TSTP Solution File: COL090-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL090-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 17:48:29 EDT 2022
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL090-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 12:00:34 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.
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(member_type, type, (
% 0.20/0.42 member: ( $i * $i ) > $o)).
% 0.20/0.42 tff(contract_type, type, (
% 0.20/0.42 contract: $i)).
% 0.20/0.42 tff(pair_type, type, (
% 0.20/0.42 pair: ( $i * $i ) > $i)).
% 0.20/0.42 tff(ap_contractE_sk3q_type, type, (
% 0.20/0.42 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(r_type, type, (
% 0.20/0.42 r: $i)).
% 0.20/0.42 tff(combK_type, type, (
% 0.20/0.42 combK: $i)).
% 0.20/0.42 tff(comb_app_type, type, (
% 0.20/0.42 comb_app: ( $i * $i ) > $i)).
% 0.20/0.42 tff(combS_type, type, (
% 0.20/0.42 combS: $i)).
% 0.20/0.42 tff(ap_contractE_c4_type, type, (
% 0.20/0.42 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(ap_contractE_c3_type, type, (
% 0.20/0.42 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(ap_contractE_sk2q_type, type, (
% 0.20/0.42 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(ap_contractE_c1_type, type, (
% 0.20/0.42 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(ap_contractE_c2_type, type, (
% 0.20/0.42 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(ap_contractE_sk1q_type, type, (
% 0.20/0.42 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(ap_contractE_sk1p_type, type, (
% 0.20/0.42 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(1,assumption,(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.20/0.42 tff(7,plain,(
% 0.20/0.42 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[6])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.20/0.42 tff(11,plain,(~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(12,assumption,(ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE4')).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.20/0.42 tff(18,plain,(
% 0.20/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[17])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[22, 19, 12, 11])).
% 0.20/0.42 tff(24,plain,(~ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(25,assumption,(member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(29,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_contractE')).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.20/0.42 tff(31,plain,(
% 0.20/0.42 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.42 inference(skolemize,[status(sab)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 32, 25])).
% 0.20/0.42 tff(35,plain,(~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(39,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE13')).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.42 tff(41,plain,(
% 0.20/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.42 inference(skolemize,[status(sab)],[40])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 42, 35])).
% 0.20/0.42 tff(47,assumption,(member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 (^[R: $i] : refl((~member(pair(combS, R), contract)) <=> (~member(pair(combS, R), contract)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[48])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(51,axiom,(![R: $i] : (~member(pair(combS, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_contractE')).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.42 tff(53,plain,(
% 0.20/0.42 ![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.42 inference(skolemize,[status(sab)],[52])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 ((~![R: $i] : (~member(pair(combS, R), contract))) | (~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 54, 47])).
% 0.20/0.42 tff(57,plain,(~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE10')).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.43 tff(63,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.43 inference(skolemize,[status(sab)],[62])).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(66,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[67, 64, 57])).
% 0.20/0.43 tff(69,assumption,(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))), introduced(assumption)).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[70, 8, 69])).
% 0.20/0.43 tff(72,plain,(~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(76,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE9')).
% 0.20/0.43 tff(77,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.20/0.43 tff(78,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[77])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))) | (combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[82, 79, 72])).
% 0.20/0.43 tff(84,plain,
% 0.20/0.43 (^[R: $i, Q: $i, P: $i] : refl((ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.43 tff(86,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) <=> (ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) <=> ((ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c3(P, Q, R)))), rewrite(((ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c3(P, Q, R)) <=> (ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) <=> (ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))))), ((((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> ((ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c4(P, Q, R)))), rewrite(((ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract))) | ap_contractE_c4(P, Q, R)) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))), ((((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.43 tff(89,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), contract)) | ap_contractE_c1(P, Q, R)) | ap_contractE_c2(P, Q, R)) | ap_contractE_c3(P, Q, R)) | ap_contractE_c4(P, Q, R))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE1')).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.44 tff(91,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.44 tff(92,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[91])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(95,plain,
% 0.20/0.44 ((ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))) <=> (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(96,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.44 tff(97,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.44 tff(98,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(99,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.20/0.44 tff(100,plain,
% 0.20/0.44 (ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[99, 93, 83])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[100, 68, 46])).
% 0.20/0.44 tff(102,plain,
% 0.20/0.44 (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[101, 24])).
% 0.20/0.44 tff(103,plain,
% 0.20/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(104,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | ((~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))) | (~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 ((~ap_contractE_c3(comb_app(combS, combK), combK, r)) | member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[105, 64])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (~ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[106, 102])).
% 0.20/0.44 tff(108,assumption,(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.44 tff(109,assumption,(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[110, 8, 109])).
% 0.20/0.44 tff(112,plain,(~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (^[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)))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 (![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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(116,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')).
% 0.20/0.44 tff(117,plain,
% 0.20/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.20/0.44 tff(118,plain,(
% 0.20/0.44 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.44 inference(skolemize,[status(sab)],[117])).
% 0.20/0.44 tff(119,plain,
% 0.20/0.44 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.20/0.44 tff(120,plain,
% 0.20/0.44 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(122,plain,
% 0.20/0.45 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.45 tff(123,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[122, 119, 112, 108])).
% 0.20/0.45 tff(124,plain,(~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(125,plain,
% 0.20/0.45 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(126,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(127,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c2(P, Q, R)) | (P = comb_app(comb_app(combS, ap_contractE_sk1p(P, Q, R)), ap_contractE_sk1q(P, Q, R))))) | (~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.45 tff(128,plain,
% 0.20/0.45 ((~ap_contractE_c2(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[127, 79])).
% 0.20/0.45 tff(129,plain,
% 0.20/0.45 (~ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[128, 124])).
% 0.20/0.45 tff(130,assumption,(comb_app(combS, combK) = comb_app(combK, r)), introduced(assumption)).
% 0.20/0.45 tff(131,plain,
% 0.20/0.45 (comb_app(combK, r) = comb_app(combS, combK)),
% 0.20/0.45 inference(symmetry,[status(thm)],[130])).
% 0.20/0.45 tff(132,assumption,(comb_app(combK, r) = comb_app(combS, combK)), introduced(assumption)).
% 0.20/0.45 tff(133,plain,
% 0.20/0.45 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(134,axiom,(~(combK = combS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_s')).
% 0.20/0.45 tff(135,plain,
% 0.20/0.45 (~(combK = combS)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.20/0.45 tff(136,plain,
% 0.20/0.45 (((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))) <=> ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(137,plain,
% 0.20/0.45 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | ((~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(138,plain,
% 0.20/0.45 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.45 tff(139,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[138, 135, 119, 132])).
% 0.20/0.45 tff(140,plain,(~(comb_app(combK, r) = comb_app(combS, combK))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(141,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[140, 131])).
% 0.20/0.45 tff(142,plain,(~(comb_app(combS, combK) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(143,assumption,(ap_contractE_c1(comb_app(combS, combK), combK, r)), introduced(assumption)).
% 0.20/0.45 tff(144,plain,
% 0.20/0.45 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(145,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r)))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(146,plain,
% 0.20/0.45 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.20/0.45 tff(147,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[146, 19, 143, 142])).
% 0.20/0.45 tff(148,plain,(~ap_contractE_c1(comb_app(combS, combK), combK, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45 tff(149,plain,
% 0.20/0.45 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract) <=> member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(150,axiom,(member(pair(comb_app(comb_app(combS, combK), combK), r), contract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','i_contract_E')).
% 0.20/0.45 tff(151,plain,
% 0.20/0.45 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.20/0.45 tff(152,plain,
% 0.20/0.45 (((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(153,plain,
% 0.20/0.46 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract)))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(154,plain,
% 0.20/0.46 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_c4(P, Q, R) | ap_contractE_c3(P, Q, R) | ap_contractE_c2(P, Q, R) | ap_contractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), contract)))) | ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r) | (~member(pair(comb_app(comb_app(combS, combK), combK), r), contract))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.20/0.46 tff(155,plain,
% 0.20/0.46 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r) | ap_contractE_c1(comb_app(combS, combK), combK, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[154, 93, 151])).
% 0.20/0.46 tff(156,plain,
% 0.20/0.46 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r) | ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[155, 148])).
% 0.20/0.46 tff(157,plain,
% 0.20/0.46 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[156, 129])).
% 0.20/0.46 tff(158,plain,
% 0.20/0.46 (ap_contractE_c4(comb_app(combS, combK), combK, r)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[157, 107])).
% 0.20/0.46 tff(159,plain,
% 0.20/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(160,plain,
% 0.20/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | ((~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(161,plain,
% 0.20/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))) | (~ap_contractE_c4(comb_app(combS, combK), combK, r)) | member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.20/0.46 tff(162,plain,
% 0.20/0.46 (member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[161, 42, 158])).
% 0.20/0.46 tff(163,plain,
% 0.20/0.46 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(164,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[163, 32, 162])).
% 0.20/0.46 % SZS output end Proof
%------------------------------------------------------------------------------