%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO084-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:05:33 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO084-1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 14:16:56 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.42 % SZS status Unsatisfiable
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(incident_c_type, type, (
% 0.20/0.42 incident_c: ( $i * $i ) > $o)).
% 0.20/0.42 tff(sk14_type, type, (
% 0.20/0.42 sk14: $i)).
% 0.20/0.42 tff(ax0_sk1_type, type, (
% 0.20/0.42 ax0_sk1: ( $i * $i ) > $i)).
% 0.20/0.42 tff(sk16_type, type, (
% 0.20/0.42 sk16: $i)).
% 0.20/0.42 tff(sum_type, type, (
% 0.20/0.42 sum: ( $i * $i ) > $i)).
% 0.20/0.42 tff(sk15_type, type, (
% 0.20/0.42 sk15: $i)).
% 0.20/0.42 tff(part_of_type, type, (
% 0.20/0.42 part_of: ( $i * $i ) > $o)).
% 0.20/0.42 tff(1,assumption,(incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)), introduced(assumption)).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 ((~part_of(sum(sk14, sk15), sk16)) <=> (~part_of(sum(sk14, sk15), sk16))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(3,axiom,(~part_of(sum(sk14, sk15), sk16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary_2_6_2_70')).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (~part_of(sum(sk14, sk15), sk16)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (^[B: $i, A: $i] : refl(((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B)) <=> ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B)))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B)) <=> ![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[5])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B)) <=> ![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(8,axiom,(![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','part_of_defn_3')).
% 0.20/0.42 tff(9,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.42 tff(10,plain,(
% 0.20/0.42 ![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.20/0.42 inference(skolemize,[status(sab)],[9])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.42 tff(12,plain,
% 0.20/0.42 (((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | ((~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16)) | part_of(sum(sk14, sk15), sk16))) <=> ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16)) | part_of(sum(sk14, sk15), sk16))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | ((~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16)) | part_of(sum(sk14, sk15), sk16))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16)) | part_of(sum(sk14, sk15), sk16)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[14, 11, 4])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (part_of(sk15, sk16) <=> part_of(sk15, sk16)),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(17,axiom,(part_of(sk15, sk16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary_2_6_2_68')).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 (part_of(sk15, sk16)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 (^[B: $i, A: $i, C: $i] : refl((incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B))) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~part_of(A, B)) | (~incident_c(C, A))) <=> ((~incident_c(C, A)) | (~part_of(A, B)))), ((((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> (((~incident_c(C, A)) | (~part_of(A, B))) | incident_c(C, B)))), rewrite((((~incident_c(C, A)) | (~part_of(A, B))) | incident_c(C, B)) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))), ((((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(23,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B)) <=> ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.42 tff(24,axiom,(![B: $i, A: $i, C: $i] : (((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','part_of_defn_1')).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42 tff(27,plain,(
% 0.20/0.42 ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(skolemize,[status(sab)],[26])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 ((incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)) | (~part_of(sk15, sk16))) <=> ((~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(31,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)) | (~part_of(sk15, sk16)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)) | (~part_of(sk15, sk16)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)))),
% 0.20/0.42 inference(transitivity,[status(thm)],[31, 29])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)) | (~part_of(sk15, sk16)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk15, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 28, 18, 15, 1])).
% 0.20/0.43 tff(36,plain,(~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(37,plain,
% 0.20/0.43 (^[B: $i, A: $i] : refl((part_of(A, B) | incident_c(ax0_sk1(A, B), A)) <=> (part_of(A, B) | incident_c(ax0_sk1(A, B), A)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A)) <=> ![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A)) <=> ![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (^[B: $i, A: $i] : rewrite((incident_c(ax0_sk1(A, B), A) | part_of(A, B)) <=> (part_of(A, B) | incident_c(ax0_sk1(A, B), A)))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(41,plain,
% 0.20/0.43 (![B: $i, A: $i] : (incident_c(ax0_sk1(A, B), A) | part_of(A, B)) <=> ![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.43 tff(42,axiom,(![B: $i, A: $i] : (incident_c(ax0_sk1(A, B), A) | part_of(A, B))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','part_of_defn_2')).
% 0.20/0.43 tff(43,plain,
% 0.20/0.43 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.43 tff(45,plain,(
% 0.20/0.43 ![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(skolemize,[status(sab)],[44])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.43 tff(47,plain,
% 0.20/0.43 (((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | (part_of(sum(sk14, sk15), sk16) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15)))) <=> ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | part_of(sum(sk14, sk15), sk16) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | (part_of(sum(sk14, sk15), sk16) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | part_of(sum(sk14, sk15), sk16) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[49, 46, 4])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (^[B: $i, D: $i, C: $i] : refl((incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C)))) <=> (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(54,plain,
% 0.20/0.43 (^[B: $i, D: $i, C: $i] : rewrite((incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C)))) <=> (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C)))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[54])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))) <=> ![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[57, 56])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[58, 55])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (^[B: $i, D: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~incident_c(D, A))) <=> ((~incident_c(D, A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) <=> (((~incident_c(D, A)) | (~(A = sum(B, C)))) | incident_c(D, B)))), rewrite((((~incident_c(D, A)) | (~(A = sum(B, C)))) | incident_c(D, B)) <=> (incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) <=> (incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) | incident_c(D, C)) <=> ((incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))) | incident_c(D, C)))), rewrite(((incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C)))) | incident_c(D, C)) <=> (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C))))), (((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) | incident_c(D, C)) <=> (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : ((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) | incident_c(D, C)) <=> ![B: $i, D: $i, A: $i, C: $i] : (incident_c(D, C) | incident_c(D, B) | (~incident_c(D, A)) | (~(A = sum(B, C))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![B: $i, D: $i, A: $i, C: $i] : ((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) | incident_c(D, C)) <=> ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(transitivity,[status(thm)],[61, 59])).
% 0.20/0.43 tff(63,axiom,(![B: $i, D: $i, A: $i, C: $i] : ((((~(A = sum(B, C))) | (~incident_c(D, A))) | incident_c(D, B)) | incident_c(D, C))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','sum_defn_4')).
% 0.20/0.43 tff(64,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.20/0.43 tff(65,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[64, 53])).
% 0.20/0.43 tff(66,plain,(
% 0.20/0.43 ![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[65])).
% 0.20/0.43 tff(67,plain,
% 0.20/0.43 (![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[66, 52])).
% 0.20/0.43 tff(68,plain,
% 0.20/0.43 (((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | ((~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))) <=> ((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(69,plain,
% 0.20/0.43 ((incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15)))) <=> ((~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(70,plain,
% 0.20/0.43 (((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))))) <=> ((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | ((~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.43 tff(71,plain,
% 0.20/0.43 (((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))))) <=> ((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15))),
% 0.20/0.43 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.43 tff(72,plain,
% 0.20/0.43 ((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(73,plain,
% 0.20/0.43 ((~![B: $i, D: $i, C: $i] : (incident_c(D, B) | incident_c(D, C) | (~incident_c(D, sum(B, C))))) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sum(sk14, sk15))) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.43 tff(74,plain,
% 0.20/0.43 (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk15)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[73, 67, 50])).
% 0.20/0.43 tff(75,plain,
% 0.20/0.43 (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[74, 36])).
% 0.20/0.43 tff(76,plain,
% 0.20/0.43 (part_of(sk14, sk16) <=> part_of(sk14, sk16)),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(77,axiom,(part_of(sk14, sk16)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary_2_6_2_67')).
% 0.20/0.43 tff(78,plain,
% 0.20/0.43 (part_of(sk14, sk16)),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.20/0.43 tff(79,plain,
% 0.20/0.43 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 ((incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)) | (~part_of(sk14, sk16))) <=> ((~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)) | (~part_of(sk14, sk16)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[80])).
% 0.20/0.44 tff(82,plain,
% 0.20/0.44 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)) | (~part_of(sk14, sk16)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[81, 79])).
% 0.20/0.44 tff(83,plain,
% 0.20/0.44 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14)) | (~part_of(sk14, sk16)))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(84,plain,
% 0.20/0.44 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk16)) | incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk16) | (~incident_c(ax0_sk1(sum(sk14, sk15), sk16), sk14))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.44 tff(85,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[84, 28, 78, 15, 75])).
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44 % E exiting
%------------------------------------------------------------------------------