64 inference(symmetry,[status(thm)],[292])).
% 0.60/0.64 tff(294,plain,
% 0.60/0.64 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(295,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(296,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.60/0.64 tff(297,plain,
% 0.60/0.64 (member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[296, 274, 288])).
% 0.60/0.64 tff(298,plain,
% 0.60/0.64 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(299,plain,
% 0.60/0.64 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[298])).
% 0.60/0.64 tff(300,plain,
% 0.60/0.64 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(301,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.60/0.64 tff(302,plain,
% 0.60/0.64 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.60/0.64 tff(303,plain,(
% 0.60/0.64 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.60/0.64 inference(skolemize,[status(sab)],[302])).
% 0.60/0.64 tff(304,plain,
% 0.60/0.64 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[303, 299])).
% 0.60/0.64 tff(305,plain,
% 0.60/0.64 (((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))) <=> ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(306,plain,
% 0.60/0.64 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(307,plain,
% 0.60/0.64 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS)),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.60/0.64 tff(308,plain,
% 0.60/0.64 (ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) = combS),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[307, 304, 297])).
% 0.60/0.64 tff(309,plain,
% 0.60/0.64 (combS = ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(symmetry,[status(thm)],[308])).
% 0.60/0.64 tff(310,plain,
% 0.60/0.64 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = comb_app(ap_parcontractE_sk2q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)), ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[309])).
% 0.60/0.64 tff(311,plain,
% 0.60/0.64 (comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.60/0.64 inference(transitivity,[status(thm)],[310, 293])).
% 0.60/0.64 tff(312,plain,
% 0.60/0.64 (comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[311])).
% 0.60/0.64 tff(313,plain,
% 0.60/0.64 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(symmetry,[status(thm)],[312])).
% 0.60/0.64 tff(314,plain,
% 0.60/0.64 (r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.64 inference(transitivity,[status(thm)],[243, 313])).
% 0.60/0.64 tff(315,plain,
% 0.60/0.64 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(316,plain,
% 0.60/0.64 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(317,plain,
% 0.60/0.65 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.60/0.65 tff(318,plain,
% 0.60/0.65 (member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[317, 259, 288])).
% 0.60/0.65 tff(319,plain,
% 0.60/0.65 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(320,plain,
% 0.60/0.65 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(321,plain,
% 0.60/0.65 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.60/0.65 tff(322,plain,
% 0.60/0.65 ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, ap_parcontractE_sk2s(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[321, 199, 318])).
% 0.60/0.65 tff(323,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[322, 314, 265])).
% 0.60/0.65 tff(324,plain,((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(325,plain,
% 0.60/0.65 ($false),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[324, 242, 233, 226, 225])).
% 0.60/0.65 tff(326,plain,(member(p, comb) | (~ap_parcontractE_c4(comb_app(combS, p), q, r))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.65 tff(327,plain,
% 0.60/0.65 (member(p, comb)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[326, 205])).
% 0.60/0.65 tff(328,plain,
% 0.60/0.65 (member(pair(p, p), parcontract)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[177, 90, 327])).
% 0.60/0.65 tff(329,plain,
% 0.60/0.65 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = r),
% 0.60/0.65 inference(symmetry,[status(thm)],[217])).
% 0.60/0.65 tff(330,plain,
% 0.60/0.65 (ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) = ap_parcontractE_sk2s(comb_app(combS, p), q, r)),
% 0.60/0.65 inference(monotonicity,[status(thm)],[329])).
% 0.60/0.65 tff(331,plain,
% 0.60/0.65 (pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) = pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[330])).
% 0.60/0.65 tff(332,plain,
% 0.60/0.65 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract) <=> member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.60/0.65 inference(monotonicity,[status(thm)],[331])).
% 0.60/0.65 tff(333,plain,
% 0.60/0.65 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))) <=> ap_parcontractE_c4(comb_app(combS, p), q, r)),
% 0.60/0.65 inference(monotonicity,[status(thm)],[329])).
% 0.60/0.65 tff(334,plain,
% 0.60/0.65 (ap_parcontractE_c4(comb_app(combS, p), q, r) <=> ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.60/0.65 inference(symmetry,[status(thm)],[333])).
% 0.60/0.65 tff(335,plain,
% 0.60/0.65 (ap_parcontractE_c4(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[205, 334])).
% 0.60/0.65 tff(336,plain,
% 0.60/0.65 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))), parcontract)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[263, 335])).
% 0.60/0.65 tff(337,plain,
% 0.60/0.65 (member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.60/0.65 tff(338,assumption,(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)), introduced(assumption)).
% 0.60/0.65 tff(339,plain,
% 0.60/0.65 (comb_app(combS, p) = ap_parcontractE_sk2q(comb_app(combS, p), q, r)),
% 0.60/0.65 inference(symmetry,[status(thm)],[338])).
% 0.60/0.65 tff(340,plain,
% 0.60/0.65 (comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[339])).
% 0.60/0.65 tff(341,plain,
% 0.60/0.65 (comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)) = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.65 inference(symmetry,[status(thm)],[340])).
% 0.60/0.65 tff(342,assumption,(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r))), introduced(assumption)).
% 0.60/0.65 tff(343,plain,
% 0.60/0.65 (r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))),
% 0.60/0.65 inference(transitivity,[status(thm)],[342, 341])).
% 0.60/0.65 tff(344,assumption,(member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)), introduced(assumption)).
% 0.60/0.65 tff(345,assumption,(member(pair(p, p), parcontract)), introduced(assumption)).
% 0.60/0.65 tff(346,plain,
% 0.60/0.65 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(347,plain,
% 0.60/0.66 (((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))) <=> ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(348,plain,
% 0.60/0.66 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[347])).
% 0.60/0.66 tff(349,plain,
% 0.60/0.66 (((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))) <=> ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(transitivity,[status(thm)],[348, 346])).
% 0.60/0.66 tff(350,plain,
% 0.60/0.66 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~member(pair(p, p), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(351,plain,
% 0.60/0.66 ((~![QP: $i, PP: $i] : ((~member(pair(q, QP), parcontract)) | (~member(pair(p, PP), parcontract)) | (~(r = comb_app(comb_app(combS, PP), QP))))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract)) | (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.60/0.66 tff(352,plain,
% 0.60/0.66 (~(r = comb_app(comb_app(combS, p), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[351, 199, 345, 344])).
% 0.60/0.66 tff(353,plain,
% 0.60/0.66 ($false),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[352, 343])).
% 0.60/0.66 tff(354,plain,((~(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))) | (~(r = comb_app(ap_parcontractE_sk2q(comb_app(combS, p), q, r), ap_parcontractE_sk2s(comb_app(combS, p), q, r)))) | (~member(pair(p, p), parcontract)) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combS, p), q, r)), parcontract))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.66 tff(355,plain,
% 0.60/0.66 (~(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[354, 337, 328, 217])).
% 0.60/0.66 tff(356,assumption,(~(ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))), introduced(assumption)).
% 0.60/0.66 tff(357,plain,
% 0.60/0.66 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(358,plain,
% 0.60/0.66 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(359,plain,
% 0.60/0.66 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.60/0.66 tff(360,plain,
% 0.60/0.66 ($false),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[359, 185, 235, 356])).
% 0.60/0.66 tff(361,plain,((~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (ap_parcontractE_sk2q(comb_app(combS, p), q, r) = comb_app(combS, p))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.66 tff(362,plain,
% 0.60/0.66 (~ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[361, 355])).
% 0.60/0.66 tff(363,assumption,(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))), introduced(assumption)).
% 0.60/0.66 tff(364,plain,
% 0.60/0.66 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(365,plain,
% 0.60/0.66 ($false),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[364, 103, 363])).
% 0.60/0.66 tff(366,plain,(~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.66 tff(367,plain,
% 0.60/0.66 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(368,plain,
% 0.60/0.66 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(369,plain,
% 0.60/0.66 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))), ap_parcontractE_sk1q(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.60/0.67 tff(370,plain,
% 0.60/0.67 (~ap_parcontractE_c3(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[369, 125, 366])).
% 0.60/0.67 tff(371,plain,
% 0.60/0.67 ((~ap_parcontractE_c4(comb_app(combS, p), q, r)) | ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r)) | ap_parcontractE_c1(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[324, 370])).
% 0.60/0.67 tff(372,plain,
% 0.60/0.67 (ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[371, 362, 205])).
% 0.60/0.67 tff(373,plain,
% 0.60/0.67 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(374,plain,
% 0.60/0.67 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(375,plain,
% 0.60/0.67 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, ap_parcontractE_sk2q(comb_app(combS, p), q, r))) | (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.60/0.67 tff(376,plain,
% 0.60/0.67 (combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[375, 150, 372])).
% 0.60/0.67 tff(377,plain,
% 0.60/0.67 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_parcontractE_sk2q(comb_app(combS, p), q, r))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(378,plain,
% 0.60/0.67 ($false),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[377, 103, 376])).
% 0.60/0.67 % SZS output end Proof
%------------------------------------------------------------------------------