%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO082-1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:05:32 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO082-1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 14:16:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% 0.19/0.41 tff(part_of_type, type, (
% 0.19/0.41 part_of: ( $i * $i ) > $o)).
% 0.19/0.41 tff(sum_type, type, (
% 0.19/0.41 sum: ( $i * $i ) > $i)).
% 0.19/0.41 tff(ax0_sk10_type, type, (
% 0.19/0.41 ax0_sk10: ( $i * $i ) > $i)).
% 0.19/0.41 tff(sk15_type, type, (
% 0.19/0.41 sk15: $i)).
% 0.19/0.41 tff(ax0_sk8_type, type, (
% 0.19/0.41 ax0_sk8: $i > $i)).
% 0.19/0.41 tff(ax0_sk9_type, type, (
% 0.19/0.41 ax0_sk9: ( $i * $i ) > $i)).
% 0.19/0.41 tff(sk14_type, type, (
% 0.19/0.41 sk14: $i)).
% 0.19/0.41 tff(inner_point_type, type, (
% 0.19/0.41 inner_point: ( $i * $i ) > $o)).
% 0.19/0.41 tff(incident_c_type, type, (
% 0.19/0.41 incident_c: ( $i * $i ) > $o)).
% 0.19/0.41 tff(ax0_sk13_type, type, (
% 0.19/0.41 ax0_sk13: ( $i * $i ) > $i)).
% 0.19/0.41 tff(1,plain,
% 0.19/0.41 (^[A: $i] : refl(inner_point(ax0_sk8(A), A) <=> inner_point(ax0_sk8(A), A))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(2,plain,
% 0.19/0.41 (![A: $i] : inner_point(ax0_sk8(A), A) <=> ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.19/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.41 tff(3,plain,
% 0.19/0.41 (![A: $i] : inner_point(ax0_sk8(A), A) <=> ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(4,axiom,(![A: $i] : inner_point(ax0_sk8(A), A)), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c3_37')).
% 0.19/0.41 tff(5,plain,
% 0.19/0.41 (![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.41 tff(6,plain,(
% 0.19/0.41 ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.19/0.41 inference(skolemize,[status(sab)],[5])).
% 0.19/0.41 tff(7,plain,
% 0.19/0.41 (![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.41 tff(8,plain,
% 0.19/0.41 ((~![A: $i] : inner_point(ax0_sk8(A), A)) | inner_point(ax0_sk8(sk15), sk15)),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(9,plain,
% 0.19/0.41 (inner_point(ax0_sk8(sk15), sk15)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.19/0.41 tff(10,plain,
% 0.19/0.41 (^[B: $i, A: $i] : refl(((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(11,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.41 tff(12,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B)))) <=> ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(13,axiom,(![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c4_39')).
% 0.19/0.41 tff(14,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.41 tff(15,plain,(
% 0.19/0.41 ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[14])).
% 0.19/0.41 tff(16,plain,
% 0.19/0.41 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.19/0.41 tff(17,plain,
% 0.19/0.41 (((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(ax0_sk8(sk15), sk15)) | (sk15 = sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))) <=> ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(ax0_sk8(sk15), sk15)) | (sk15 = sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(ax0_sk8(sk15), sk15)) | (sk15 = sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(ax0_sk8(sk15), sk15)) | (sk15 = sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (sk15 = sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk15),
% 0.19/0.42 inference(symmetry,[status(thm)],[20])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) <=> part_of(sk14, sk15)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.42 tff(23,plain,
% 0.19/0.42 (part_of(sk14, sk15) <=> part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[22])).
% 0.19/0.42 tff(24,plain,
% 0.19/0.42 (part_of(sk14, sk15) <=> part_of(sk14, sk15)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(25,axiom,(part_of(sk14, sk15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_of_antisymmetry_67')).
% 0.19/0.42 tff(26,plain,
% 0.19/0.42 (part_of(sk14, sk15)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.19/0.42 tff(27,plain,
% 0.19/0.42 (part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.19/0.42 tff(28,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) <=> incident_c(ax0_sk13(sk14, sk15), sk15)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.42 tff(29,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sk15), sk15) <=> incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(symmetry,[status(thm)],[28])).
% 0.19/0.42 tff(30,plain,
% 0.19/0.42 ((~incident_c(ax0_sk13(sk14, sk15), sk15)) <=> (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[29])).
% 0.19/0.42 tff(31,plain,
% 0.19/0.42 (ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) = ax0_sk13(sk14, sk15)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.42 tff(32,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) <=> incident_c(ax0_sk13(sk14, sk15), sk15)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[31, 21])).
% 0.19/0.42 tff(33,plain,
% 0.19/0.42 ((sk15 = sk14) <=> (sk14 = sk15)),
% 0.19/0.42 inference(commutativity,[status(thm)],[])).
% 0.19/0.42 tff(34,plain,
% 0.19/0.42 ((sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) <=> (sk15 = sk14)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.42 tff(35,plain,
% 0.19/0.42 ((sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) <=> (sk14 = sk15)),
% 0.19/0.42 inference(transitivity,[status(thm)],[34, 33])).
% 0.19/0.42 tff(36,plain,
% 0.19/0.42 ((sk14 = sk15) <=> (sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14)),
% 0.19/0.42 inference(symmetry,[status(thm)],[35])).
% 0.19/0.42 tff(37,plain,
% 0.19/0.42 ((~(sk14 = sk15)) <=> (~(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.42 tff(38,plain,
% 0.19/0.42 ((~(sk14 = sk15)) <=> (~(sk14 = sk15))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(39,axiom,(~(sk14 = sk15)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_of_antisymmetry_69')).
% 0.19/0.42 tff(40,plain,
% 0.19/0.42 (~(sk14 = sk15)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.42 tff(41,plain,
% 0.19/0.42 (~(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[40, 37])).
% 0.19/0.42 tff(42,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) <=> incident_c(ax0_sk13(sk14, sk15), sk14)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[31])).
% 0.19/0.42 tff(43,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sk15), sk14) <=> incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14)),
% 0.19/0.42 inference(symmetry,[status(thm)],[42])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~incident_c(ax0_sk13(sk14, sk15), sk14)) <=> (~incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[43])).
% 0.19/0.42 tff(45,assumption,(~incident_c(ax0_sk13(sk14, sk15), sk14)), introduced(assumption)).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (~incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (^[B: $i, A: $i] : refl(((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)) <=> ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(48,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)) <=> ![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.42 tff(49,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)) <=> ![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(50,plain,
% 0.19/0.42 (^[B: $i, A: $i] : trans(monotonicity(rewrite((incident_c(ax0_sk13(A, B), B) | incident_c(ax0_sk13(A, B), A)) <=> (incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))), (((incident_c(ax0_sk13(A, B), B) | incident_c(ax0_sk13(A, B), A)) | (B = A)) <=> ((incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)) | (B = A)))), rewrite(((incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B)) | (B = A)) <=> ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))), (((incident_c(ax0_sk13(A, B), B) | incident_c(ax0_sk13(A, B), A)) | (B = A)) <=> ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(51,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((incident_c(ax0_sk13(A, B), B) | incident_c(ax0_sk13(A, B), A)) | (B = A)) <=> ![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.42 tff(52,axiom,(![B: $i, A: $i] : ((incident_c(ax0_sk13(A, B), B) | incident_c(ax0_sk13(A, B), A)) | (B = A))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c9_45')).
% 0.19/0.42 tff(53,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.19/0.42 tff(54,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.19/0.42 tff(55,plain,(
% 0.19/0.42 ![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(skolemize,[status(sab)],[54])).
% 0.19/0.42 tff(56,plain,
% 0.19/0.42 (![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.19/0.42 tff(57,plain,
% 0.19/0.42 (((~![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))) | ((sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))) <=> ((~![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))) | (sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(58,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))) | ((sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(59,plain,
% 0.19/0.42 ((~![B: $i, A: $i] : ((B = A) | incident_c(ax0_sk13(A, B), A) | incident_c(ax0_sk13(A, B), B))) | (sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.19/0.42 tff(60,plain,
% 0.19/0.42 ((sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)) = sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sk14) | incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.19/0.42 tff(61,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[60, 46, 41])).
% 0.19/0.42 tff(62,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sk15), sk15)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[61, 32])).
% 0.19/0.42 tff(63,plain,
% 0.19/0.42 (incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[62, 29])).
% 0.19/0.42 tff(64,plain,
% 0.19/0.42 (part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14) <=> part_of(sk15, sk14)),
% 0.19/0.42 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.42 tff(65,plain,
% 0.19/0.42 (part_of(sk15, sk14) <=> part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)),
% 0.19/0.42 inference(symmetry,[status(thm)],[64])).
% 0.19/0.42 tff(66,plain,
% 0.19/0.42 (part_of(sk15, sk14) <=> part_of(sk15, sk14)),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(67,axiom,(part_of(sk15, sk14)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_of_antisymmetry_68')).
% 0.19/0.42 tff(68,plain,
% 0.19/0.42 (part_of(sk15, sk14)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.19/0.42 tff(69,plain,
% 0.19/0.42 (part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[68, 65])).
% 0.19/0.42 tff(70,plain,
% 0.19/0.42 (^[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))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(71,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.42 tff(72,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(73,plain,
% 0.19/0.42 (^[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)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(74,plain,
% 0.19/0.42 (![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)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[73])).
% 0.19/0.42 tff(75,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')).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.19/0.42 tff(77,plain,
% 0.19/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.19/0.42 tff(78,plain,(
% 0.19/0.42 ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.19/0.42 inference(skolemize,[status(sab)],[77])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 71])).
% 0.19/0.42 tff(80,plain,
% 0.19/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 ((incident_c(ax0_sk13(sk14, sk15), sk14) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14))) <=> (incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sk14) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sk14) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[82, 80])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sk14) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(ax0_sk13(sk14, sk15), sk14) | (~part_of(sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)), sk14)) | (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[85, 79, 45, 69])).
% 0.19/0.43 tff(87,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[86, 63])).
% 0.19/0.43 tff(88,plain,(incident_c(ax0_sk13(sk14, sk15), sk14)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.43 tff(89,plain,
% 0.19/0.43 ((sk14 = sk15) <=> (sk15 = sk14)),
% 0.19/0.43 inference(symmetry,[status(thm)],[33])).
% 0.19/0.43 tff(90,plain,
% 0.19/0.43 ((~(sk14 = sk15)) <=> (~(sk15 = sk14))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[89])).
% 0.19/0.43 tff(91,plain,
% 0.19/0.43 (~(sk15 = sk14)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[40, 90])).
% 0.19/0.43 tff(92,plain,
% 0.19/0.43 (^[B: $i, A: $i] : refl(((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A))) <=> ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(93,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A))) <=> ![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[92])).
% 0.19/0.43 tff(94,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A))) <=> ![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(95,plain,
% 0.19/0.43 (^[B: $i, A: $i] : rewrite((((~incident_c(ax0_sk13(A, B), A)) | (~incident_c(ax0_sk13(A, B), B))) | (B = A)) <=> ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(96,plain,
% 0.19/0.43 (![B: $i, A: $i] : (((~incident_c(ax0_sk13(A, B), A)) | (~incident_c(ax0_sk13(A, B), B))) | (B = A)) <=> ![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[95])).
% 0.19/0.43 tff(97,axiom,(![B: $i, A: $i] : (((~incident_c(ax0_sk13(A, B), A)) | (~incident_c(ax0_sk13(A, B), B))) | (B = A))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004-0.ax','c9_48')).
% 0.19/0.43 tff(98,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.19/0.43 tff(99,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.19/0.43 tff(100,plain,(
% 0.19/0.43 ![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[99])).
% 0.19/0.43 tff(101,plain,
% 0.19/0.43 (![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.19/0.43 tff(102,plain,
% 0.19/0.43 (((~![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))) | ((sk15 = sk14) | (~incident_c(ax0_sk13(sk14, sk15), sk15)) | (~incident_c(ax0_sk13(sk14, sk15), sk14)))) <=> ((~![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))) | (sk15 = sk14) | (~incident_c(ax0_sk13(sk14, sk15), sk15)) | (~incident_c(ax0_sk13(sk14, sk15), sk14)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(103,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))) | ((sk15 = sk14) | (~incident_c(ax0_sk13(sk14, sk15), sk15)) | (~incident_c(ax0_sk13(sk14, sk15), sk14)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(104,plain,
% 0.19/0.43 ((~![B: $i, A: $i] : ((B = A) | (~incident_c(ax0_sk13(A, B), B)) | (~incident_c(ax0_sk13(A, B), A)))) | (sk15 = sk14) | (~incident_c(ax0_sk13(sk14, sk15), sk15)) | (~incident_c(ax0_sk13(sk14, sk15), sk14))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.43 tff(105,plain,
% 0.19/0.43 ((~incident_c(ax0_sk13(sk14, sk15), sk15)) | (~incident_c(ax0_sk13(sk14, sk15), sk14))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[104, 101, 91])).
% 0.19/0.43 tff(106,plain,
% 0.19/0.43 (~incident_c(ax0_sk13(sk14, sk15), sk15)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[105, 88])).
% 0.19/0.43 tff(107,plain,
% 0.19/0.43 (~incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[106, 30])).
% 0.19/0.43 tff(108,plain,
% 0.19/0.43 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(109,plain,
% 0.19/0.43 ((incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))) <=> ((~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(110,plain,
% 0.19/0.43 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[109])).
% 0.19/0.43 tff(111,plain,
% 0.19/0.43 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[110, 108])).
% 0.19/0.43 tff(112,plain,
% 0.19/0.43 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(113,plain,
% 0.19/0.43 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~incident_c(ax0_sk13(sk14, sk15), sk14)) | (~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.19/0.43 tff(114,plain,
% 0.19/0.43 ((~part_of(sk14, sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))) | incident_c(ax0_sk13(sk14, sk15), sum(ax0_sk9(ax0_sk8(sk15), sk15), ax0_sk10(ax0_sk8(sk15), sk15)))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[113, 79, 88])).
% 0.19/0.43 tff(115,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[114, 107, 27])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------