%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL091-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COL091-1 : TPTP v9.0.0. Released v2.7.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:17:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(member_type, type, (
% 0.12/0.38 member: ( $i * $i ) > $o)).
% 0.12/0.38 tff(contract_type, type, (
% 0.12/0.38 contract: $i)).
% 0.12/0.38 tff(pair_type, type, (
% 0.12/0.38 pair: ( $i * $i ) > $i)).
% 0.12/0.38 tff(ap_contractE_sk2q_type, type, (
% 0.12/0.38 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(r_type, type, (
% 0.12/0.38 r: $i)).
% 0.12/0.38 tff(p_type, type, (
% 0.12/0.38 p: $i)).
% 0.12/0.38 tff(combK_type, type, (
% 0.12/0.38 combK: $i)).
% 0.12/0.38 tff(ap_contractE_c3_type, type, (
% 0.12/0.38 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(ap_contractE_c1_type, type, (
% 0.12/0.38 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(comb_app_type, type, (
% 0.12/0.38 comb_app: ( $i * $i ) > $i)).
% 0.12/0.38 tff(ap_contractE_c2_type, type, (
% 0.12/0.38 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(ap_contractE_sk1q_type, type, (
% 0.12/0.38 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(ap_contractE_sk1p_type, type, (
% 0.12/0.38 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(combS_type, type, (
% 0.12/0.38 combS: $i)).
% 0.12/0.38 tff(ap_contractE_c4_type, type, (
% 0.12/0.38 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.12/0.38 tff(ap_contractE_sk3q_type, type, (
% 0.12/0.38 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.12/0.38 tff(1,assumption,(combK = comb_app(combK, r)), introduced(assumption)).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (comb_app(combK, r) = combK),
% 0.12/0.38 inference(symmetry,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (comb_app(comb_app(combK, r), r) = comb_app(combK, r)),
% 0.12/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (comb_app(combK, r) = comb_app(comb_app(combK, r), r)),
% 0.12/0.38 inference(symmetry,[status(thm)],[3])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (combK = comb_app(comb_app(combK, r), r)),
% 0.12/0.38 inference(transitivity,[status(thm)],[1, 4])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(9,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_app')).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.12/0.38 tff(11,plain,(
% 0.12/0.38 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[10])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combK, r), r)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (~(combK = comb_app(comb_app(combK, r), r))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[14, 5])).
% 0.12/0.38 tff(16,plain,(~(combK = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(17,assumption,(ap_contractE_c1(combK, p, r)), introduced(assumption)).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (^[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))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[18])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(21,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')).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.12/0.38 tff(23,plain,(
% 0.12/0.38 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[22])).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combK, p, r)) | (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(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_contractE_c1(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combK, p, r)) | (combK = comb_app(combK, r))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[27, 24, 17, 16])).
% 0.12/0.38 tff(29,plain,(~ap_contractE_c1(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(30,assumption,(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))), introduced(assumption)).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 ($false),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 12, 30])).
% 0.12/0.38 tff(33,plain,(~(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r)))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (^[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)))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[34])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(37,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')).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,(
% 0.12/0.38 ![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))))),
% 0.12/0.38 inference(skolemize,[status(sab)],[38])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (![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))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, 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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 ((~![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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (~ap_contractE_c2(combK, p, r)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.12/0.38 tff(45,assumption,(ap_contractE_c4(combK, p, r)), introduced(assumption)).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (^[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)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[46])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (![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))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(49,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')).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.12/0.38 tff(51,plain,(
% 0.12/0.38 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.12/0.38 inference(skolemize,[status(sab)],[50])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[51, 47])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, 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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 ((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 ((~![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(combK, p, r)) | member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[55, 52, 45])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (^[R: $i, Q: $i, P: $i] : refl(((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(58,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[57])).
% 0.12/0.39 tff(59,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(60,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_contractE15')).
% 0.12/0.39 tff(61,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.12/0.39 tff(62,plain,(
% 0.12/0.39 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.12/0.39 inference(skolemize,[status(sab)],[61])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 (((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | ((~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | (~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | ((~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))) | (~ap_contractE_c4(combK, p, r)) | (r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[66, 63, 45])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (^[Q: $i] : refl(((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[68])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(71,axiom,(![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_contractD_c1')).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.12/0.39 tff(73,plain,(
% 0.12/0.39 ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[72])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | ((~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))) <=> ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | (~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | ((~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(77,plain,
% 0.12/0.39 ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | (~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.12/0.39 tff(78,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[77, 74, 67, 56])).
% 0.12/0.39 tff(79,plain,(~ap_contractE_c4(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.12/0.39 tff(80,plain,
% 0.12/0.39 (member(pair(comb_app(combK, p), r), contract) <=> member(pair(comb_app(combK, p), r), contract)),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(81,axiom,(member(pair(comb_app(combK, p), r), contract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k1_contractD_h1')).
% 0.12/0.39 tff(82,plain,
% 0.12/0.39 (member(pair(comb_app(combK, p), r), contract)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.12/0.39 tff(83,plain,
% 0.12/0.39 (^[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))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(84,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[83])).
% 0.12/0.39 tff(85,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(86,plain,
% 0.12/0.39 (^[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)))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(87,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[86])).
% 0.12/0.39 tff(88,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')).
% 0.12/0.39 tff(89,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.12/0.39 tff(90,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.12/0.39 tff(91,plain,(
% 0.12/0.39 ![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)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[90])).
% 0.12/0.39 tff(92,plain,
% 0.12/0.39 (![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)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[91, 84])).
% 0.12/0.39 tff(93,plain,
% 0.12/0.39 (((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), 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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), contract)))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(94,plain,
% 0.12/0.39 ((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), contract)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(95,plain,
% 0.12/0.39 ((~![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(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), contract))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.39 tff(96,plain,
% 0.12/0.39 (ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[95, 92, 82])).
% 0.12/0.39 tff(97,plain,
% 0.12/0.39 (ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[96, 79])).
% 0.12/0.39 tff(98,plain,
% 0.12/0.39 (ap_contractE_c3(combK, p, r)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[97, 44, 29])).
% 0.12/0.39 tff(99,plain,
% 0.12/0.39 (^[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)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(100,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[99])).
% 0.12/0.39 tff(101,plain,
% 0.12/0.39 (![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))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(102,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')).
% 0.12/0.39 tff(103,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.12/0.39 tff(104,plain,(
% 0.12/0.39 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.12/0.39 inference(skolemize,[status(sab)],[103])).
% 0.12/0.39 tff(105,plain,
% 0.12/0.39 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c3(P, Q, R)) | member(pair(P, ap_contractE_sk2q(P, Q, R)), contract))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.12/0.39 tff(106,plain,
% 0.12/0.39 (((~![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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, 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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(107,plain,
% 0.12/0.39 ((~![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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(108,plain,
% 0.12/0.39 ((~![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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.12/0.39 tff(109,plain,
% 0.12/0.39 (member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[108, 105, 98])).
% 0.12/0.39 tff(110,plain,
% 0.12/0.39 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(111,plain,
% 0.12/0.39 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[110])).
% 0.12/0.39 tff(112,plain,
% 0.12/0.39 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(113,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','k_contractE')).
% 0.12/0.39 tff(114,plain,
% 0.12/0.39 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.12/0.39 tff(115,plain,(
% 0.12/0.39 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.12/0.39 inference(skolemize,[status(sab)],[114])).
% 0.12/0.40 tff(116,plain,
% 0.12/0.40 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.12/0.40 tff(117,plain,
% 0.12/0.40 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.12/0.40 inference(quant_inst,[status(thm)],[])).
% 0.12/0.40 tff(118,plain,
% 0.12/0.40 ($false),
% 0.12/0.40 inference(unit_resolution,[status(thm)],[117, 116, 109])).
% 0.12/0.40 % SZS output end Proof
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------