%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COL093-2 : TPTP v9.0.0. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : COL093-2 : TPTP v9.0.0. Released v2.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n003.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 12:16:09 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.23/0.46 % SZS status Unsatisfiable
% 0.23/0.46 % SZS output start Proof
% 0.23/0.46 tff(comb_app_type, type, (
% 0.23/0.46 comb_app: ( $i * $i ) > $i)).
% 0.23/0.46 tff(ap_parcontractE_sk1q_type, type, (
% 0.23/0.46 ap_parcontractE_sk1q: ( $i * $i * $i ) > $i)).
% 0.23/0.46 tff(r_type, type, (
% 0.23/0.46 r: $i)).
% 0.23/0.46 tff(p_type, type, (
% 0.23/0.46 p: $i)).
% 0.23/0.46 tff(combS_type, type, (
% 0.23/0.46 combS: $i)).
% 0.23/0.46 tff(ap_parcontractE_sk1p_type, type, (
% 0.23/0.46 ap_parcontractE_sk1p: ( $i * $i * $i ) > $i)).
% 0.23/0.46 tff(ap_parcontractE_c3_type, type, (
% 0.23/0.46 ap_parcontractE_c3: ( $i * $i * $i ) > $o)).
% 0.23/0.46 tff(ap_parcontractE_c2_type, type, (
% 0.23/0.46 ap_parcontractE_c2: ( $i * $i * $i ) > $o)).
% 0.23/0.46 tff(combK_type, type, (
% 0.23/0.46 combK: $i)).
% 0.23/0.46 tff(ap_parcontractE_c4_type, type, (
% 0.23/0.46 ap_parcontractE_c4: ( $i * $i * $i ) > $o)).
% 0.23/0.46 tff(ap_parcontractE_sk2s_type, type, (
% 0.23/0.46 ap_parcontractE_sk2s: ( $i * $i * $i ) > $i)).
% 0.23/0.46 tff(ap_parcontractE_sk2q_type, type, (
% 0.23/0.46 ap_parcontractE_sk2q: ( $i * $i * $i ) > $i)).
% 0.23/0.46 tff(member_type, type, (
% 0.23/0.46 member: ( $i * $i ) > $o)).
% 0.23/0.46 tff(parcontract_type, type, (
% 0.23/0.46 parcontract: $i)).
% 0.23/0.46 tff(pair_type, type, (
% 0.23/0.46 pair: ( $i * $i ) > $i)).
% 0.23/0.46 tff(ap_parcontractE_c1_type, type, (
% 0.23/0.46 ap_parcontractE_c1: ( $i * $i * $i ) > $o)).
% 0.23/0.46 tff(comb_type, type, (
% 0.23/0.46 comb: $i)).
% 0.23/0.46 tff(1,assumption,(combS = comb_app(combK, r)), introduced(assumption)).
% 0.23/0.46 tff(2,plain,
% 0.23/0.46 (^[Q: $i, P: $i] : refl((~(combS = comb_app(P, Q))) <=> (~(combS = comb_app(P, Q))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(3,plain,
% 0.23/0.46 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[2])).
% 0.23/0.46 tff(4,plain,
% 0.23/0.46 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q))) <=> ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(5,axiom,(![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_app')).
% 0.23/0.46 tff(6,plain,
% 0.23/0.46 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.23/0.46 tff(7,plain,(
% 0.23/0.46 ![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[6])).
% 0.23/0.46 tff(8,plain,
% 0.23/0.46 (![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.23/0.46 tff(9,plain,
% 0.23/0.46 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(combK, r)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(10,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 0.23/0.46 tff(11,plain,(~(combS = comb_app(combK, r))), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(12,assumption,(ap_parcontractE_c2(combS, p, r)), introduced(assumption)).
% 0.23/0.46 tff(13,plain,
% 0.23/0.46 (^[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))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(14,plain,
% 0.23/0.46 (![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)))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[13])).
% 0.23/0.46 tff(15,plain,
% 0.23/0.46 (![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)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(16,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE6')).
% 0.23/0.46 tff(17,plain,
% 0.23/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.23/0.46 tff(18,plain,(
% 0.23/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.23/0.46 inference(skolemize,[status(sab)],[17])).
% 0.23/0.46 tff(19,plain,
% 0.23/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.23/0.46 tff(20,plain,
% 0.23/0.46 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(21,plain,
% 0.23/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | ((~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r)))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(22,plain,
% 0.23/0.46 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c2(P, Q, R)) | (P = comb_app(combK, R)))) | (~ap_parcontractE_c2(combS, p, r)) | (combS = comb_app(combK, r))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.23/0.46 tff(23,plain,
% 0.23/0.46 ($false),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[22, 19, 12, 11])).
% 0.23/0.46 tff(24,plain,(~ap_parcontractE_c2(combS, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.46 tff(25,assumption,(ap_parcontractE_c4(combS, p, r)), introduced(assumption)).
% 0.23/0.46 tff(26,plain,
% 0.23/0.46 (^[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)))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(27,plain,
% 0.23/0.46 (![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))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.46 tff(28,plain,
% 0.23/0.46 (![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))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(29,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE12')).
% 0.23/0.46 tff(30,plain,
% 0.23/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.23/0.46 tff(31,plain,(
% 0.23/0.46 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.23/0.46 inference(skolemize,[status(sab)],[30])).
% 0.23/0.46 tff(32,plain,
% 0.23/0.46 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(P, ap_parcontractE_sk2q(P, Q, R)), parcontract))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.23/0.46 tff(33,plain,
% 0.23/0.46 (((~![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(combS, p, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, 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(combS, p, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(34,plain,
% 0.23/0.46 ((~![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(combS, p, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(35,plain,
% 0.23/0.46 ((~![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(combS, p, r)) | member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.23/0.46 tff(36,plain,
% 0.23/0.46 (member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[35, 32, 25])).
% 0.23/0.46 tff(37,plain,
% 0.23/0.46 (^[R: $i] : refl(((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ((~member(pair(combS, R), parcontract)) | (R = combS)))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(38,plain,
% 0.23/0.46 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[37])).
% 0.23/0.46 tff(39,plain,
% 0.23/0.46 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS)) <=> ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(40,axiom,(![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s_parcontractE2')).
% 0.23/0.46 tff(41,plain,
% 0.23/0.46 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.23/0.46 tff(42,plain,(
% 0.23/0.46 ![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.23/0.46 inference(skolemize,[status(sab)],[41])).
% 0.23/0.46 tff(43,plain,
% 0.23/0.46 (![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.23/0.46 tff(44,plain,
% 0.23/0.46 (((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))) <=> ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(45,plain,
% 0.23/0.46 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | ((~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS))),
% 0.23/0.46 inference(quant_inst,[status(thm)],[])).
% 0.23/0.46 tff(46,plain,
% 0.23/0.46 ((~![R: $i] : ((~member(pair(combS, R), parcontract)) | (R = combS))) | (~member(pair(combS, ap_parcontractE_sk2q(combS, p, r)), parcontract)) | (ap_parcontractE_sk2q(combS, p, r) = combS)),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.23/0.46 tff(47,plain,
% 0.23/0.46 (ap_parcontractE_sk2q(combS, p, r) = combS),
% 0.23/0.46 inference(unit_resolution,[status(thm)],[46, 43, 36])).
% 0.23/0.46 tff(48,plain,
% 0.23/0.46 (combS = ap_parcontractE_sk2q(combS, p, r)),
% 0.23/0.46 inference(symmetry,[status(thm)],[47])).
% 0.23/0.46 tff(49,plain,
% 0.23/0.46 (comb_app(combS, ap_parcontractE_sk2s(combS, p, r)) = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[48])).
% 0.23/0.46 tff(50,plain,
% 0.23/0.46 (comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r)) = comb_app(combS, ap_parcontractE_sk2s(combS, p, r))),
% 0.23/0.46 inference(symmetry,[status(thm)],[49])).
% 0.23/0.46 tff(51,plain,
% 0.23/0.46 (^[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)))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(52,plain,
% 0.23/0.46 (![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))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[51])).
% 0.23/0.46 tff(53,plain,
% 0.23/0.46 (![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))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(54,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE14')).
% 0.23/0.46 tff(55,plain,
% 0.23/0.46 (![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))))),
% 0.23/0.46 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.23/0.46 tff(56,plain,(
% 0.23/0.46 ![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))))),
% 0.23/0.47 inference(skolemize,[status(sab)],[55])).
% 0.23/0.47 tff(57,plain,
% 0.23/0.47 (![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))))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.23/0.47 tff(58,plain,
% 0.23/0.47 (((~![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(combS, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, 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(combS, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(59,plain,
% 0.23/0.47 ((~![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(combS, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(60,plain,
% 0.23/0.47 ((~![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(combS, p, r)) | (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.23/0.47 tff(61,plain,
% 0.23/0.47 (r = comb_app(ap_parcontractE_sk2q(combS, p, r), ap_parcontractE_sk2s(combS, p, r))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[60, 57, 25])).
% 0.23/0.47 tff(62,plain,
% 0.23/0.47 (r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r))),
% 0.23/0.47 inference(transitivity,[status(thm)],[61, 50])).
% 0.23/0.47 tff(63,plain,
% 0.23/0.47 (^[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)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(64,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.23/0.47 tff(65,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(66,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE13')).
% 0.23/0.47 tff(67,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.23/0.47 tff(68,plain,(
% 0.23/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.23/0.47 inference(skolemize,[status(sab)],[67])).
% 0.23/0.47 tff(69,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c4(P, Q, R)) | member(pair(Q, ap_parcontractE_sk2s(P, Q, R)), parcontract))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.23/0.47 tff(70,plain,
% 0.23/0.47 (((~![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(combS, p, r)) | member(pair(p, ap_parcontractE_sk2s(combS, 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(combS, p, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(71,plain,
% 0.23/0.47 ((~![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(combS, p, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(72,plain,
% 0.23/0.47 ((~![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(combS, p, r)) | member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.23/0.47 tff(73,plain,
% 0.23/0.47 (member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[72, 69, 25])).
% 0.23/0.47 tff(74,plain,
% 0.23/0.47 (^[PP: $i] : refl(((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(75,plain,
% 0.23/0.47 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[74])).
% 0.23/0.47 tff(76,plain,
% 0.23/0.47 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract))) <=> ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(77,axiom,(![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_parcontractD_c1')).
% 0.23/0.47 tff(78,plain,
% 0.23/0.47 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.23/0.47 tff(79,plain,(
% 0.23/0.47 ![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[78])).
% 0.23/0.47 tff(80,plain,
% 0.23/0.47 (![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.23/0.47 tff(81,plain,
% 0.23/0.47 (((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(82,plain,
% 0.23/0.47 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(83,plain,
% 0.23/0.47 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))) | (~member(pair(p, ap_parcontractE_sk2s(combS, p, r)), parcontract))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.23/0.47 tff(84,plain,
% 0.23/0.47 (~(r = comb_app(combS, ap_parcontractE_sk2s(combS, p, r)))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[83, 80, 73])).
% 0.23/0.47 tff(85,plain,
% 0.23/0.47 ($false),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[84, 62])).
% 0.23/0.47 tff(86,plain,(~ap_parcontractE_c4(combS, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.47 tff(87,assumption,(ap_parcontractE_c1(combS, p, r)), introduced(assumption)).
% 0.23/0.47 tff(88,plain,
% 0.23/0.47 (^[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)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(89,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[88])).
% 0.23/0.47 tff(90,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(91,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE2')).
% 0.23/0.47 tff(92,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.23/0.47 tff(93,plain,(
% 0.23/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.23/0.47 inference(skolemize,[status(sab)],[92])).
% 0.23/0.47 tff(94,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.23/0.47 tff(95,plain,
% 0.23/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(96,plain,
% 0.23/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | ((~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(97,plain,
% 0.23/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | member(comb_app(P, Q), comb))) | (~ap_parcontractE_c1(combS, p, r)) | member(comb_app(combS, p), comb)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.23/0.47 tff(98,plain,
% 0.23/0.47 (member(comb_app(combS, p), comb)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[97, 94, 87])).
% 0.23/0.47 tff(99,plain,
% 0.23/0.47 (^[Q: $i, P: $i] : refl(((~member(comb_app(P, Q), comb)) | member(Q, comb)) <=> ((~member(comb_app(P, Q), comb)) | member(Q, comb)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(100,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[99])).
% 0.23/0.47 tff(101,plain,
% 0.23/0.47 (![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))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(102,axiom,(![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_E2')).
% 0.23/0.47 tff(103,plain,
% 0.23/0.47 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.23/0.47 tff(104,plain,(
% 0.23/0.47 ![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.23/0.47 inference(skolemize,[status(sab)],[103])).
% 0.23/0.47 tff(105,plain,
% 0.23/0.47 (![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[104, 100])).
% 0.23/0.47 tff(106,plain,
% 0.23/0.47 (((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))) <=> ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(107,plain,
% 0.23/0.47 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | ((~member(comb_app(combS, p), comb)) | member(p, comb))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(108,plain,
% 0.23/0.47 ((~![Q: $i, P: $i] : ((~member(comb_app(P, Q), comb)) | member(Q, comb))) | (~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.23/0.47 tff(109,plain,
% 0.23/0.47 ((~member(comb_app(combS, p), comb)) | member(p, comb)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[108, 105])).
% 0.23/0.47 tff(110,plain,
% 0.23/0.47 (member(p, comb)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[109, 98])).
% 0.23/0.47 tff(111,plain,
% 0.23/0.47 (^[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))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(112,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[111])).
% 0.23/0.47 tff(113,plain,
% 0.23/0.47 (![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)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(114,axiom,(![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ap_parcontractE3')).
% 0.23/0.47 tff(115,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.23/0.47 tff(116,plain,(
% 0.23/0.47 ![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.23/0.47 inference(skolemize,[status(sab)],[115])).
% 0.23/0.47 tff(117,plain,
% 0.23/0.47 (![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[116, 112])).
% 0.23/0.47 tff(118,plain,
% 0.23/0.47 (((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p)))) <=> ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(119,plain,
% 0.23/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | ((~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(120,plain,
% 0.23/0.47 ((~![R: $i, Q: $i, P: $i] : ((~ap_parcontractE_c1(P, Q, R)) | (R = comb_app(P, Q)))) | (~ap_parcontractE_c1(combS, p, r)) | (r = comb_app(combS, p))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.23/0.47 tff(121,plain,
% 0.23/0.47 (r = comb_app(combS, p)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[120, 117, 87])).
% 0.23/0.47 tff(122,plain,
% 0.23/0.47 (((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))) <=> ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(123,plain,
% 0.23/0.47 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract)))),
% 0.23/0.47 inference(quant_inst,[status(thm)],[])).
% 0.23/0.47 tff(124,plain,
% 0.23/0.47 ((~![PP: $i] : ((~(r = comb_app(combS, PP))) | (~member(pair(p, PP), parcontract)))) | (~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.23/0.47 tff(125,plain,
% 0.23/0.47 ((~(r = comb_app(combS, p))) | (~member(pair(p, p), parcontract))),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[124, 80])).
% 0.23/0.47 tff(126,plain,
% 0.23/0.47 (~member(pair(p, p), parcontract)),
% 0.23/0.47 inference(unit_resolution,[status(thm)],[125, 121])).
% 0.23/0.47 tff(127,plain,
% 0.23/0.47 (^[P: $i] : refl(((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ((~member(P, comb)) | member(pair(P, P), parcontract)))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(128,plain,
% 0.23/0.47 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[127])).
% 0.23/0.47 tff(129,plain,
% 0.23/0.47 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract)) <=> ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(130,axiom,(![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','parcontract_intros1')).
% 0.23/0.47 tff(131,plain,
% 0.23/0.47 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.23/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.23/0.48 tff(132,plain,(
% 0.23/0.48 ![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.23/0.48 inference(skolemize,[status(sab)],[131])).
% 0.23/0.48 tff(133,plain,
% 0.23/0.48 (![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[132, 128])).
% 0.23/0.48 tff(134,plain,
% 0.23/0.48 (((~![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))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(135,plain,
% 0.23/0.48 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | ((~member(p, comb)) | member(pair(p, p), parcontract))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(136,plain,
% 0.23/0.48 ((~![P: $i] : ((~member(P, comb)) | member(pair(P, P), parcontract))) | (~member(p, comb)) | member(pair(p, p), parcontract)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.23/0.48 tff(137,plain,
% 0.23/0.48 ($false),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[136, 133, 126, 110])).
% 0.23/0.48 tff(138,plain,(~ap_parcontractE_c1(combS, p, r)), inference(lemma,lemma(discharge,[]))).
% 0.23/0.48 tff(139,plain,
% 0.23/0.48 (member(pair(comb_app(combS, p), r), parcontract) <=> member(pair(comb_app(combS, p), r), parcontract)),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(140,axiom,(member(pair(comb_app(combS, p), r), parcontract)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','s1_parcontractD_h1')).
% 0.23/0.48 tff(141,plain,
% 0.23/0.48 (member(pair(comb_app(combS, p), r), parcontract)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.23/0.48 tff(142,plain,
% 0.23/0.48 (^[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))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(143,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[142])).
% 0.23/0.48 tff(144,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(145,plain,
% 0.23/0.48 (^[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)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(146,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[145])).
% 0.23/0.48 tff(147,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE1')).
% 0.23/0.48 tff(148,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.23/0.48 tff(149,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[148, 144])).
% 0.23/0.48 tff(150,plain,(
% 0.23/0.48 ![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)))),
% 0.23/0.48 inference(skolemize,[status(sab)],[149])).
% 0.23/0.48 tff(151,plain,
% 0.23/0.48 (![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)))),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[150, 143])).
% 0.23/0.48 tff(152,plain,
% 0.23/0.48 (((~![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)))) | ((~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, 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)))) | (~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(153,plain,
% 0.23/0.48 ((ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, p), r), parcontract))) <=> ((~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(154,plain,
% 0.23/0.48 (((~![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(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, 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)))) | ((~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r)))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[153])).
% 0.23/0.48 tff(155,plain,
% 0.23/0.48 (((~![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(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, 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)))) | (~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r))),
% 0.23/0.48 inference(transitivity,[status(thm)],[154, 152])).
% 0.23/0.48 tff(156,plain,
% 0.23/0.48 ((~![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(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r) | (~member(pair(comb_app(combS, p), r), parcontract)))),
% 0.23/0.48 inference(quant_inst,[status(thm)],[])).
% 0.23/0.48 tff(157,plain,
% 0.23/0.48 ((~![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)))) | (~member(pair(comb_app(combS, p), r), parcontract)) | ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r)),
% 0.23/0.48 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.23/0.48 tff(158,plain,
% 0.23/0.48 (ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r) | ap_parcontractE_c1(combS, p, r)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[157, 151, 141])).
% 0.23/0.48 tff(159,plain,
% 0.23/0.48 (ap_parcontractE_c4(combS, p, r) | ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[158, 138])).
% 0.23/0.48 tff(160,plain,
% 0.23/0.48 (ap_parcontractE_c3(combS, p, r) | ap_parcontractE_c2(combS, p, r)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[159, 86])).
% 0.23/0.48 tff(161,plain,
% 0.23/0.48 (ap_parcontractE_c3(combS, p, r)),
% 0.23/0.48 inference(unit_resolution,[status(thm)],[160, 24])).
% 0.23/0.48 tff(162,plain,
% 0.23/0.48 (^[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)))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(163,plain,
% 0.23/0.48 (![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))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[162])).
% 0.23/0.49 tff(164,plain,
% 0.23/0.49 (![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))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(165,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/sandbox2/benchmark/theBenchmark.p','ap_parcontractE11')).
% 0.23/0.49 tff(166,plain,
% 0.23/0.49 (![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))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.23/0.49 tff(167,plain,(
% 0.23/0.49 ![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))))),
% 0.23/0.49 inference(skolemize,[status(sab)],[166])).
% 0.23/0.49 tff(168,plain,
% 0.23/0.49 (![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))))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.23/0.49 tff(169,plain,
% 0.23/0.49 (((~![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(combS, p, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, 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(combS, p, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(170,plain,
% 0.23/0.49 ((~![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(combS, p, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(171,plain,
% 0.23/0.49 ((~![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(combS, p, r)) | (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r)))),
% 0.23/0.49 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.23/0.49 tff(172,plain,
% 0.23/0.49 (combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[171, 168, 161])).
% 0.23/0.49 tff(173,plain,
% 0.23/0.49 ((~![Q: $i, P: $i] : (~(combS = comb_app(P, Q)))) | (~(combS = comb_app(comb_app(combS, ap_parcontractE_sk1p(combS, p, r)), ap_parcontractE_sk1q(combS, p, r))))),
% 0.23/0.49 inference(quant_inst,[status(thm)],[])).
% 0.23/0.49 tff(174,plain,
% 0.23/0.49 ($false),
% 0.23/0.49 inference(unit_resolution,[status(thm)],[173, 8, 172])).
% 0.23/0.49 % SZS output end Proof
% 0.23/0.49 % E exiting
%------------------------------------------------------------------------------