TSTP Solution File: COL095-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL095-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : COL095-1 : TPTP v8.1.0. Released v2.7.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 30 12:09:07 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.43 % SZS status Unsatisfiable
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(member_type, type, (
% 0.21/0.43 member: ( $i * $i ) > $o)).
% 0.21/0.43 tff(parcontract_type, type, (
% 0.21/0.43 parcontract: $i)).
% 0.21/0.43 tff(pair_type, type, (
% 0.21/0.43 pair: ( $i * $i ) > $i)).
% 0.21/0.43 tff(yp_type, type, (
% 0.21/0.43 yp: $i)).
% 0.21/0.43 tff(p_type, type, (
% 0.21/0.43 p: $i)).
% 0.21/0.43 tff(k1_parcontractD_sk1_type, type, (
% 0.21/0.43 k1_parcontractD_sk1: ( $i * $i ) > $i)).
% 0.21/0.43 tff(comb_app_type, type, (
% 0.21/0.43 comb_app: ( $i * $i ) > $i)).
% 0.21/0.43 tff(combK_type, type, (
% 0.21/0.43 combK: $i)).
% 0.21/0.43 tff(comb_type, type, (
% 0.21/0.43 comb: $i)).
% 0.21/0.43 tff(ap_parcontractE_c2_type, type, (
% 0.21/0.43 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(q_type, type, (
% 0.21/0.43 q: $i)).
% 0.21/0.43 tff(ap_parcontractE_c1_type, type, (
% 0.21/0.43 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(ap_parcontractE_c3_type, type, (
% 0.21/0.43 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(ap_parcontractE_sk1q_type, type, (
% 0.21/0.43 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(ap_parcontractE_sk1p_type, type, (
% 0.21/0.43 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(combS_type, type, (
% 0.21/0.43 combS: $i)).
% 0.21/0.43 tff(ap_parcontractE_c4_type, type, (
% 0.21/0.43 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.21/0.43 tff(ap_parcontractE_sk2q_type, type, (
% 0.21/0.43 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(ap_parcontractE_sk2s_type, type, (
% 0.21/0.43 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (member(p, comb) <=> member(p, comb)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(2,axiom,(member(p, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2h1')).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (member(p, comb)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (^[Q: $i, P: $i] : refl((member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb))) <=> (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb))) <=> ![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.43 tff(6,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb))) <=> ![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (^[Q: $i, P: $i] : rewrite((((~member(P, comb)) | (~member(Q, comb))) | member(comb_app(P, Q), comb)) <=> (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(8,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (((~member(P, comb)) | (~member(Q, comb))) | member(comb_app(P, Q), comb)) <=> ![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.43 tff(9,axiom,(![Q: $i, P: $i] : (((~member(P, comb)) | (~member(Q, comb))) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','comb_intros3')).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.21/0.43 tff(12,plain,(
% 0.21/0.43 ![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[11])).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (member(combK, comb) <=> member(combK, comb)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,axiom,(member(combK, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','comb_intros1')).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 (member(combK, comb)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | (member(comb_app(combK, p), comb) | (~member(p, comb)) | (~member(combK, comb)))) <=> ((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | member(comb_app(combK, p), comb) | (~member(p, comb)) | (~member(combK, comb)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 ((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | (member(comb_app(combK, p), comb) | (~member(p, comb)) | (~member(combK, comb)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 ((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | member(comb_app(combK, p), comb) | (~member(p, comb)) | (~member(combK, comb))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (member(comb_app(combK, p), comb)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[19, 16, 13, 3])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[21])).
% 0.21/0.43 tff(23,plain,
% 0.21/0.43 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(24,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.21/0.43 tff(25,plain,
% 0.21/0.43 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.21/0.43 tff(26,plain,(
% 0.21/0.43 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.43 inference(skolemize,[status(sab)],[25])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(comb_app(combK, p), comb)) | member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(comb_app(combK, p), comb)) | member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(comb_app(combK, p), comb)) | member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(comb_app(combK, p), comb)) | member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[30, 27, 20])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[R: $i, P: $i] : refl(((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R)))) <=> ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R)))) <=> ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R)))) <=> ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(35,axiom,(![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_parcontractD_1')).
% 0.21/0.44 tff(36,plain,
% 0.21/0.44 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.21/0.44 tff(37,plain,(
% 0.21/0.44 ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[36])).
% 0.21/0.44 tff(38,plain,
% 0.21/0.44 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.21/0.44 tff(39,plain,
% 0.21/0.44 (((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | ((~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))))) <=> ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | (~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(40,plain,
% 0.21/0.44 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | ((~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(41,plain,
% 0.21/0.44 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | (~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.21/0.44 tff(42,plain,
% 0.21/0.44 (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[41, 38, 31])).
% 0.21/0.44 tff(43,plain,
% 0.21/0.44 (^[P2: $i, Q2: $i, Q1: $i, P1: $i] : refl(((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2)) <=> ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(44,plain,
% 0.21/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.44 tff(45,plain,
% 0.21/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2)) <=> ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(46,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','app_app2')).
% 0.21/0.44 tff(47,plain,
% 0.21/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.44 tff(48,plain,(
% 0.21/0.44 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.21/0.44 inference(skolemize,[status(sab)],[47])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (p = k1_parcontractD_sk1(p, comb_app(combK, p))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | (~(comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (p = k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (p = k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | (~(comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (p = k1_parcontractD_sk1(p, comb_app(combK, p)))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 (p = k1_parcontractD_sk1(p, comb_app(combK, p))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[52, 49, 42])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (k1_parcontractD_sk1(p, comb_app(combK, p)) = p),
% 0.21/0.44 inference(symmetry,[status(thm)],[53])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, p)),
% 0.21/0.44 inference(symmetry,[status(thm)],[42])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 (ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) <=> ap_parcontractE_c2(comb_app(combK, p), q, yp)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.44 tff(57,plain,
% 0.21/0.44 (ap_parcontractE_c2(comb_app(combK, p), q, yp) <=> ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.44 inference(symmetry,[status(thm)],[56])).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) <=> ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (ap_parcontractE_c1(comb_app(combK, p), q, yp) <=> ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.44 inference(symmetry,[status(thm)],[58])).
% 0.21/0.44 tff(60,assumption,(ap_parcontractE_c1(comb_app(combK, p), q, yp)), introduced(assumption)).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.21/0.44 tff(62,plain,
% 0.21/0.44 (comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q) = comb_app(comb_app(combK, p), q)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.44 tff(63,assumption,(yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)), introduced(assumption)).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (yp = comb_app(comb_app(combK, p), q)),
% 0.21/0.44 inference(transitivity,[status(thm)],[63, 62])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))) = pair(comb_app(comb_app(combK, p), q), p)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[64, 54])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract) <=> member(pair(comb_app(comb_app(combK, p), q), p), parcontract)),
% 0.21/0.44 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (member(pair(comb_app(comb_app(combK, p), q), p), parcontract) <=> member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.21/0.44 inference(symmetry,[status(thm)],[66])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (member(q, comb) <=> member(q, comb)),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(69,axiom,(member(q, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2h2')).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (member(q, comb)),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (^[Q: $i, P: $i] : refl(((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)) <=> ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)) <=> ![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)) <=> ![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(74,plain,
% 0.21/0.45 (^[Q: $i, P: $i] : rewrite((((~member(P, comb)) | (~member(Q, comb))) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)) <=> ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(75,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (((~member(P, comb)) | (~member(Q, comb))) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract)) <=> ![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[74])).
% 0.21/0.45 tff(76,axiom,(![Q: $i, P: $i] : (((~member(P, comb)) | (~member(Q, comb))) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros2')).
% 0.21/0.45 tff(77,plain,
% 0.21/0.45 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.21/0.45 tff(78,plain,
% 0.21/0.45 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[77, 73])).
% 0.21/0.45 tff(79,plain,(
% 0.21/0.45 ![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(skolemize,[status(sab)],[78])).
% 0.21/0.45 tff(80,plain,
% 0.21/0.45 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.21/0.45 tff(81,plain,
% 0.21/0.45 (((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))) <=> ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | (~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (((~member(q, comb)) | (~member(p, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract)) <=> ((~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(q, comb)) | (~member(p, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))) <=> ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[82])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(q, comb)) | (~member(p, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))) <=> ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | (~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))),
% 0.21/0.45 inference(transitivity,[status(thm)],[83, 81])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(q, comb)) | (~member(p, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | (~member(p, comb)) | (~member(q, comb)) | member(pair(comb_app(comb_app(combK, p), q), p), parcontract)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (member(pair(comb_app(comb_app(combK, p), q), p), parcontract)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[86, 80, 3, 70])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[87, 67])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 (^[R: $i, P: $i] : refl(((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract)) <=> ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract)) <=> ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract)) <=> ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(92,axiom,(![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_parcontractD_2')).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.21/0.45 tff(94,plain,(
% 0.21/0.45 ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.21/0.45 inference(skolemize,[status(sab)],[93])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | ((~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract))) <=> ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | (~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | ((~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | (~member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)) | member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[98, 95, 31])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (^[Z: $i] : refl(((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[100])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(103,axiom,(![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2c2')).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.21/0.45 tff(105,plain,(
% 0.21/0.45 ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[104])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)))) <=> ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[109, 106, 99])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[110, 88])).
% 0.21/0.45 tff(112,plain,(~(yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (^[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))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[113])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![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)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(116,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.45 tff(118,plain,(
% 0.21/0.45 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[117])).
% 0.21/0.45 tff(119,plain,
% 0.21/0.45 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[122, 119, 112])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[123, 61])).
% 0.21/0.45 tff(125,plain,(~ap_parcontractE_c1(comb_app(combK, p), q, yp)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(126,assumption,(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), introduced(assumption)).
% 0.21/0.45 tff(127,assumption,(combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), introduced(assumption)).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[128])).
% 0.21/0.45 tff(130,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(131,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_app')).
% 0.21/0.45 tff(132,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.21/0.45 tff(133,plain,(
% 0.21/0.45 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[132])).
% 0.21/0.45 tff(134,plain,
% 0.21/0.45 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.21/0.45 tff(135,plain,
% 0.21/0.45 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(136,plain,
% 0.21/0.45 ($false),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[135, 134, 127])).
% 0.21/0.45 tff(137,plain,(~(combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.45 tff(138,plain,
% 0.21/0.45 (^[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)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(139,plain,
% 0.21/0.45 (![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))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[138])).
% 0.21/0.45 tff(140,plain,
% 0.21/0.45 (![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))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(141,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','app_app1')).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.21/0.46 tff(143,plain,(
% 0.21/0.46 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.46 inference(skolemize,[status(sab)],[142])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[143, 139])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))) | (combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))) | (combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))) | (combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))) | (combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[147, 144, 137, 126])).
% 0.21/0.46 tff(149,plain,(~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (^[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)))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[150])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(153,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.21/0.46 tff(155,plain,(
% 0.21/0.46 ![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))))),
% 0.21/0.46 inference(skolemize,[status(sab)],[154])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (![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))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.21/0.46 tff(157,plain,
% 0.21/0.46 (((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))) <=> ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.21/0.46 tff(160,plain,
% 0.21/0.46 ((~ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[159, 156])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (~ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[160, 149])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) <=> ap_parcontractE_c3(comb_app(combK, p), q, yp)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 (ap_parcontractE_c3(comb_app(combK, p), q, yp) <=> ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.46 inference(symmetry,[status(thm)],[162])).
% 0.21/0.46 tff(164,assumption,(ap_parcontractE_c3(comb_app(combK, p), q, yp)), introduced(assumption)).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.21/0.46 tff(166,assumption,(~ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 ($false),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.21/0.46 tff(168,plain,((~ap_parcontractE_c3(comb_app(combK, p), q, yp)) | ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (~ap_parcontractE_c3(comb_app(combK, p), q, yp)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[168, 161])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 (ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) <=> ap_parcontractE_c4(comb_app(combK, p), q, yp)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[55])).
% 0.21/0.46 tff(171,plain,
% 0.21/0.46 ((~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) <=> (~ap_parcontractE_c4(comb_app(combK, p), q, yp))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[170])).
% 0.21/0.46 tff(172,plain,
% 0.21/0.46 (pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))) = pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[53])).
% 0.21/0.46 tff(173,plain,
% 0.21/0.46 (member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract) <=> member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[172])).
% 0.21/0.46 tff(174,plain,
% 0.21/0.46 (member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract) <=> member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.46 inference(symmetry,[status(thm)],[173])).
% 0.21/0.46 tff(175,assumption,(ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.21/0.46 tff(176,plain,
% 0.21/0.46 (^[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)))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(177,plain,
% 0.21/0.46 (![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))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[176])).
% 0.21/0.46 tff(178,plain,
% 0.21/0.46 (![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))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(179,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.21/0.47 tff(181,plain,(
% 0.21/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.47 inference(skolemize,[status(sab)],[180])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), 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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ((~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[186, 175])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | ((~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))) <=> ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | (~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(189,plain,
% 0.21/0.47 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | ((~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(190,plain,
% 0.21/0.47 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))) | (~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.47 tff(191,plain,
% 0.21/0.47 (member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[190, 95, 187])).
% 0.21/0.47 tff(192,plain,
% 0.21/0.47 (member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[191, 174])).
% 0.21/0.47 tff(193,plain,
% 0.21/0.47 (^[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)))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(194,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[193])).
% 0.21/0.47 tff(195,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(196,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.21/0.47 tff(197,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.21/0.47 tff(198,plain,(
% 0.21/0.47 ![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))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[197])).
% 0.21/0.47 tff(199,plain,
% 0.21/0.47 (![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))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[198, 194])).
% 0.21/0.47 tff(200,plain,
% 0.21/0.47 (((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))) <=> ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(201,plain,
% 0.21/0.47 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(202,plain,
% 0.21/0.47 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.21/0.47 tff(203,plain,
% 0.21/0.47 ((~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.21/0.47 tff(204,plain,
% 0.21/0.47 (yp = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[203, 175])).
% 0.21/0.47 tff(205,plain,
% 0.21/0.47 (comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) = yp),
% 0.21/0.47 inference(symmetry,[status(thm)],[204])).
% 0.21/0.47 tff(206,plain,
% 0.21/0.47 (((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | ((~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | (ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) = comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))))) <=> ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | (~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | (ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) = comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | ((~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | (ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) = comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 ((~![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))) | (~member(pair(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | (ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) = comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 (ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp) = comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[208, 38, 187])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))) = ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.48 inference(symmetry,[status(thm)],[209])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 (comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) = comb_app(ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[210])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 (comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) = yp),
% 0.21/0.48 inference(transitivity,[status(thm)],[211, 205])).
% 0.21/0.48 tff(213,plain,
% 0.21/0.48 (pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))) = pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[212])).
% 0.21/0.48 tff(214,plain,
% 0.21/0.48 (member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract) <=> member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[213])).
% 0.21/0.48 tff(215,plain,
% 0.21/0.48 (^[B: $i, A: $i] : refl(((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ((~member(pair(A, B), parcontract)) | member(B, comb)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(216,plain,
% 0.21/0.48 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[215])).
% 0.21/0.48 tff(217,plain,
% 0.21/0.48 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(218,axiom,(![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_combD2')).
% 0.21/0.48 tff(219,plain,
% 0.21/0.48 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.21/0.48 tff(220,plain,(
% 0.21/0.48 ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.21/0.48 inference(skolemize,[status(sab)],[219])).
% 0.21/0.48 tff(221,plain,
% 0.21/0.48 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.21/0.48 tff(222,plain,
% 0.21/0.48 (((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb))) <=> ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(223,plain,
% 0.21/0.48 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(224,plain,
% 0.21/0.48 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(k1_parcontractD_sk1(p, comb_app(combK, p)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.21/0.48 tff(225,plain,
% 0.21/0.48 (member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[224, 221, 191])).
% 0.21/0.48 tff(226,plain,
% 0.21/0.48 (^[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)))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(227,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.48 tff(228,plain,
% 0.21/0.48 (![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))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(229,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.21/0.48 tff(230,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.48 tff(231,plain,(
% 0.21/0.48 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.48 inference(skolemize,[status(sab)],[230])).
% 0.21/0.48 tff(232,plain,
% 0.21/0.48 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[231, 227])).
% 0.21/0.48 tff(233,plain,
% 0.21/0.48 (((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), 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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(234,plain,
% 0.21/0.48 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(235,plain,
% 0.21/0.48 ((~![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(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.21/0.48 tff(236,plain,
% 0.21/0.48 ((~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[235, 232])).
% 0.21/0.48 tff(237,plain,
% 0.21/0.48 (member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[236, 175])).
% 0.21/0.48 tff(238,plain,
% 0.21/0.48 (((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb))) <=> ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(239,plain,
% 0.21/0.48 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(240,plain,
% 0.21/0.48 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)) | member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.21/0.48 tff(241,plain,
% 0.21/0.48 (member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[240, 221, 237])).
% 0.21/0.48 tff(242,plain,
% 0.21/0.48 (((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)) | (~member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)) | member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))) <=> ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | (~member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)) | (~member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)) | member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(243,plain,
% 0.21/0.48 ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | ((~member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)) | (~member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)) | member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(244,plain,
% 0.21/0.48 ((~![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))) | (~member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)) | (~member(k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), comb)) | member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.21/0.48 tff(245,plain,
% 0.21/0.48 (member(pair(comb_app(comb_app(combK, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[244, 80, 241, 225])).
% 0.21/0.48 tff(246,plain,
% 0.21/0.48 (member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[245, 214])).
% 0.21/0.48 tff(247,plain,
% 0.21/0.48 (((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)))) <=> ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(248,plain,
% 0.21/0.48 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(249,plain,
% 0.21/0.48 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.21/0.48 tff(250,plain,
% 0.21/0.48 ((~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[249, 106])).
% 0.21/0.48 tff(251,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[250, 246, 192])).
% 0.21/0.48 tff(252,plain,(~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(253,plain,
% 0.21/0.49 (~ap_parcontractE_c4(comb_app(combK, p), q, yp)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[252, 171])).
% 0.21/0.49 tff(254,plain,
% 0.21/0.49 (member(pair(comb_app(comb_app(combK, p), q), yp), parcontract) <=> member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(255,axiom,(member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2c1')).
% 0.21/0.49 tff(256,plain,
% 0.21/0.49 (member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.49 tff(257,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(258,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[257])).
% 0.21/0.49 tff(259,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(260,plain,
% 0.21/0.49 (^[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)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(261,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[260])).
% 0.21/0.49 tff(262,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.21/0.49 tff(263,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.21/0.49 tff(264,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.21/0.49 tff(265,plain,(
% 0.21/0.49 ![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)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[264])).
% 0.21/0.49 tff(266,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.21/0.49 tff(267,plain,
% 0.21/0.49 (((~![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(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp))) <=> ((~![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(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(268,plain,
% 0.21/0.49 ((ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp) | (~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract))) <=> ((~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(269,plain,
% 0.21/0.49 (((~![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(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp) | (~member(pair(comb_app(comb_app(combK, p), q), yp), 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(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[268])).
% 0.21/0.49 tff(270,plain,
% 0.21/0.49 (((~![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(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp) | (~member(pair(comb_app(comb_app(combK, p), q), yp), 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(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp))),
% 0.21/0.49 inference(transitivity,[status(thm)],[269, 267])).
% 0.21/0.49 tff(271,plain,
% 0.21/0.49 ((~![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(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp) | (~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(272,plain,
% 0.21/0.49 ((~![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(combK, p), q), yp), parcontract)) | ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.21/0.49 tff(273,plain,
% 0.21/0.49 (ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[272, 266, 256])).
% 0.21/0.49 tff(274,plain,
% 0.21/0.49 (ap_parcontractE_c3(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[273, 253])).
% 0.21/0.49 tff(275,plain,
% 0.21/0.49 (ap_parcontractE_c2(comb_app(combK, p), q, yp)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[274, 169, 125])).
% 0.21/0.49 tff(276,plain,
% 0.21/0.49 (ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[275, 57])).
% 0.21/0.49 tff(277,plain,
% 0.21/0.49 (^[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))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(278,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[277])).
% 0.21/0.49 tff(279,plain,
% 0.21/0.49 (![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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(280,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.21/0.49 tff(281,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.21/0.49 tff(282,plain,(
% 0.21/0.49 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[281])).
% 0.21/0.49 tff(283,plain,
% 0.21/0.49 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[282, 278])).
% 0.21/0.49 tff(284,plain,
% 0.21/0.49 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(285,plain,
% 0.21/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(286,plain,
% 0.21/0.49 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.21/0.49 tff(287,plain,
% 0.21/0.49 ((~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[286, 283])).
% 0.21/0.49 tff(288,plain,
% 0.21/0.49 (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[287, 276])).
% 0.21/0.49 tff(289,assumption,(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)), introduced(assumption)).
% 0.21/0.49 tff(290,assumption,(~(k1_parcontractD_sk1(p, comb_app(combK, p)) = yp)), introduced(assumption)).
% 0.21/0.49 tff(291,plain,
% 0.21/0.49 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))) | (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))) | (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(292,plain,
% 0.21/0.49 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))) | (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(293,plain,
% 0.21/0.49 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))) | (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.21/0.49 tff(294,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[293, 49, 290, 289])).
% 0.21/0.49 tff(295,plain,((~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))) | (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(296,plain,
% 0.21/0.49 (k1_parcontractD_sk1(p, comb_app(combK, p)) = yp),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[295, 288])).
% 0.21/0.49 tff(297,plain,
% 0.21/0.49 (yp = k1_parcontractD_sk1(p, comb_app(combK, p))),
% 0.21/0.49 inference(symmetry,[status(thm)],[296])).
% 0.21/0.49 tff(298,plain,
% 0.21/0.49 (yp = p),
% 0.21/0.49 inference(transitivity,[status(thm)],[297, 54])).
% 0.21/0.49 tff(299,plain,
% 0.21/0.49 (pair(p, yp) = pair(p, p)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[298])).
% 0.21/0.49 tff(300,plain,
% 0.21/0.49 (member(pair(p, yp), parcontract) <=> member(pair(p, p), parcontract)),
% 0.21/0.49 inference(monotonicity,[status(thm)],[299])).
% 0.21/0.49 tff(301,plain,
% 0.21/0.49 (member(pair(p, p), parcontract) <=> member(pair(p, yp), parcontract)),
% 0.21/0.49 inference(symmetry,[status(thm)],[300])).
% 0.21/0.49 tff(302,plain,
% 0.21/0.49 (((~![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))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(303,plain,
% 0.21/0.49 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(304,plain,
% 0.21/0.49 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.21/0.49 tff(305,plain,
% 0.21/0.49 (member(pair(p, p), parcontract)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[304, 27, 3])).
% 0.21/0.49 tff(306,plain,
% 0.21/0.49 (member(pair(p, yp), parcontract)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.21/0.49 tff(307,plain,
% 0.21/0.49 (((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)) | member(yp, comb))) <=> ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)) | member(yp, comb))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(308,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | ((~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)) | member(yp, comb))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(309,plain,
% 0.21/0.49 ((~![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))) | (~member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)) | member(yp, comb)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.21/0.49 tff(310,plain,
% 0.21/0.49 (member(yp, comb)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[309, 221, 256])).
% 0.21/0.49 tff(311,plain,
% 0.21/0.49 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(yp, comb)) | member(pair(yp, yp), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(yp, comb)) | member(pair(yp, yp), parcontract))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(312,plain,
% 0.21/0.49 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(yp, comb)) | member(pair(yp, yp), parcontract))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(313,plain,
% 0.21/0.49 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(yp, comb)) | member(pair(yp, yp), parcontract)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.21/0.49 tff(314,plain,
% 0.21/0.49 (member(pair(yp, yp), parcontract)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[313, 27, 310])).
% 0.21/0.49 tff(315,plain,
% 0.21/0.49 (((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract)))) <=> ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(316,plain,
% 0.21/0.49 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(317,plain,
% 0.21/0.50 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.21/0.50 tff(318,plain,
% 0.21/0.50 (~member(pair(p, yp), parcontract)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[317, 106, 314])).
% 0.21/0.50 tff(319,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[318, 306])).
% 0.21/0.50 % SZS output end Proof
%------------------------------------------------------------------------------