TSTP Solution File: COL095-2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL095-2 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 0.62s 0.66s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL095-2 : TPTP v8.1.0. Released v2.7.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 11:34:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.62/0.66 % SZS status Unsatisfiable
% 0.62/0.66 % SZS output start Proof
% 0.62/0.66 tff(member_type, type, (
% 0.62/0.66 member: ( $i * $i ) > $o)).
% 0.62/0.66 tff(parcontract_type, type, (
% 0.62/0.66 parcontract: $i)).
% 0.62/0.66 tff(pair_type, type, (
% 0.62/0.66 pair: ( $i * $i ) > $i)).
% 0.62/0.66 tff(yp_type, type, (
% 0.62/0.66 yp: $i)).
% 0.62/0.66 tff(p_type, type, (
% 0.62/0.66 p: $i)).
% 0.62/0.66 tff(k1_parcontractD_sk1_type, type, (
% 0.62/0.66 k1_parcontractD_sk1: ( $i * $i ) > $i)).
% 0.62/0.66 tff(comb_app_type, type, (
% 0.62/0.66 comb_app: ( $i * $i ) > $i)).
% 0.62/0.66 tff(combK_type, type, (
% 0.62/0.66 combK: $i)).
% 0.62/0.66 tff(comb_type, type, (
% 0.62/0.66 comb: $i)).
% 0.62/0.66 tff(ap_parcontractE_c2_type, type, (
% 0.62/0.66 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.62/0.66 tff(q_type, type, (
% 0.62/0.66 q: $i)).
% 0.62/0.66 tff(ap_parcontractE_c4_type, type, (
% 0.62/0.66 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.62/0.66 tff(ap_parcontractE_sk2q_type, type, (
% 0.62/0.66 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.62/0.66 tff(ap_parcontractE_sk2s_type, type, (
% 0.62/0.66 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.62/0.66 tff(ap_parcontractE_c1_type, type, (
% 0.62/0.66 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.62/0.66 tff(ap_parcontractE_c3_type, type, (
% 0.62/0.66 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.62/0.66 tff(ap_parcontractE_sk1q_type, type, (
% 0.62/0.66 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.62/0.66 tff(ap_parcontractE_sk1p_type, type, (
% 0.62/0.66 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.62/0.66 tff(combS_type, type, (
% 0.62/0.66 combS: $i)).
% 0.62/0.66 tff(1,plain,
% 0.62/0.66 (member(p, comb) <=> member(p, comb)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(2,axiom,(member(p, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2h1')).
% 0.62/0.66 tff(3,plain,
% 0.62/0.66 (member(p, comb)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.62/0.66 tff(4,plain,
% 0.62/0.66 (^[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))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(5,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[4])).
% 0.62/0.66 tff(6,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(7,plain,
% 0.62/0.66 (^[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))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(8,plain,
% 0.62/0.66 (![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)))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[7])).
% 0.62/0.66 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')).
% 0.62/0.66 tff(10,plain,
% 0.62/0.66 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.62/0.66 tff(11,plain,
% 0.62/0.66 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.62/0.66 tff(12,plain,(
% 0.62/0.66 ![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.62/0.66 inference(skolemize,[status(sab)],[11])).
% 0.62/0.66 tff(13,plain,
% 0.62/0.66 (![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.62/0.66 tff(14,plain,
% 0.62/0.66 (member(combK, comb) <=> member(combK, comb)),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(15,axiom,(member(combK, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','comb_intros1')).
% 0.62/0.66 tff(16,plain,
% 0.62/0.66 (member(combK, comb)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.62/0.66 tff(17,plain,
% 0.62/0.66 (((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | ((~member(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb))) <=> ((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | (~member(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(18,plain,
% 0.62/0.66 ((member(comb_app(combK, p), comb) | (~member(p, comb)) | (~member(combK, comb))) <=> ((~member(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(19,plain,
% 0.62/0.66 (((~![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(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb)))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[18])).
% 0.62/0.66 tff(20,plain,
% 0.62/0.66 (((~![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(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb))),
% 0.62/0.66 inference(transitivity,[status(thm)],[19, 17])).
% 0.62/0.66 tff(21,plain,
% 0.62/0.66 ((~![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)))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(22,plain,
% 0.62/0.66 ((~![Q: $i, P: $i] : (member(comb_app(P, Q), comb) | (~member(Q, comb)) | (~member(P, comb)))) | (~member(combK, comb)) | (~member(p, comb)) | member(comb_app(combK, p), comb)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.62/0.66 tff(23,plain,
% 0.62/0.66 (member(comb_app(combK, p), comb)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[22, 16, 13, 3])).
% 0.62/0.66 tff(24,plain,
% 0.62/0.66 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(25,plain,
% 0.62/0.66 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[24])).
% 0.62/0.66 tff(26,plain,
% 0.62/0.66 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(27,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.62/0.66 tff(28,plain,
% 0.62/0.66 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.62/0.66 tff(29,plain,(
% 0.62/0.66 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.62/0.66 inference(skolemize,[status(sab)],[28])).
% 0.62/0.66 tff(30,plain,
% 0.62/0.66 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.62/0.66 tff(31,plain,
% 0.62/0.66 (((~![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))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(32,plain,
% 0.62/0.66 ((~![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))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(33,plain,
% 0.62/0.66 ((~![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)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.62/0.66 tff(34,plain,
% 0.62/0.66 (member(pair(comb_app(combK, p), comb_app(combK, p)), parcontract)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[33, 30, 23])).
% 0.62/0.66 tff(35,plain,
% 0.62/0.66 (^[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)))))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(36,plain,
% 0.62/0.66 (![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))))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[35])).
% 0.62/0.66 tff(37,plain,
% 0.62/0.66 (![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))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(38,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')).
% 0.62/0.66 tff(39,plain,
% 0.62/0.66 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.62/0.66 tff(40,plain,(
% 0.62/0.66 ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.62/0.66 inference(skolemize,[status(sab)],[39])).
% 0.62/0.66 tff(41,plain,
% 0.62/0.66 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | (R = comb_app(combK, k1_parcontractD_sk1(P, R))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[40, 36])).
% 0.62/0.66 tff(42,plain,
% 0.62/0.66 (((~![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)))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(43,plain,
% 0.62/0.66 ((~![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)))))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(44,plain,
% 0.62/0.66 ((~![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))))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.62/0.66 tff(45,plain,
% 0.62/0.66 (comb_app(combK, p) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[44, 41, 34])).
% 0.62/0.66 tff(46,plain,
% 0.62/0.66 (^[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)))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(47,plain,
% 0.62/0.66 (![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))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[46])).
% 0.62/0.66 tff(48,plain,
% 0.62/0.66 (![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))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(49,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')).
% 0.62/0.66 tff(50,plain,
% 0.62/0.66 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.62/0.66 tff(51,plain,(
% 0.62/0.66 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.62/0.66 inference(skolemize,[status(sab)],[50])).
% 0.62/0.66 tff(52,plain,
% 0.62/0.66 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.62/0.66 tff(53,plain,
% 0.62/0.66 (((~![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))))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(54,plain,
% 0.62/0.66 ((~![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))))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(55,plain,
% 0.62/0.66 ((~![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)))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.62/0.66 tff(56,plain,
% 0.62/0.66 (p = k1_parcontractD_sk1(p, comb_app(combK, p))),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[55, 52, 45])).
% 0.62/0.66 tff(57,plain,
% 0.62/0.66 (k1_parcontractD_sk1(p, comb_app(combK, p)) = p),
% 0.62/0.66 inference(symmetry,[status(thm)],[56])).
% 0.62/0.66 tff(58,plain,
% 0.62/0.66 (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, p)),
% 0.62/0.66 inference(symmetry,[status(thm)],[45])).
% 0.62/0.66 tff(59,plain,
% 0.62/0.66 (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)),
% 0.62/0.66 inference(monotonicity,[status(thm)],[58])).
% 0.62/0.66 tff(60,plain,
% 0.62/0.66 ((~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))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[59])).
% 0.62/0.66 tff(61,plain,
% 0.62/0.66 (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)))),
% 0.62/0.66 inference(monotonicity,[status(thm)],[56])).
% 0.62/0.66 tff(62,plain,
% 0.62/0.66 (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)),
% 0.62/0.66 inference(monotonicity,[status(thm)],[61])).
% 0.62/0.66 tff(63,plain,
% 0.62/0.66 (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)),
% 0.62/0.66 inference(symmetry,[status(thm)],[62])).
% 0.62/0.66 tff(64,assumption,(ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.62/0.66 tff(65,plain,
% 0.62/0.66 (^[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)))),
% 0.62/0.66 inference(bind,[status(th)],[])).
% 0.62/0.66 tff(66,plain,
% 0.62/0.66 (![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))),
% 0.62/0.66 inference(quant_intro,[status(thm)],[65])).
% 0.62/0.66 tff(67,plain,
% 0.62/0.66 (![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))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(68,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')).
% 0.62/0.66 tff(69,plain,
% 0.62/0.66 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.62/0.66 tff(70,plain,(
% 0.62/0.66 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.62/0.66 inference(skolemize,[status(sab)],[69])).
% 0.62/0.66 tff(71,plain,
% 0.62/0.66 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.62/0.66 tff(72,plain,
% 0.62/0.66 (((~![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))),
% 0.62/0.66 inference(rewrite,[status(thm)],[])).
% 0.62/0.66 tff(73,plain,
% 0.62/0.66 ((~![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))),
% 0.62/0.66 inference(quant_inst,[status(thm)],[])).
% 0.62/0.66 tff(74,plain,
% 0.62/0.66 ((~![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)),
% 0.62/0.66 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.62/0.66 tff(75,plain,
% 0.62/0.66 ((~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)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[74, 71])).
% 0.62/0.66 tff(76,plain,
% 0.62/0.66 (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)),
% 0.62/0.66 inference(unit_resolution,[status(thm)],[75, 64])).
% 0.62/0.67 tff(77,plain,
% 0.62/0.67 (^[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)))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(78,plain,
% 0.62/0.67 (![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))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[77])).
% 0.62/0.67 tff(79,plain,
% 0.62/0.67 (![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))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(80,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')).
% 0.62/0.67 tff(81,plain,
% 0.62/0.67 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.62/0.67 tff(82,plain,(
% 0.62/0.67 ![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.62/0.67 inference(skolemize,[status(sab)],[81])).
% 0.62/0.67 tff(83,plain,
% 0.62/0.67 (![R: $i, P: $i] : ((~member(pair(comb_app(combK, P), R), parcontract)) | member(pair(P, k1_parcontractD_sk1(P, R)), parcontract))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.62/0.67 tff(84,plain,
% 0.62/0.67 (((~![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))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(85,plain,
% 0.62/0.67 ((~![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))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(86,plain,
% 0.62/0.67 ((~![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)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.62/0.67 tff(87,plain,
% 0.62/0.67 (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)),
% 0.62/0.67 inference(unit_resolution,[status(thm)],[86, 83, 76])).
% 0.62/0.67 tff(88,plain,
% 0.62/0.67 (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)),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[87, 63])).
% 0.62/0.67 tff(89,plain,
% 0.62/0.67 (^[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)))))),
% 0.62/0.67 inference(bind,[status(th)],[])).
% 0.62/0.67 tff(90,plain,
% 0.62/0.67 (![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))))),
% 0.62/0.67 inference(quant_intro,[status(thm)],[89])).
% 0.62/0.67 tff(91,plain,
% 0.62/0.67 (![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))))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(92,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')).
% 0.62/0.67 tff(93,plain,
% 0.62/0.67 (![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))))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.62/0.67 tff(94,plain,(
% 0.62/0.67 ![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))))),
% 0.62/0.67 inference(skolemize,[status(sab)],[93])).
% 0.62/0.67 tff(95,plain,
% 0.62/0.67 (![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))))),
% 0.62/0.67 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.62/0.67 tff(96,plain,
% 0.62/0.67 (((~![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))))),
% 0.62/0.67 inference(rewrite,[status(thm)],[])).
% 0.62/0.67 tff(97,plain,
% 0.62/0.67 ((~![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))))),
% 0.62/0.67 inference(quant_inst,[status(thm)],[])).
% 0.62/0.67 tff(98,plain,
% 0.62/0.67 ((~![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)))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.67/0.67 tff(99,plain,
% 0.67/0.67 ((~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)))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.67/0.67 tff(100,plain,
% 0.67/0.67 (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))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[99, 64])).
% 0.67/0.67 tff(101,plain,
% 0.67/0.67 (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),
% 0.67/0.67 inference(symmetry,[status(thm)],[100])).
% 0.67/0.67 tff(102,plain,
% 0.67/0.67 (((~![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)))))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(103,plain,
% 0.67/0.67 ((~![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)))))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(104,plain,
% 0.67/0.67 ((~![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))))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.67/0.67 tff(105,plain,
% 0.67/0.67 (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)))),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[104, 41, 76])).
% 0.67/0.67 tff(106,plain,
% 0.67/0.67 (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)),
% 0.67/0.67 inference(symmetry,[status(thm)],[105])).
% 0.67/0.67 tff(107,plain,
% 0.67/0.67 (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))),
% 0.67/0.67 inference(monotonicity,[status(thm)],[106])).
% 0.67/0.67 tff(108,plain,
% 0.67/0.67 (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),
% 0.67/0.67 inference(transitivity,[status(thm)],[107, 101])).
% 0.67/0.67 tff(109,plain,
% 0.67/0.67 (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)))),
% 0.67/0.67 inference(monotonicity,[status(thm)],[108])).
% 0.67/0.67 tff(110,plain,
% 0.67/0.67 (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)),
% 0.67/0.67 inference(monotonicity,[status(thm)],[109])).
% 0.67/0.67 tff(111,plain,
% 0.67/0.67 (^[B: $i, A: $i] : refl(((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ((~member(pair(A, B), parcontract)) | member(B, comb)))),
% 0.67/0.67 inference(bind,[status(th)],[])).
% 0.67/0.67 tff(112,plain,
% 0.67/0.67 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.67/0.67 inference(quant_intro,[status(thm)],[111])).
% 0.67/0.67 tff(113,plain,
% 0.67/0.67 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb)) <=> ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(114,axiom,(![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_combD2')).
% 0.67/0.67 tff(115,plain,
% 0.67/0.67 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.67/0.67 tff(116,plain,(
% 0.67/0.67 ![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.67/0.67 inference(skolemize,[status(sab)],[115])).
% 0.67/0.67 tff(117,plain,
% 0.67/0.67 (![B: $i, A: $i] : ((~member(pair(A, B), parcontract)) | member(B, comb))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.67/0.67 tff(118,plain,
% 0.67/0.67 (((~![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))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(119,plain,
% 0.67/0.67 ((~![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))),
% 0.67/0.67 inference(quant_inst,[status(thm)],[])).
% 0.67/0.67 tff(120,plain,
% 0.67/0.67 ((~![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)),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.67/0.67 tff(121,plain,
% 0.67/0.67 (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)),
% 0.67/0.67 inference(unit_resolution,[status(thm)],[120, 117, 87])).
% 0.67/0.67 tff(122,plain,
% 0.67/0.67 (^[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)))),
% 0.67/0.67 inference(bind,[status(th)],[])).
% 0.67/0.67 tff(123,plain,
% 0.67/0.67 (![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))),
% 0.67/0.67 inference(quant_intro,[status(thm)],[122])).
% 0.67/0.67 tff(124,plain,
% 0.67/0.67 (![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))),
% 0.67/0.67 inference(rewrite,[status(thm)],[])).
% 0.67/0.67 tff(125,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')).
% 0.67/0.67 tff(126,plain,
% 0.67/0.67 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.67/0.67 tff(127,plain,(
% 0.67/0.67 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.67/0.67 inference(skolemize,[status(sab)],[126])).
% 0.67/0.67 tff(128,plain,
% 0.67/0.67 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.67/0.67 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.67/0.67 tff(129,plain,
% 0.67/0.67 (((~![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(130,plain,
% 0.67/0.68 ((~![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))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(131,plain,
% 0.67/0.68 ((~![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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.67/0.68 tff(132,plain,
% 0.67/0.68 ((~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)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.67/0.68 tff(133,plain,
% 0.67/0.68 (member(pair(q, ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), parcontract)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[132, 64])).
% 0.67/0.68 tff(134,plain,
% 0.67/0.68 (((~![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(135,plain,
% 0.67/0.68 ((~![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))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(136,plain,
% 0.67/0.68 ((~![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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.67/0.68 tff(137,plain,
% 0.67/0.68 (member(ap_parcontractE_sk2s(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp), comb)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[136, 117, 133])).
% 0.67/0.68 tff(138,plain,
% 0.67/0.68 (^[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)))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(139,plain,
% 0.67/0.68 (![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))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[138])).
% 0.67/0.68 tff(140,plain,
% 0.67/0.68 (![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(141,plain,
% 0.67/0.68 (^[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)))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(142,plain,
% 0.67/0.68 (![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))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[141])).
% 0.67/0.68 tff(143,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')).
% 0.67/0.68 tff(144,plain,
% 0.67/0.68 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.67/0.68 tff(145,plain,
% 0.67/0.68 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.67/0.68 tff(146,plain,(
% 0.67/0.68 ![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.67/0.68 inference(skolemize,[status(sab)],[145])).
% 0.67/0.68 tff(147,plain,
% 0.67/0.68 (![Q: $i, P: $i] : ((~member(Q, comb)) | (~member(P, comb)) | member(pair(comb_app(comb_app(combK, P), Q), P), parcontract))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.67/0.68 tff(148,plain,
% 0.67/0.68 (((~![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(149,plain,
% 0.67/0.68 ((~![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))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(150,plain,
% 0.67/0.68 ((~![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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.67/0.68 tff(151,plain,
% 0.67/0.68 (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)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[150, 147, 137, 121])).
% 0.67/0.68 tff(152,plain,
% 0.67/0.68 (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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[151, 110])).
% 0.67/0.68 tff(153,plain,
% 0.67/0.68 (^[Z: $i] : refl(((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))))),
% 0.67/0.68 inference(bind,[status(th)],[])).
% 0.67/0.68 tff(154,plain,
% 0.67/0.68 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.67/0.68 inference(quant_intro,[status(thm)],[153])).
% 0.67/0.68 tff(155,plain,
% 0.67/0.68 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract))) <=> ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(156,axiom,(![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2c2')).
% 0.67/0.68 tff(157,plain,
% 0.67/0.68 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.67/0.68 tff(158,plain,(
% 0.67/0.68 ![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.67/0.68 inference(skolemize,[status(sab)],[157])).
% 0.67/0.68 tff(159,plain,
% 0.67/0.68 (![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.67/0.68 tff(160,plain,
% 0.67/0.68 (((~![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)))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(161,plain,
% 0.67/0.68 ((~![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)))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(162,plain,
% 0.67/0.68 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.67/0.68 tff(163,plain,
% 0.67/0.68 ((~member(pair(p, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(k1_parcontractD_sk1(p, comb_app(combK, p)), ap_parcontractE_sk2q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), parcontract))),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.67/0.68 tff(164,plain,
% 0.67/0.68 ($false),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[163, 152, 88])).
% 0.67/0.68 tff(165,plain,(~ap_parcontractE_c4(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.68 tff(166,plain,
% 0.67/0.68 (~ap_parcontractE_c4(comb_app(combK, p), q, yp)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[165, 60])).
% 0.67/0.68 tff(167,assumption,(comb_app(comb_app(combK, p), q) = yp), introduced(assumption)).
% 0.67/0.68 tff(168,plain,
% 0.67/0.68 (yp = comb_app(comb_app(combK, p), q)),
% 0.67/0.68 inference(symmetry,[status(thm)],[167])).
% 0.67/0.68 tff(169,plain,
% 0.67/0.68 (pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))) = pair(comb_app(comb_app(combK, p), q), p)),
% 0.67/0.68 inference(monotonicity,[status(thm)],[168, 57])).
% 0.67/0.68 tff(170,plain,
% 0.67/0.68 (member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract) <=> member(pair(comb_app(comb_app(combK, p), q), p), parcontract)),
% 0.67/0.68 inference(monotonicity,[status(thm)],[169])).
% 0.67/0.68 tff(171,plain,
% 0.67/0.68 (member(pair(comb_app(comb_app(combK, p), q), p), parcontract) <=> member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.67/0.68 inference(symmetry,[status(thm)],[170])).
% 0.67/0.68 tff(172,plain,
% 0.67/0.68 (member(q, comb) <=> member(q, comb)),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(173,axiom,(member(q, comb)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2h2')).
% 0.67/0.68 tff(174,plain,
% 0.67/0.68 (member(q, comb)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.67/0.68 tff(175,plain,
% 0.67/0.68 (((~![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(176,plain,
% 0.67/0.68 (((~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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(177,plain,
% 0.67/0.68 (((~![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)))),
% 0.67/0.68 inference(monotonicity,[status(thm)],[176])).
% 0.67/0.68 tff(178,plain,
% 0.67/0.68 (((~![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))),
% 0.67/0.68 inference(transitivity,[status(thm)],[177, 175])).
% 0.67/0.68 tff(179,plain,
% 0.67/0.68 ((~![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))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(180,plain,
% 0.67/0.68 ((~![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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.67/0.68 tff(181,plain,
% 0.67/0.68 (member(pair(comb_app(comb_app(combK, p), q), p), parcontract)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[180, 147, 3, 174])).
% 0.67/0.68 tff(182,plain,
% 0.67/0.68 (member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[181, 171])).
% 0.67/0.68 tff(183,plain,
% 0.67/0.68 (((~![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))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(184,plain,
% 0.67/0.68 ((~![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))),
% 0.67/0.68 inference(quant_inst,[status(thm)],[])).
% 0.67/0.68 tff(185,plain,
% 0.67/0.68 ((~![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)),
% 0.67/0.68 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.67/0.68 tff(186,plain,
% 0.67/0.68 (member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.67/0.68 inference(unit_resolution,[status(thm)],[185, 83, 34])).
% 0.67/0.68 tff(187,plain,
% 0.67/0.68 (((~![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)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(188,plain,
% 0.67/0.69 ((~![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)))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(189,plain,
% 0.67/0.69 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)) | (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.67/0.69 tff(190,plain,
% 0.67/0.69 (~member(pair(yp, k1_parcontractD_sk1(p, comb_app(combK, p))), parcontract)),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[189, 159, 186])).
% 0.67/0.69 tff(191,plain,
% 0.67/0.69 ($false),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[190, 182])).
% 0.67/0.69 tff(192,plain,(~(comb_app(comb_app(combK, p), q) = yp)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.69 tff(193,assumption,(ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.67/0.69 tff(194,plain,
% 0.67/0.69 ((yp = comb_app(comb_app(combK, p), q)) <=> (comb_app(comb_app(combK, p), q) = yp)),
% 0.67/0.69 inference(commutativity,[status(thm)],[])).
% 0.67/0.69 tff(195,plain,
% 0.67/0.69 (comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q) = comb_app(comb_app(combK, p), q)),
% 0.67/0.69 inference(monotonicity,[status(thm)],[58])).
% 0.67/0.69 tff(196,plain,
% 0.67/0.69 ((yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)) <=> (yp = comb_app(comb_app(combK, p), q))),
% 0.67/0.69 inference(monotonicity,[status(thm)],[195])).
% 0.67/0.69 tff(197,plain,
% 0.67/0.69 ((yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)) <=> (comb_app(comb_app(combK, p), q) = yp)),
% 0.67/0.69 inference(transitivity,[status(thm)],[196, 194])).
% 0.67/0.69 tff(198,plain,
% 0.67/0.69 ((comb_app(comb_app(combK, p), q) = yp) <=> (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))),
% 0.67/0.69 inference(symmetry,[status(thm)],[197])).
% 0.67/0.69 tff(199,plain,
% 0.67/0.69 ((~(comb_app(comb_app(combK, p), q) = yp)) <=> (~(yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q)))),
% 0.67/0.69 inference(monotonicity,[status(thm)],[198])).
% 0.67/0.69 tff(200,assumption,(~(comb_app(comb_app(combK, p), q) = yp)), introduced(assumption)).
% 0.67/0.69 tff(201,plain,
% 0.67/0.69 (~(yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.67/0.69 tff(202,plain,
% 0.67/0.69 (^[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))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(203,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[202])).
% 0.67/0.69 tff(204,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(205,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')).
% 0.67/0.69 tff(206,plain,
% 0.67/0.69 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.67/0.69 tff(207,plain,(
% 0.67/0.69 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.67/0.69 inference(skolemize,[status(sab)],[206])).
% 0.67/0.69 tff(208,plain,
% 0.67/0.69 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.67/0.69 tff(209,plain,
% 0.67/0.69 (((~![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)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(210,plain,
% 0.67/0.69 ((~![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)))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(211,plain,
% 0.67/0.69 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.67/0.69 tff(212,plain,
% 0.67/0.69 ((~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (yp = comb_app(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q))),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[211, 208])).
% 0.67/0.69 tff(213,plain,
% 0.67/0.69 ($false),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[212, 201, 193])).
% 0.67/0.69 tff(214,plain,((~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(comb_app(combK, p), q) = yp)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.69 tff(215,plain,
% 0.67/0.69 (~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[214, 192])).
% 0.67/0.69 tff(216,plain,
% 0.67/0.69 (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)),
% 0.67/0.69 inference(monotonicity,[status(thm)],[58])).
% 0.67/0.69 tff(217,plain,
% 0.67/0.69 (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)),
% 0.67/0.69 inference(symmetry,[status(thm)],[216])).
% 0.67/0.69 tff(218,assumption,(ap_parcontractE_c1(comb_app(combK, p), q, yp)), introduced(assumption)).
% 0.67/0.69 tff(219,plain,
% 0.67/0.69 (ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.67/0.69 tff(220,assumption,(~ap_parcontractE_c1(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.67/0.69 tff(221,plain,
% 0.67/0.69 ($false),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.67/0.69 tff(222,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.69 tff(223,plain,
% 0.67/0.69 (~ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[222, 215])).
% 0.67/0.69 tff(224,plain,
% 0.67/0.69 (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)),
% 0.67/0.69 inference(monotonicity,[status(thm)],[58])).
% 0.67/0.69 tff(225,plain,
% 0.67/0.69 ((~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))),
% 0.67/0.69 inference(monotonicity,[status(thm)],[224])).
% 0.67/0.69 tff(226,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)).
% 0.67/0.69 tff(227,assumption,(combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))), introduced(assumption)).
% 0.67/0.69 tff(228,plain,
% 0.67/0.69 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(229,plain,
% 0.67/0.69 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[228])).
% 0.67/0.69 tff(230,plain,
% 0.67/0.69 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(231,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_app')).
% 0.67/0.69 tff(232,plain,
% 0.67/0.69 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.67/0.69 tff(233,plain,(
% 0.67/0.69 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.67/0.69 inference(skolemize,[status(sab)],[232])).
% 0.67/0.69 tff(234,plain,
% 0.67/0.69 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[233, 229])).
% 0.67/0.69 tff(235,plain,
% 0.67/0.69 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp))))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(236,plain,
% 0.67/0.69 ($false),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[235, 234, 227])).
% 0.67/0.69 tff(237,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,[]))).
% 0.67/0.69 tff(238,plain,
% 0.67/0.69 (^[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)))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(239,plain,
% 0.67/0.69 (![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))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[238])).
% 0.67/0.69 tff(240,plain,
% 0.67/0.69 (![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))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(241,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')).
% 0.67/0.69 tff(242,plain,
% 0.67/0.69 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.67/0.69 tff(243,plain,(
% 0.67/0.69 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.67/0.69 inference(skolemize,[status(sab)],[242])).
% 0.67/0.69 tff(244,plain,
% 0.67/0.69 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.67/0.69 tff(245,plain,
% 0.67/0.69 (((~![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))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(246,plain,
% 0.67/0.69 ((~![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))))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(247,plain,
% 0.67/0.69 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), ap_parcontractE_sk1q(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))) | (combK = comb_app(combS, ap_parcontractE_sk1p(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.67/0.69 tff(248,plain,
% 0.67/0.69 ($false),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[247, 244, 237, 226])).
% 0.67/0.69 tff(249,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,[]))).
% 0.67/0.69 tff(250,plain,
% 0.67/0.69 (^[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)))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(251,plain,
% 0.67/0.69 (![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))))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[250])).
% 0.67/0.69 tff(252,plain,
% 0.67/0.69 (![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))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(253,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')).
% 0.67/0.69 tff(254,plain,
% 0.67/0.69 (![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))))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.67/0.69 tff(255,plain,(
% 0.67/0.69 ![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))))),
% 0.67/0.69 inference(skolemize,[status(sab)],[254])).
% 0.67/0.69 tff(256,plain,
% 0.67/0.69 (![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))))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.67/0.69 tff(257,plain,
% 0.67/0.69 (((~![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))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(258,plain,
% 0.67/0.69 ((~![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))))),
% 0.67/0.69 inference(quant_inst,[status(thm)],[])).
% 0.67/0.69 tff(259,plain,
% 0.67/0.69 ((~![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)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.67/0.69 tff(260,plain,
% 0.67/0.69 ((~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)))),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[259, 256])).
% 0.67/0.69 tff(261,plain,
% 0.67/0.69 (~ap_parcontractE_c3(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.67/0.69 inference(unit_resolution,[status(thm)],[260, 249])).
% 0.67/0.69 tff(262,plain,
% 0.67/0.69 (~ap_parcontractE_c3(comb_app(combK, p), q, yp)),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[261, 225])).
% 0.67/0.69 tff(263,plain,
% 0.67/0.69 (member(pair(comb_app(comb_app(combK, p), q), yp), parcontract) <=> member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(264,axiom,(member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','diamond_parcontract_2c1')).
% 0.67/0.69 tff(265,plain,
% 0.67/0.69 (member(pair(comb_app(comb_app(combK, p), q), yp), parcontract)),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.67/0.69 tff(266,plain,
% 0.67/0.69 (^[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))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(267,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[266])).
% 0.67/0.69 tff(268,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(269,plain,
% 0.67/0.69 (^[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)))))),
% 0.67/0.69 inference(bind,[status(th)],[])).
% 0.67/0.69 tff(270,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(quant_intro,[status(thm)],[269])).
% 0.67/0.69 tff(271,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')).
% 0.67/0.69 tff(272,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.67/0.69 tff(273,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.69 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.67/0.69 tff(274,plain,(
% 0.67/0.69 ![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)))),
% 0.67/0.69 inference(skolemize,[status(sab)],[273])).
% 0.67/0.69 tff(275,plain,
% 0.67/0.69 (![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)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.67/0.70 tff(276,plain,
% 0.67/0.70 (((~![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))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(277,plain,
% 0.67/0.70 ((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))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(278,plain,
% 0.67/0.70 (((~![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)))),
% 0.67/0.70 inference(monotonicity,[status(thm)],[277])).
% 0.67/0.70 tff(279,plain,
% 0.67/0.70 (((~![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))),
% 0.67/0.70 inference(transitivity,[status(thm)],[278, 276])).
% 0.67/0.70 tff(280,plain,
% 0.67/0.70 ((~![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)))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(281,plain,
% 0.67/0.70 ((~![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)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.67/0.70 tff(282,plain,
% 0.67/0.70 (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)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[281, 275, 265])).
% 0.67/0.70 tff(283,plain,
% 0.67/0.70 (ap_parcontractE_c4(comb_app(combK, p), q, yp) | ap_parcontractE_c2(comb_app(combK, p), q, yp) | ap_parcontractE_c1(comb_app(combK, p), q, yp)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[282, 262])).
% 0.67/0.70 tff(284,plain,
% 0.67/0.70 (ap_parcontractE_c2(comb_app(combK, p), q, yp)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[283, 223, 166])).
% 0.67/0.70 tff(285,plain,
% 0.67/0.70 (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)),
% 0.67/0.70 inference(monotonicity,[status(thm)],[58])).
% 0.67/0.70 tff(286,plain,
% 0.67/0.70 (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)),
% 0.67/0.70 inference(symmetry,[status(thm)],[285])).
% 0.67/0.70 tff(287,assumption,(ap_parcontractE_c2(comb_app(combK, p), q, yp)), introduced(assumption)).
% 0.67/0.70 tff(288,plain,
% 0.67/0.70 (ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.67/0.70 tff(289,assumption,(~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.67/0.70 tff(290,plain,
% 0.67/0.70 ($false),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.67/0.70 tff(291,plain,((~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)), inference(lemma,lemma(discharge,[]))).
% 0.67/0.70 tff(292,plain,
% 0.67/0.70 (ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[291, 284])).
% 0.67/0.70 tff(293,assumption,(ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)), introduced(assumption)).
% 0.67/0.70 tff(294,plain,
% 0.67/0.70 ((comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)) <=> (comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.67/0.70 inference(commutativity,[status(thm)],[])).
% 0.67/0.70 tff(295,plain,
% 0.67/0.70 ((comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))) <=> (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.67/0.70 inference(symmetry,[status(thm)],[294])).
% 0.67/0.70 tff(296,plain,
% 0.67/0.70 ((~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) <=> (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp)))),
% 0.67/0.70 inference(monotonicity,[status(thm)],[295])).
% 0.67/0.70 tff(297,assumption,(~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))), introduced(assumption)).
% 0.67/0.70 tff(298,plain,
% 0.67/0.70 (~(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.67/0.70 tff(299,plain,
% 0.67/0.70 (^[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))))),
% 0.67/0.70 inference(bind,[status(th)],[])).
% 0.67/0.70 tff(300,plain,
% 0.67/0.70 (![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)))),
% 0.67/0.70 inference(quant_intro,[status(thm)],[299])).
% 0.67/0.70 tff(301,plain,
% 0.67/0.70 (![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)))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(302,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')).
% 0.67/0.70 tff(303,plain,
% 0.67/0.70 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.67/0.70 tff(304,plain,(
% 0.67/0.70 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.67/0.70 inference(skolemize,[status(sab)],[303])).
% 0.67/0.70 tff(305,plain,
% 0.67/0.70 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.67/0.70 tff(306,plain,
% 0.67/0.70 (((~![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)))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(307,plain,
% 0.67/0.70 ((~![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)))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(308,plain,
% 0.67/0.70 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.67/0.70 tff(309,plain,
% 0.67/0.70 ((~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))) = comb_app(combK, yp))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[308, 305])).
% 0.67/0.70 tff(310,plain,
% 0.67/0.70 ($false),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[309, 298, 293])).
% 0.67/0.70 tff(311,plain,((~ap_parcontractE_c2(comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))), q, yp)) | (comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.70 tff(312,plain,
% 0.67/0.70 (comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[311, 292])).
% 0.67/0.70 tff(313,assumption,(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p)))), introduced(assumption)).
% 0.67/0.70 tff(314,assumption,(~(yp = k1_parcontractD_sk1(p, comb_app(combK, p)))), introduced(assumption)).
% 0.67/0.70 tff(315,plain,
% 0.67/0.70 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (yp = 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, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (yp = k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(316,plain,
% 0.67/0.70 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | ((~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (yp = k1_parcontractD_sk1(p, comb_app(combK, p))))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(317,plain,
% 0.67/0.70 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (Q1 = Q2))) | (~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (yp = k1_parcontractD_sk1(p, comb_app(combK, p)))),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.67/0.70 tff(318,plain,
% 0.67/0.70 ($false),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[317, 52, 314, 313])).
% 0.67/0.70 tff(319,plain,((~(comb_app(combK, yp) = comb_app(combK, k1_parcontractD_sk1(p, comb_app(combK, p))))) | (yp = k1_parcontractD_sk1(p, comb_app(combK, p)))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.70 tff(320,plain,
% 0.67/0.70 (yp = k1_parcontractD_sk1(p, comb_app(combK, p))),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[319, 312])).
% 0.67/0.70 tff(321,plain,
% 0.67/0.70 (yp = p),
% 0.67/0.70 inference(transitivity,[status(thm)],[320, 57])).
% 0.67/0.70 tff(322,plain,
% 0.67/0.70 (pair(p, yp) = pair(p, p)),
% 0.67/0.70 inference(monotonicity,[status(thm)],[321])).
% 0.67/0.70 tff(323,plain,
% 0.67/0.70 (member(pair(p, yp), parcontract) <=> member(pair(p, p), parcontract)),
% 0.67/0.70 inference(monotonicity,[status(thm)],[322])).
% 0.67/0.70 tff(324,plain,
% 0.67/0.70 (member(pair(p, p), parcontract) <=> member(pair(p, yp), parcontract)),
% 0.67/0.70 inference(symmetry,[status(thm)],[323])).
% 0.67/0.70 tff(325,plain,
% 0.67/0.70 (((~![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))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(326,plain,
% 0.67/0.70 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(327,plain,
% 0.67/0.70 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.67/0.70 tff(328,plain,
% 0.67/0.70 (member(pair(p, p), parcontract)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[327, 30, 3])).
% 0.67/0.70 tff(329,plain,
% 0.67/0.70 (member(pair(p, yp), parcontract)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[328, 324])).
% 0.67/0.70 tff(330,plain,
% 0.67/0.70 (((~![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))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(331,plain,
% 0.67/0.70 ((~![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))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(332,plain,
% 0.67/0.70 ((~![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)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.67/0.70 tff(333,plain,
% 0.67/0.70 (member(yp, comb)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[332, 117, 265])).
% 0.67/0.70 tff(334,plain,
% 0.67/0.70 (((~![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))),
% 0.67/0.70 inference(rewrite,[status(thm)],[])).
% 0.67/0.70 tff(335,plain,
% 0.67/0.70 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(yp, comb)) | member(pair(yp, yp), parcontract))),
% 0.67/0.70 inference(quant_inst,[status(thm)],[])).
% 0.67/0.70 tff(336,plain,
% 0.67/0.70 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(yp, comb)) | member(pair(yp, yp), parcontract)),
% 0.67/0.70 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.67/0.70 tff(337,plain,
% 0.67/0.70 (member(pair(yp, yp), parcontract)),
% 0.67/0.70 inference(unit_resolution,[status(thm)],[336, 30, 333])).
% 0.67/0.70 tff(338,plain,
% 0.67/0.70 (((~![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)))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(339,plain,
% 0.67/0.71 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | ((~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract)))),
% 0.67/0.71 inference(quant_inst,[status(thm)],[])).
% 0.67/0.71 tff(340,plain,
% 0.67/0.71 ((~![Z: $i] : ((~member(pair(p, Z), parcontract)) | (~member(pair(yp, Z), parcontract)))) | (~member(pair(p, yp), parcontract)) | (~member(pair(yp, yp), parcontract))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.67/0.71 tff(341,plain,
% 0.67/0.71 (~member(pair(p, yp), parcontract)),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[340, 159, 337])).
% 0.67/0.71 tff(342,plain,
% 0.67/0.71 ($false),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[341, 329])).
% 0.67/0.71 % SZS output end Proof
%------------------------------------------------------------------------------