%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL090-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:00:46 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : COL090-1 : TPTP v9.0.0. Released v2.7.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 12:15:05 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.38 % SZS status Unsatisfiable
% 0.11/0.38 % SZS output start Proof
% 0.11/0.38 tff(comb_app_type, type, (
% 0.11/0.38 comb_app: ( $i * $i ) > $i)).
% 0.11/0.38 tff(ap_contractE_sk2q_type, type, (
% 0.11/0.38 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(r_type, type, (
% 0.11/0.38 r: $i)).
% 0.11/0.38 tff(combK_type, type, (
% 0.11/0.38 combK: $i)).
% 0.11/0.38 tff(combS_type, type, (
% 0.11/0.38 combS: $i)).
% 0.11/0.38 tff(ap_contractE_c1_type, type, (
% 0.11/0.38 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(ap_contractE_c4_type, type, (
% 0.11/0.38 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(member_type, type, (
% 0.11/0.38 member: ( $i * $i ) > $o)).
% 0.11/0.38 tff(contract_type, type, (
% 0.11/0.38 contract: $i)).
% 0.11/0.38 tff(pair_type, type, (
% 0.11/0.38 pair: ( $i * $i ) > $i)).
% 0.11/0.38 tff(ap_contractE_sk3q_type, type, (
% 0.11/0.38 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(ap_contractE_c3_type, type, (
% 0.11/0.38 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(ap_contractE_c2_type, type, (
% 0.11/0.38 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.11/0.38 tff(ap_contractE_sk1q_type, type, (
% 0.11/0.38 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(ap_contractE_sk1p_type, type, (
% 0.11/0.38 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.11/0.38 tff(1,assumption,(member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.11/0.38 tff(2,plain,
% 0.11/0.38 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(3,plain,
% 0.11/0.38 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[2])).
% 0.11/0.38 tff(4,plain,
% 0.11/0.38 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(5,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_contractE')).
% 0.11/0.38 tff(6,plain,
% 0.11/0.38 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.11/0.38 tff(7,plain,(
% 0.11/0.38 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.11/0.38 inference(skolemize,[status(sab)],[6])).
% 0.11/0.38 tff(8,plain,
% 0.11/0.38 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.11/0.38 tff(9,plain,
% 0.11/0.38 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.11/0.38 inference(quant_inst,[status(thm)],[])).
% 0.11/0.38 tff(10,plain,
% 0.11/0.38 ($false),
% 0.11/0.38 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.11/0.38 tff(11,plain,(~member(pair(combK, ap_contractE_sk3q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.38 tff(12,plain,
% 0.11/0.38 (^[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)))),
% 0.11/0.38 inference(bind,[status(th)],[])).
% 0.11/0.38 tff(13,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(quant_intro,[status(thm)],[12])).
% 0.11/0.38 tff(14,plain,
% 0.11/0.38 (![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))),
% 0.11/0.38 inference(rewrite,[status(thm)],[])).
% 0.11/0.38 tff(15,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/sandbox/benchmark/theBenchmark.p','ap_contractE13')).
% 0.11/0.38 tff(16,plain,
% 0.11/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.11/0.38 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.11/0.38 tff(17,plain,(
% 0.11/0.38 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.11/0.38 inference(skolemize,[status(sab)],[16])).
% 0.11/0.38 tff(18,plain,
% 0.11/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.11/0.39 tff(19,plain,
% 0.11/0.39 (((~![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))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(20,plain,
% 0.11/0.39 ((~![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))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(21,plain,
% 0.11/0.39 ((~![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)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.11/0.39 tff(22,plain,
% 0.11/0.39 (~ap_contractE_c4(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[21, 18, 11])).
% 0.11/0.39 tff(23,assumption,(member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), introduced(assumption)).
% 0.11/0.39 tff(24,plain,
% 0.11/0.39 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(25,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[24, 8, 23])).
% 0.11/0.39 tff(26,plain,(~member(pair(combK, ap_contractE_sk3q(comb_app(combS, combK), combK, r)), contract)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(27,plain,
% 0.11/0.39 (((~![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))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(28,plain,
% 0.11/0.39 ((~![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))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(29,plain,
% 0.11/0.39 ((~![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)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.11/0.39 tff(30,plain,
% 0.11/0.39 (~ap_contractE_c4(comb_app(combS, combK), combK, r)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[29, 18, 26])).
% 0.11/0.39 tff(31,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)).
% 0.11/0.39 tff(32,assumption,(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))), introduced(assumption)).
% 0.11/0.39 tff(33,plain,
% 0.11/0.39 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(34,plain,
% 0.11/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[33])).
% 0.11/0.39 tff(35,plain,
% 0.11/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(36,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_app')).
% 0.11/0.39 tff(37,plain,
% 0.11/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.11/0.39 tff(38,plain,(
% 0.11/0.39 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[37])).
% 0.11/0.39 tff(39,plain,
% 0.11/0.39 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.11/0.39 tff(40,plain,
% 0.11/0.39 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(41,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[40, 39, 32])).
% 0.11/0.39 tff(42,plain,(~(combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(43,plain,
% 0.11/0.39 (^[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)))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(44,plain,
% 0.11/0.39 (![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))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.11/0.39 tff(45,plain,
% 0.11/0.39 (![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))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(46,axiom,(![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_app1')).
% 0.11/0.39 tff(47,plain,
% 0.11/0.39 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.11/0.39 tff(48,plain,(
% 0.11/0.39 ![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.11/0.39 inference(skolemize,[status(sab)],[47])).
% 0.11/0.39 tff(49,plain,
% 0.11/0.39 (![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.11/0.39 tff(50,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(51,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(52,plain,
% 0.11/0.39 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combS, combK) = comb_app(comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)), ap_contractE_sk1q(comb_app(combS, combK), combK, r)))) | (combS = comb_app(combS, ap_contractE_sk1p(comb_app(combS, combK), combK, r)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.11/0.39 tff(53,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[52, 49, 42, 31])).
% 0.11/0.39 tff(54,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,[]))).
% 0.11/0.39 tff(55,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(56,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[55])).
% 0.11/0.39 tff(57,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(58,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/sandbox/benchmark/theBenchmark.p','ap_contractE9')).
% 0.11/0.39 tff(59,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.11/0.39 tff(60,plain,(
% 0.11/0.39 ![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))))),
% 0.11/0.39 inference(skolemize,[status(sab)],[59])).
% 0.11/0.39 tff(61,plain,
% 0.11/0.39 (![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))))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.11/0.39 tff(62,plain,
% 0.11/0.39 (((~![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))))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(63,plain,
% 0.11/0.39 ((~![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))))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(64,plain,
% 0.11/0.39 ((~![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)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.11/0.39 tff(65,plain,
% 0.11/0.39 ((~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)))),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[64, 61])).
% 0.11/0.39 tff(66,plain,
% 0.11/0.39 (~ap_contractE_c2(comb_app(combS, combK), combK, r)),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[65, 54])).
% 0.11/0.39 tff(67,assumption,(comb_app(combS, combK) = comb_app(combK, r)), introduced(assumption)).
% 0.11/0.39 tff(68,plain,
% 0.11/0.39 (comb_app(combK, r) = comb_app(combS, combK)),
% 0.11/0.39 inference(symmetry,[status(thm)],[67])).
% 0.11/0.39 tff(69,assumption,(comb_app(combK, r) = comb_app(combS, combK)), introduced(assumption)).
% 0.11/0.39 tff(70,plain,
% 0.11/0.39 ((~(combK = combS)) <=> (~(combK = combS))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(71,axiom,(~(combK = combS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_s')).
% 0.11/0.39 tff(72,plain,
% 0.11/0.39 (~(combK = combS)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.11/0.39 tff(73,plain,
% 0.11/0.39 (((~![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))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(74,plain,
% 0.11/0.39 ((~![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))),
% 0.11/0.39 inference(quant_inst,[status(thm)],[])).
% 0.11/0.39 tff(75,plain,
% 0.11/0.39 ((~![P2: $i, Q2: $i, Q1: $i, P1: $i] : ((~(comb_app(P1, Q1) = comb_app(P2, Q2))) | (P1 = P2))) | (~(comb_app(combK, r) = comb_app(combS, combK))) | (combK = combS)),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.11/0.39 tff(76,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[75, 72, 49, 69])).
% 0.11/0.39 tff(77,plain,(~(comb_app(combK, r) = comb_app(combS, combK))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(78,plain,
% 0.11/0.39 ($false),
% 0.11/0.39 inference(unit_resolution,[status(thm)],[77, 68])).
% 0.11/0.39 tff(79,plain,(~(comb_app(combS, combK) = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.11/0.39 tff(80,assumption,(ap_contractE_c1(comb_app(combS, combK), combK, r)), introduced(assumption)).
% 0.11/0.39 tff(81,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(82,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[81])).
% 0.11/0.39 tff(83,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(84,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_contractE4')).
% 0.11/0.39 tff(85,plain,
% 0.11/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.11/0.39 tff(86,plain,(
% 0.11/0.39 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.11/0.39 inference(skolemize,[status(sab)],[85])).
% 0.11/0.39 tff(87,plain,
% 0.11/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.11/0.39 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.11/0.39 tff(88,plain,
% 0.11/0.39 (((~![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(89,plain,
% 0.11/0.40 ((~![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)))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(90,plain,
% 0.11/0.40 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(comb_app(combS, combK), combK, r)) | (comb_app(combS, combK) = comb_app(combK, r))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.11/0.40 tff(91,plain,
% 0.11/0.40 ($false),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[90, 87, 80, 79])).
% 0.11/0.40 tff(92,plain,(~ap_contractE_c1(comb_app(combS, combK), combK, r)), inference(lemma,lemma(discharge,[]))).
% 0.11/0.40 tff(93,plain,
% 0.11/0.40 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract) <=> member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(94,axiom,(member(pair(comb_app(comb_app(combS, combK), combK), r), contract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','i_contract_E')).
% 0.11/0.40 tff(95,plain,
% 0.11/0.40 (member(pair(comb_app(comb_app(combS, combK), combK), r), contract)),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.11/0.40 tff(96,plain,
% 0.11/0.40 (^[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))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(97,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[96])).
% 0.11/0.40 tff(98,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(99,plain,
% 0.11/0.40 (^[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)))))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[99])).
% 0.19/0.40 tff(101,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/sandbox/benchmark/theBenchmark.p','ap_contractE1')).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.19/0.40 tff(104,plain,(
% 0.19/0.40 ![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)))),
% 0.19/0.40 inference(skolemize,[status(sab)],[103])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 (![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)))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 (((~![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)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 ((~![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)))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(108,plain,
% 0.19/0.40 ((~![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))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.19/0.40 tff(109,plain,
% 0.19/0.40 (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)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[108, 105, 95])).
% 0.19/0.40 tff(110,plain,
% 0.19/0.40 (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)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[109, 92])).
% 0.19/0.40 tff(111,plain,
% 0.19/0.40 (ap_contractE_c4(comb_app(combS, combK), combK, r) | ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[110, 66])).
% 0.19/0.40 tff(112,plain,
% 0.19/0.40 (ap_contractE_c3(comb_app(combS, combK), combK, r)),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[111, 30])).
% 0.19/0.40 tff(113,plain,
% 0.19/0.40 (^[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)))),
% 0.19/0.40 inference(bind,[status(th)],[])).
% 0.19/0.40 tff(114,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(quant_intro,[status(thm)],[113])).
% 0.19/0.40 tff(115,plain,
% 0.19/0.40 (![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(116,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/sandbox/benchmark/theBenchmark.p','ap_contractE10')).
% 0.19/0.40 tff(117,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.40 tff(118,plain,(
% 0.19/0.40 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.19/0.40 inference(skolemize,[status(sab)],[117])).
% 0.19/0.40 tff(119,plain,
% 0.19/0.40 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.40 tff(120,plain,
% 0.19/0.40 (((~![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))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(121,plain,
% 0.19/0.40 ((~![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))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(122,plain,
% 0.19/0.40 ((~![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)),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.19/0.40 tff(123,plain,
% 0.19/0.40 ((~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)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[122, 119])).
% 0.19/0.41 tff(124,plain,
% 0.19/0.41 (member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[123, 112])).
% 0.19/0.41 tff(125,assumption,(member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), introduced(assumption)).
% 0.19/0.41 tff(126,plain,
% 0.19/0.41 (^[R: $i] : refl((~member(pair(combS, R), contract)) <=> (~member(pair(combS, R), contract)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(127,plain,
% 0.19/0.41 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.19/0.41 tff(128,plain,
% 0.19/0.41 (![R: $i] : (~member(pair(combS, R), contract)) <=> ![R: $i] : (~member(pair(combS, R), contract))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(129,axiom,(![R: $i] : (~member(pair(combS, R), contract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','s_contractE')).
% 0.19/0.41 tff(130,plain,
% 0.19/0.41 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.19/0.41 tff(131,plain,(
% 0.19/0.41 ![R: $i] : (~member(pair(combS, R), contract))),
% 0.19/0.41 inference(skolemize,[status(sab)],[130])).
% 0.19/0.41 tff(132,plain,
% 0.19/0.41 (![R: $i] : (~member(pair(combS, R), contract))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.19/0.41 tff(133,plain,
% 0.19/0.41 ((~![R: $i] : (~member(pair(combS, R), contract))) | (~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(134,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[133, 132, 125])).
% 0.19/0.41 tff(135,plain,(~member(pair(combS, ap_contractE_sk2q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), contract)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.41 tff(136,plain,
% 0.19/0.41 (((~![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))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(137,plain,
% 0.19/0.41 ((~![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))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(138,plain,
% 0.19/0.41 ((~![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)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.41 tff(139,plain,
% 0.19/0.41 (~ap_contractE_c3(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[138, 119, 135])).
% 0.19/0.41 tff(140,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)).
% 0.19/0.41 tff(141,plain,
% 0.19/0.41 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_contractE_sk1p(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))), ap_contractE_sk1q(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(142,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[141, 39, 140])).
% 0.19/0.41 tff(143,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,[]))).
% 0.19/0.41 tff(144,plain,
% 0.19/0.41 (((~![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)))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(145,plain,
% 0.19/0.41 ((~![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)))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(146,plain,
% 0.19/0.41 ((~![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))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.19/0.41 tff(147,plain,
% 0.19/0.41 (~ap_contractE_c2(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[146, 61, 143])).
% 0.19/0.41 tff(148,plain,
% 0.19/0.41 (((~![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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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)))) <=> ((~![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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(149,plain,
% 0.19/0.41 ((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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(150,plain,
% 0.19/0.41 (((~![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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[149])).
% 0.19/0.41 tff(151,plain,
% 0.19/0.41 (((~![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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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)))),
% 0.19/0.41 inference(transitivity,[status(thm)],[150, 148])).
% 0.19/0.41 tff(152,plain,
% 0.19/0.41 ((~![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)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(153,plain,
% 0.19/0.42 ((~![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)) | (~member(pair(comb_app(combS, combK), ap_contractE_sk2q(comb_app(combS, combK), combK, r)), contract)) | 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))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.19/0.42 tff(154,plain,
% 0.19/0.42 (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))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[153, 105, 147])).
% 0.19/0.42 tff(155,plain,
% 0.19/0.42 (ap_contractE_c4(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))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[154, 139])).
% 0.19/0.42 tff(156,plain,
% 0.19/0.42 (ap_contractE_c1(combS, combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[155, 124, 22])).
% 0.19/0.42 tff(157,plain,
% 0.19/0.42 (((~![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))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(158,plain,
% 0.19/0.42 ((~![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))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(159,plain,
% 0.19/0.42 ((~![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)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.19/0.42 tff(160,plain,
% 0.19/0.42 (combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[159, 87, 156])).
% 0.19/0.42 tff(161,plain,
% 0.19/0.42 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, ap_contractE_sk2q(comb_app(combS, combK), combK, r))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(162,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[161, 39, 160])).
% 0.19/0.42 % SZS output end Proof
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------