%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL091-2 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.20s 0.43s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL091-2 : TPTP v9.0.0. Released v2.7.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n008.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 : Thu Jun 19 12:15:48 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.43 % SZS status Unsatisfiable
% 0.20/0.43 % SZS output start Proof
% 0.20/0.43 tff(comb_app_type, type, (
% 0.20/0.43 comb_app: ( $i * $i ) > $i)).
% 0.20/0.43 tff(ap_contractE_sk1q_type, type, (
% 0.20/0.43 ap_contractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(r_type, type, (
% 0.20/0.43 r: $i)).
% 0.20/0.43 tff(p_type, type, (
% 0.20/0.43 p: $i)).
% 0.20/0.43 tff(combK_type, type, (
% 0.20/0.43 combK: $i)).
% 0.20/0.43 tff(ap_contractE_sk1p_type, type, (
% 0.20/0.43 ap_contractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(combS_type, type, (
% 0.20/0.43 combS: $i)).
% 0.20/0.43 tff(ap_contractE_c2_type, type, (
% 0.20/0.43 ap_contractE_c2: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_contractE_c1_type, type, (
% 0.20/0.43 ap_contractE_c1: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_contractE_c3_type, type, (
% 0.20/0.43 ap_contractE_c3: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(member_type, type, (
% 0.20/0.43 member: ( $i * $i ) > $o)).
% 0.20/0.43 tff(contract_type, type, (
% 0.20/0.43 contract: $i)).
% 0.20/0.43 tff(pair_type, type, (
% 0.20/0.43 pair: ( $i * $i ) > $i)).
% 0.20/0.43 tff(ap_contractE_sk2q_type, type, (
% 0.20/0.43 ap_contractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(ap_contractE_c4_type, type, (
% 0.20/0.43 ap_contractE_c4: ( $i * $i * $i ) > $o)).
% 0.20/0.43 tff(ap_contractE_sk3q_type, type, (
% 0.20/0.43 ap_contractE_sk3q: ( $i * $i * $i ) > $i)).
% 0.20/0.43 tff(1,assumption,(combK = comb_app(combK, r)), introduced(assumption)).
% 0.20/0.43 tff(2,plain,
% 0.20/0.43 (comb_app(combK, r) = combK),
% 0.20/0.43 inference(symmetry,[status(thm)],[1])).
% 0.20/0.43 tff(3,plain,
% 0.20/0.43 (comb_app(comb_app(combK, r), r) = comb_app(combK, r)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[2])).
% 0.20/0.43 tff(4,plain,
% 0.20/0.43 (comb_app(combK, r) = comb_app(comb_app(combK, r), r)),
% 0.20/0.43 inference(symmetry,[status(thm)],[3])).
% 0.20/0.43 tff(5,plain,
% 0.20/0.43 (combK = comb_app(comb_app(combK, r), r)),
% 0.20/0.43 inference(transitivity,[status(thm)],[1, 4])).
% 0.20/0.43 tff(6,plain,
% 0.20/0.43 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(7,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.43 tff(8,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(9,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_app')).
% 0.20/0.43 tff(10,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.43 tff(11,plain,(
% 0.20/0.43 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[10])).
% 0.20/0.43 tff(12,plain,
% 0.20/0.43 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.20/0.43 tff(13,plain,
% 0.20/0.43 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combK, r), r)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(14,plain,
% 0.20/0.43 (~(combK = comb_app(comb_app(combK, r), r))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.43 tff(15,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[14, 5])).
% 0.20/0.43 tff(16,plain,(~(combK = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(17,assumption,(ap_contractE_c1(combK, p, r)), introduced(assumption)).
% 0.20/0.43 tff(18,plain,
% 0.20/0.43 (^[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))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(19,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 (![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(21,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')).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.43 tff(23,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.43 tff(25,plain,
% 0.20/0.43 (((~![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)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 ((~![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)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(27,plain,
% 0.20/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_contractE_c1(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_contractE_c1(combK, p, r)) | (combK = comb_app(combK, r))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[27, 24, 17, 16])).
% 0.20/0.43 tff(29,plain,(~ap_contractE_c1(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(30,assumption,(member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)), introduced(assumption)).
% 0.20/0.43 tff(31,plain,
% 0.20/0.43 (^[R: $i] : refl((~member(pair(combK, R), contract)) <=> (~member(pair(combK, R), contract)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (![R: $i] : (~member(pair(combK, R), contract)) <=> ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(34,axiom,(![R: $i] : (~member(pair(combK, R), contract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_contractE')).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.20/0.43 tff(36,plain,(
% 0.20/0.43 ![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.43 inference(skolemize,[status(sab)],[35])).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (![R: $i] : (~member(pair(combK, R), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 ((~![R: $i] : (~member(pair(combK, R), contract))) | (~member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[38, 37, 30])).
% 0.20/0.43 tff(40,plain,(~member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(42,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(quant_intro,[status(thm)],[41])).
% 0.20/0.43 tff(43,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(44,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')).
% 0.20/0.43 tff(45,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)],[44, 43])).
% 0.20/0.43 tff(46,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)],[45])).
% 0.20/0.43 tff(47,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)],[46, 42])).
% 0.20/0.43 tff(48,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(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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(49,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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(50,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(combK, p, r)) | member(pair(combK, ap_contractE_sk2q(combK, p, r)), contract)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (~ap_contractE_c3(combK, p, r)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[50, 47, 40])).
% 0.20/0.43 tff(52,assumption,(ap_contractE_c4(combK, p, r)), introduced(assumption)).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (^[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)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(56,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')).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.20/0.43 tff(58,plain,(
% 0.20/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.43 inference(skolemize,[status(sab)],[57])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | member(pair(Q, ap_contractE_sk3q(P, Q, R)), contract))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (((~![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))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 ((~![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))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 ((~![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)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.44 tff(63,plain,
% 0.20/0.44 (member(pair(p, ap_contractE_sk3q(combK, p, r)), contract)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[62, 59, 52])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(67,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/sandbox/benchmark/theBenchmark.p','ap_contractE15')).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.44 tff(69,plain,(
% 0.20/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(skolemize,[status(sab)],[68])).
% 0.20/0.44 tff(70,plain,
% 0.20/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_contractE_c4(P, Q, R)) | (R = comb_app(P, ap_contractE_sk3q(P, Q, R))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (((~![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 ((~![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))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(73,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (r = comb_app(combK, ap_contractE_sk3q(combK, p, r))),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[73, 70, 52])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (^[Q: $i] : refl(((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract))) <=> ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(78,axiom,(![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_contractD_c1')).
% 0.20/0.44 tff(79,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.44 tff(80,plain,(
% 0.20/0.44 ![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[79])).
% 0.20/0.44 tff(81,plain,
% 0.20/0.44 (![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![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)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![Q: $i] : ((~(r = comb_app(combK, Q))) | (~member(pair(p, Q), contract)))) | (~(r = comb_app(combK, ap_contractE_sk3q(combK, p, r)))) | (~member(pair(p, ap_contractE_sk3q(combK, p, r)), contract))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 81, 74, 63])).
% 0.20/0.44 tff(86,plain,(~ap_contractE_c4(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.44 tff(87,plain,
% 0.20/0.44 (member(pair(comb_app(combK, p), r), contract) <=> member(pair(comb_app(combK, p), r), contract)),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(88,axiom,(member(pair(comb_app(combK, p), r), contract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_contractD_h1')).
% 0.20/0.44 tff(89,plain,
% 0.20/0.44 (member(pair(comb_app(combK, p), r), contract)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.20/0.44 tff(90,plain,
% 0.20/0.44 (^[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))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 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))) <=> ![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(quant_intro,[status(thm)],[90])).
% 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))) <=> ![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(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(93,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(94,plain,
% 0.20/0.44 (![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)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.44 tff(95,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')).
% 0.20/0.44 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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[95, 94])).
% 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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[96, 92])).
% 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)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[97])).
% 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)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.44 tff(100,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)))) | ((~member(pair(comb_app(combK, p), 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))) <=> ((~![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)))) | (~member(pair(comb_app(combK, p), 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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(101,plain,
% 0.20/0.44 ((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))) <=> ((~member(pair(comb_app(combK, p), 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))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(102,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(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)))) | ((~member(pair(comb_app(combK, p), 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)))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[101])).
% 0.20/0.44 tff(103,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(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)))) | (~member(pair(comb_app(combK, p), 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))),
% 0.20/0.44 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.44 tff(104,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(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)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(105,plain,
% 0.20/0.44 ((~![R: $i, Q: $i, P: $i] : (ap_contractE_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(combK, p), 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)),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.44 tff(106,plain,
% 0.20/0.44 (ap_contractE_c4(combK, p, r) | ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[105, 99, 89])).
% 0.20/0.44 tff(107,plain,
% 0.20/0.44 (ap_contractE_c3(combK, p, r) | ap_contractE_c2(combK, p, r) | ap_contractE_c1(combK, p, r)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[106, 86])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (ap_contractE_c2(combK, p, r)),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[107, 51, 29])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (^[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)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(112,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')).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (![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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.45 tff(114,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))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[113])).
% 0.20/0.45 tff(115,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))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.20/0.45 tff(116,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(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))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(117,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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(118,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(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r)))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.45 tff(119,plain,
% 0.20/0.45 (combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[118, 115, 108])).
% 0.20/0.45 tff(120,plain,
% 0.20/0.45 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combS, ap_contractE_sk1p(combK, p, r)), ap_contractE_sk1q(combK, p, r))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(121,plain,
% 0.20/0.45 ($false),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[120, 12, 119])).
% 0.20/0.45 % SZS output end Proof
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------