%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL092-1 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:00:47 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : COL092-1 : TPTP v9.0.0. Released v2.7.0.
% 0.14/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:14:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(comb_app_type, type, (
% 0.14/0.41 comb_app: ( $i * $i ) > $i)).
% 0.14/0.41 tff(ap_parcontractE_sk1q_type, type, (
% 0.14/0.41 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(r_type, type, (
% 0.14/0.41 r: $i)).
% 0.14/0.41 tff(p_type, type, (
% 0.14/0.41 p: $i)).
% 0.14/0.41 tff(combK_type, type, (
% 0.14/0.41 combK: $i)).
% 0.14/0.41 tff(ap_parcontractE_sk1p_type, type, (
% 0.14/0.41 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(combS_type, type, (
% 0.14/0.41 combS: $i)).
% 0.14/0.41 tff(ap_parcontractE_c3_type, type, (
% 0.14/0.41 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(ap_parcontractE_c2_type, type, (
% 0.14/0.41 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(ap_parcontractE_c1_type, type, (
% 0.14/0.41 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(member_type, type, (
% 0.14/0.41 member: ( $i * $i ) > $o)).
% 0.14/0.41 tff(parcontract_type, type, (
% 0.14/0.41 parcontract: $i)).
% 0.14/0.41 tff(pair_type, type, (
% 0.14/0.41 pair: ( $i * $i ) > $i)).
% 0.14/0.41 tff(comb_type, type, (
% 0.14/0.41 comb: $i)).
% 0.14/0.41 tff(ap_parcontractE_c4_type, type, (
% 0.14/0.41 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(ap_parcontractE_sk2s_type, type, (
% 0.14/0.41 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(ap_parcontractE_sk2q_type, type, (
% 0.14/0.41 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.14/0.41 tff(1,assumption,(combK = comb_app(combK, r)), introduced(assumption)).
% 0.14/0.41 tff(2,plain,
% 0.14/0.41 (comb_app(combK, r) = combK),
% 0.14/0.41 inference(symmetry,[status(thm)],[1])).
% 0.14/0.41 tff(3,plain,
% 0.14/0.41 (comb_app(comb_app(combK, r), r) = comb_app(combK, r)),
% 0.14/0.41 inference(monotonicity,[status(thm)],[2])).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 (comb_app(combK, r) = comb_app(comb_app(combK, r), r)),
% 0.14/0.41 inference(symmetry,[status(thm)],[3])).
% 0.14/0.41 tff(5,plain,
% 0.14/0.41 (combK = comb_app(comb_app(combK, r), r)),
% 0.14/0.41 inference(transitivity,[status(thm)],[1, 4])).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (^[Q: $i, P: $i] : refl((~(combK = comb_app(P, Q))) <=> (~(combK = comb_app(P, Q))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(9,axiom,(![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_app')).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.14/0.41 tff(11,plain,(
% 0.14/0.41 ![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[10])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.14/0.41 tff(13,plain,
% 0.14/0.41 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combK, r), r)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (~(combK = comb_app(comb_app(combK, r), r))),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[14, 5])).
% 0.14/0.41 tff(16,plain,(~(combK = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(17,assumption,(ap_parcontractE_c2(combK, p, r)), introduced(assumption)).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[18])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(21,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.14/0.41 tff(22,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.14/0.41 tff(23,plain,(
% 0.14/0.41 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.14/0.41 inference(skolemize,[status(sab)],[22])).
% 0.14/0.41 tff(24,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.14/0.41 tff(25,plain,
% 0.14/0.41 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(26,plain,
% 0.14/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r)))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(27,plain,
% 0.14/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combK, p, r)) | (combK = comb_app(combK, r))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.14/0.41 tff(28,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[27, 24, 17, 16])).
% 0.14/0.41 tff(29,plain,(~ap_parcontractE_c2(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(30,assumption,(~member(p, comb)), introduced(assumption)).
% 0.14/0.41 tff(31,plain,
% 0.14/0.41 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(32,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[31])).
% 0.14/0.41 tff(33,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(34,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE5')).
% 0.14/0.41 tff(35,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.41 tff(36,plain,(
% 0.14/0.41 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.14/0.41 inference(skolemize,[status(sab)],[35])).
% 0.14/0.41 tff(37,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.14/0.41 tff(38,plain,
% 0.14/0.41 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combK, p, r)) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combK, p, r)) | member(p, comb))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(39,plain,
% 0.14/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c2(combK, p, r)) | member(p, comb))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(40,plain,
% 0.14/0.41 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c2(combK, p, r)) | member(p, comb)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.14/0.41 tff(41,plain,
% 0.14/0.41 ($false),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[40, 37, 30, 17])).
% 0.14/0.41 tff(42,plain,((~ap_parcontractE_c2(combK, p, r)) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.41 tff(43,plain,
% 0.14/0.41 (~ap_parcontractE_c2(combK, p, r)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[42, 30])).
% 0.14/0.41 tff(44,assumption,(ap_parcontractE_c3(combK, p, r)), introduced(assumption)).
% 0.14/0.41 tff(45,plain,
% 0.14/0.41 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(46,plain,
% 0.14/0.41 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[45])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(48,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE9')).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.14/0.42 tff(50,plain,(
% 0.14/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.14/0.42 inference(skolemize,[status(sab)],[49])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combK, p, r)) | member(p, comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combK, p, r)) | member(p, comb))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | ((~ap_parcontractE_c3(combK, p, r)) | member(p, comb))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | member(Q, comb))) | (~ap_parcontractE_c3(combK, p, r)) | member(p, comb)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.14/0.42 tff(55,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[54, 51, 30, 44])).
% 0.14/0.42 tff(56,plain,((~ap_parcontractE_c3(combK, p, r)) | member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 (~ap_parcontractE_c3(combK, p, r)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[56, 30])).
% 0.14/0.42 tff(58,assumption,(ap_parcontractE_c4(combK, p, r)), introduced(assumption)).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(60,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[59])).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(62,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.42 tff(64,plain,(
% 0.14/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.14/0.42 inference(skolemize,[status(sab)],[63])).
% 0.14/0.42 tff(65,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.14/0.42 tff(66,plain,
% 0.14/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(67,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combK, p, r)) | member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 (member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[68, 65, 58])).
% 0.14/0.42 tff(70,plain,
% 0.14/0.42 (^[R: $i] : refl(((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ((~member(pair(combK, R), parcontract)) | (R = combK)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(71,plain,
% 0.14/0.42 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.14/0.42 tff(72,plain,
% 0.14/0.42 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK)) <=> ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(73,axiom,(![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k_parcontractE2')).
% 0.14/0.42 tff(74,plain,
% 0.14/0.42 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.14/0.42 tff(75,plain,(
% 0.14/0.42 ![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.14/0.42 inference(skolemize,[status(sab)],[74])).
% 0.14/0.42 tff(76,plain,
% 0.14/0.42 (![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.14/0.42 tff(77,plain,
% 0.14/0.42 (((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | ((~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))) <=> ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | (~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | ((~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 ((~![R: $i] : ((~member(pair(combK, R), parcontract)) | (R = combK))) | (~member(pair(combK, ap_parcontractE_sk2q(combK, p, r)), parcontract)) | (ap_parcontractE_sk2q(combK, p, r) = combK)),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.14/0.42 tff(80,plain,
% 0.14/0.42 (ap_parcontractE_sk2q(combK, p, r) = combK),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[79, 76, 69])).
% 0.14/0.42 tff(81,plain,
% 0.14/0.42 (combK = ap_parcontractE_sk2q(combK, p, r)),
% 0.14/0.42 inference(symmetry,[status(thm)],[80])).
% 0.14/0.42 tff(82,plain,
% 0.14/0.42 (comb_app(combK, ap_parcontractE_sk2s(combK, p, r)) = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.14/0.42 tff(83,plain,
% 0.14/0.42 (comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r)) = comb_app(combK, ap_parcontractE_sk2s(combK, p, r))),
% 0.14/0.42 inference(symmetry,[status(thm)],[82])).
% 0.14/0.42 tff(84,plain,
% 0.14/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(85,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[84])).
% 0.14/0.42 tff(86,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(87,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.14/0.42 tff(88,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.14/0.42 tff(89,plain,(
% 0.14/0.42 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.14/0.42 inference(skolemize,[status(sab)],[88])).
% 0.14/0.42 tff(90,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.14/0.42 tff(91,plain,
% 0.14/0.42 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(92,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | ((~ap_parcontractE_c4(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(93,plain,
% 0.14/0.42 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | (R = comb_app(ap_parcontractE_sk2q(P, Q, R), ap_parcontractE_sk2s(P, Q, R))))) | (~ap_parcontractE_c4(combK, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.14/0.42 tff(94,plain,
% 0.14/0.42 (r = comb_app(ap_parcontractE_sk2q(combK, p, r), ap_parcontractE_sk2s(combK, p, r))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[93, 90, 58])).
% 0.14/0.42 tff(95,plain,
% 0.14/0.42 (r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r))),
% 0.14/0.42 inference(transitivity,[status(thm)],[94, 83])).
% 0.14/0.42 tff(96,plain,
% 0.14/0.42 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(97,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[96])).
% 0.14/0.42 tff(98,plain,
% 0.14/0.42 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(99,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.14/0.43 tff(100,plain,
% 0.14/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.14/0.43 tff(101,plain,(
% 0.14/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.14/0.43 inference(skolemize,[status(sab)],[100])).
% 0.14/0.43 tff(102,plain,
% 0.14/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.14/0.43 tff(103,plain,
% 0.14/0.43 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(104,plain,
% 0.14/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | ((~ap_parcontractE_c4(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(105,plain,
% 0.14/0.43 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))) | (~ap_parcontractE_c4(combK, p, r)) | member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.14/0.43 tff(106,plain,
% 0.14/0.43 (member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[105, 102, 58])).
% 0.14/0.43 tff(107,plain,
% 0.14/0.43 (^[PP: $i] : refl(((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))))),
% 0.14/0.43 inference(bind,[status(th)],[])).
% 0.14/0.43 tff(108,plain,
% 0.14/0.43 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.14/0.43 inference(quant_intro,[status(thm)],[107])).
% 0.14/0.43 tff(109,plain,
% 0.14/0.43 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(110,axiom,(![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_parcontractD_c1')).
% 0.14/0.43 tff(111,plain,
% 0.14/0.43 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.14/0.43 tff(112,plain,(
% 0.14/0.43 ![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.14/0.43 inference(skolemize,[status(sab)],[111])).
% 0.14/0.43 tff(113,plain,
% 0.14/0.43 (![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.14/0.43 tff(114,plain,
% 0.14/0.43 (((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(115,plain,
% 0.14/0.43 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(116,plain,
% 0.22/0.43 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combK, p, r)), parcontract))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.22/0.43 tff(117,plain,
% 0.22/0.43 (~(r = comb_app(combK, ap_parcontractE_sk2s(combK, p, r)))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[116, 113, 106])).
% 0.22/0.43 tff(118,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[117, 95])).
% 0.22/0.43 tff(119,plain,(~ap_parcontractE_c4(combK, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.43 tff(120,plain,
% 0.22/0.43 (member(pair(comb_app(combK, p), r), parcontract) <=> member(pair(comb_app(combK, p), r), parcontract)),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(121,axiom,(member(pair(comb_app(combK, p), r), parcontract)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','k1_parcontractD_h1')).
% 0.22/0.43 tff(122,plain,
% 0.22/0.43 (member(pair(comb_app(combK, p), r), parcontract)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.22/0.43 tff(123,plain,
% 0.22/0.43 (^[R: $i, Q: $i, P: $i] : refl((ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(124,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[123])).
% 0.22/0.43 tff(125,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(126,plain,
% 0.22/0.43 (^[R: $i, Q: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) <=> (ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> ((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)))), rewrite(((ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) <=> (ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)))), rewrite(((ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract))) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))), ((((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(127,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R)) <=> ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[126])).
% 0.22/0.43 tff(128,axiom,(![R: $i, Q: $i, P: $i] : (((((~member(pair(comb_app(P, Q), R), parcontract)) | ap_parcontractE_c1(P, Q, R)) | ap_parcontractE_c2(P, Q, R)) | ap_parcontractE_c3(P, Q, R)) | ap_parcontractE_c4(P, Q, R))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.22/0.43 tff(129,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.22/0.43 tff(130,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.22/0.43 tff(131,plain,(
% 0.22/0.43 ![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[130])).
% 0.22/0.43 tff(132,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.22/0.43 tff(133,plain,
% 0.22/0.43 (((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))) <=> ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(134,plain,
% 0.22/0.43 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | (ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract)))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(135,plain,
% 0.22/0.43 ((~![R: $i, Q: $i, P: $i] : (ap_parcontractE_c4(P, Q, R) | ap_parcontractE_c3(P, Q, R) | ap_parcontractE_c2(P, Q, R) | ap_parcontractE_c1(P, Q, R) | (~member(pair(comb_app(P, Q), R), parcontract)))) | ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r) | (~member(pair(comb_app(combK, p), r), parcontract))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.22/0.43 tff(136,plain,
% 0.22/0.43 (ap_parcontractE_c4(combK, p, r) | ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[135, 132, 122])).
% 0.22/0.43 tff(137,plain,
% 0.22/0.43 (ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r) | ap_parcontractE_c1(combK, p, r)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[136, 119])).
% 0.22/0.43 tff(138,plain,
% 0.22/0.43 (ap_parcontractE_c1(combK, p, r)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[137, 57, 43])).
% 0.22/0.43 tff(139,plain,
% 0.22/0.43 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(140,plain,
% 0.22/0.43 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[139])).
% 0.22/0.43 tff(141,plain,
% 0.22/0.43 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(142,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_E2')).
% 0.22/0.43 tff(143,plain,
% 0.22/0.43 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.22/0.43 tff(144,plain,(
% 0.22/0.43 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.22/0.43 inference(skolemize,[status(sab)],[143])).
% 0.22/0.43 tff(145,plain,
% 0.22/0.43 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.22/0.43 tff(146,plain,
% 0.22/0.43 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combK, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combK, p), comb)) | member(p, comb))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(147,plain,
% 0.22/0.43 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combK, p), comb)) | member(p, comb))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(148,plain,
% 0.22/0.43 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combK, p), comb)) | member(p, comb)),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.22/0.43 tff(149,plain,
% 0.22/0.43 ((~member(comb_app(combK, p), comb)) | member(p, comb)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[148, 145])).
% 0.22/0.43 tff(150,plain,
% 0.22/0.43 (~member(comb_app(combK, p), comb)),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[149, 30])).
% 0.22/0.43 tff(151,plain,
% 0.22/0.43 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(152,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[151])).
% 0.22/0.43 tff(153,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb)) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(154,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.22/0.43 tff(155,plain,
% 0.22/0.43 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.22/0.43 tff(156,plain,(
% 0.22/0.43 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.22/0.43 inference(skolemize,[status(sab)],[155])).
% 0.22/0.44 tff(157,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.22/0.44 tff(158,plain,
% 0.22/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(159,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(160,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combK, p, r)) | member(comb_app(combK, p), comb)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.22/0.44 tff(161,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[160, 157, 150, 138])).
% 0.22/0.44 tff(162,plain,(member(p, comb)), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(163,plain,
% 0.22/0.44 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(164,plain,
% 0.22/0.44 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[163])).
% 0.22/0.44 tff(165,plain,
% 0.22/0.44 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(166,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.22/0.44 tff(167,plain,
% 0.22/0.44 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.22/0.44 tff(168,plain,(
% 0.22/0.44 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.22/0.44 inference(skolemize,[status(sab)],[167])).
% 0.22/0.44 tff(169,plain,
% 0.22/0.44 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.22/0.44 tff(170,plain,
% 0.22/0.44 (((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))) <=> ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(171,plain,
% 0.22/0.44 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(172,plain,
% 0.22/0.44 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.22/0.44 tff(173,plain,
% 0.22/0.44 (member(pair(p, p), parcontract)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[172, 169, 162])).
% 0.22/0.44 tff(174,plain,
% 0.22/0.44 (((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(175,plain,
% 0.22/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(176,plain,
% 0.22/0.44 ((~![PP: $i] : ((~(r = comb_app(combK, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.22/0.44 tff(177,plain,
% 0.22/0.44 ((~(r = comb_app(combK, p))) | (~member(pair(p, p), parcontract))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[176, 113])).
% 0.22/0.44 tff(178,plain,
% 0.22/0.44 (~(r = comb_app(combK, p))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.22/0.44 tff(179,assumption,(ap_parcontractE_c1(combK, p, r)), introduced(assumption)).
% 0.22/0.44 tff(180,assumption,(~(r = comb_app(combK, p))), introduced(assumption)).
% 0.22/0.44 tff(181,plain,
% 0.22/0.44 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(182,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[181])).
% 0.22/0.44 tff(183,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(184,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.22/0.44 tff(185,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.22/0.44 tff(186,plain,(
% 0.22/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[185])).
% 0.22/0.44 tff(187,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.22/0.44 tff(188,plain,
% 0.22/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(189,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p)))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(190,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.22/0.44 tff(191,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[190, 187, 180, 179])).
% 0.22/0.44 tff(192,plain,((~ap_parcontractE_c1(combK, p, r)) | (r = comb_app(combK, p))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.44 tff(193,plain,
% 0.22/0.44 (~ap_parcontractE_c1(combK, p, r)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[192, 178])).
% 0.22/0.44 tff(194,plain,
% 0.22/0.44 (ap_parcontractE_c3(combK, p, r) | ap_parcontractE_c2(combK, p, r)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[137, 193])).
% 0.22/0.44 tff(195,plain,
% 0.22/0.44 (ap_parcontractE_c3(combK, p, r)),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[194, 29])).
% 0.22/0.44 tff(196,plain,
% 0.22/0.44 (^[R: $i, Q: $i, P: $i] : refl(((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(197,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[196])).
% 0.22/0.44 tff(198,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R)))) <=> ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(199,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.22/0.44 tff(200,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.22/0.44 tff(201,plain,(
% 0.22/0.44 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.22/0.44 inference(skolemize,[status(sab)],[200])).
% 0.22/0.44 tff(202,plain,
% 0.22/0.44 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[201, 197])).
% 0.22/0.44 tff(203,plain,
% 0.22/0.44 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(204,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | ((~ap_parcontractE_c3(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(205,plain,
% 0.22/0.44 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c3(P, Q, R)) | (P = comb_app(comb_app(combS, ap_parcontractE_sk1p(P, Q, R)), ap_parcontractE_sk1q(P, Q, R))))) | (~ap_parcontractE_c3(combK, p, r)) | (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.22/0.44 tff(206,plain,
% 0.22/0.44 (combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[205, 202, 195])).
% 0.22/0.44 tff(207,plain,
% 0.22/0.44 ((~![Q: $i, P: $i] : (~(combK = comb_app(P, Q)))) | (~(combK = comb_app(comb_app(combS, ap_parcontractE_sk1p(combK, p, r)), ap_parcontractE_sk1q(combK, p, r))))),
% 0.22/0.44 inference(quant_inst,[status(thm)],[])).
% 0.22/0.44 tff(208,plain,
% 0.22/0.44 ($false),
% 0.22/0.44 inference(unit_resolution,[status(thm)],[207, 12, 206])).
% 0.22/0.44 % SZS output end Proof
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------