TSTP Solution File: GEO081-1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO081-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n028.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 : Fri Sep 16 20:34:44 EDT 2022
% Result : Unsatisfiable 0.20s 0.59s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO081-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n028.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 : Wed Aug 31 05:28:19 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.59 % SZS status Unsatisfiable
% 0.20/0.59 % SZS output start Proof
% 0.20/0.59 tff(incident_c_type, type, (
% 0.20/0.59 incident_c: ( $i * $i ) > $o)).
% 0.20/0.59 tff(sk15_type, type, (
% 0.20/0.59 sk15: $i)).
% 0.20/0.59 tff(ax0_sk1_type, type, (
% 0.20/0.59 ax0_sk1: ( $i * $i ) > $i)).
% 0.20/0.59 tff(sk16_type, type, (
% 0.20/0.59 sk16: $i)).
% 0.20/0.59 tff(sk14_type, type, (
% 0.20/0.59 sk14: $i)).
% 0.20/0.59 tff(part_of_type, type, (
% 0.20/0.59 part_of: ( $i * $i ) > $o)).
% 0.20/0.59 tff(sum_type, type, (
% 0.20/0.59 sum: ( $i * $i ) > $i)).
% 0.20/0.59 tff(ax0_sk10_type, type, (
% 0.20/0.59 ax0_sk10: ( $i * $i ) > $i)).
% 0.20/0.59 tff(ax0_sk8_type, type, (
% 0.20/0.59 ax0_sk8: $i > $i)).
% 0.20/0.59 tff(ax0_sk9_type, type, (
% 0.20/0.59 ax0_sk9: ( $i * $i ) > $i)).
% 0.20/0.59 tff(inner_point_type, type, (
% 0.20/0.59 inner_point: ( $i * $i ) > $o)).
% 0.20/0.59 tff(1,plain,
% 0.20/0.59 (^[A: $i] : refl(inner_point(ax0_sk8(A), A) <=> inner_point(ax0_sk8(A), A))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(2,plain,
% 0.20/0.59 (![A: $i] : inner_point(ax0_sk8(A), A) <=> ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.20/0.59 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.59 tff(3,plain,
% 0.20/0.59 (![A: $i] : inner_point(ax0_sk8(A), A) <=> ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(4,axiom,(![A: $i] : inner_point(ax0_sk8(A), A)), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax','c3_37')).
% 0.20/0.59 tff(5,plain,
% 0.20/0.59 (![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.59 tff(6,plain,(
% 0.20/0.59 ![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.20/0.59 inference(skolemize,[status(sab)],[5])).
% 0.20/0.59 tff(7,plain,
% 0.20/0.59 (![A: $i] : inner_point(ax0_sk8(A), A)),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.59 tff(8,plain,
% 0.20/0.59 ((~![A: $i] : inner_point(ax0_sk8(A), A)) | inner_point(ax0_sk8(sk16), sk16)),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(9,plain,
% 0.20/0.59 (inner_point(ax0_sk8(sk16), sk16)),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.59 tff(10,plain,
% 0.20/0.59 (^[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)))))),
% 0.20/0.59 inference(bind,[status(th)],[])).
% 0.20/0.59 tff(11,plain,
% 0.20/0.59 (![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))))),
% 0.20/0.59 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.59 tff(12,plain,
% 0.20/0.59 (![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))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(13,axiom,(![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax','c4_39')).
% 0.20/0.59 tff(14,plain,
% 0.20/0.59 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.59 tff(15,plain,(
% 0.20/0.59 ![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.59 inference(skolemize,[status(sab)],[14])).
% 0.20/0.59 tff(16,plain,
% 0.20/0.59 (![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.59 tff(17,plain,
% 0.20/0.59 (((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(ax0_sk8(sk16), sk16)) | (sk16 = sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))))) <=> ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(ax0_sk8(sk16), sk16)) | (sk16 = sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(18,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | ((~inner_point(ax0_sk8(sk16), sk16)) | (sk16 = sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(19,plain,
% 0.20/0.59 ((~![B: $i, A: $i] : ((~inner_point(A, B)) | (B = sum(ax0_sk9(A, B), ax0_sk10(A, B))))) | (~inner_point(ax0_sk8(sk16), sk16)) | (sk16 = sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.20/0.59 tff(20,plain,
% 0.20/0.59 (sk16 = sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[19, 16, 9])).
% 0.20/0.59 tff(21,plain,
% 0.20/0.59 (sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)) = sk16),
% 0.20/0.59 inference(symmetry,[status(thm)],[20])).
% 0.20/0.59 tff(22,plain,
% 0.20/0.59 (part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) <=> part_of(sk15, sk16)),
% 0.20/0.59 inference(monotonicity,[status(thm)],[21])).
% 0.20/0.59 tff(23,plain,
% 0.20/0.59 (part_of(sk15, sk16) <=> part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))),
% 0.20/0.59 inference(symmetry,[status(thm)],[22])).
% 0.20/0.59 tff(24,plain,
% 0.20/0.59 (part_of(sk15, sk16) <=> part_of(sk15, sk16)),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(25,axiom,(part_of(sk15, sk16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_of_transitivity_68')).
% 0.20/0.59 tff(26,plain,
% 0.20/0.59 (part_of(sk15, sk16)),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.59 tff(27,plain,
% 0.20/0.59 (part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[26, 23])).
% 0.57/0.59 tff(28,plain,
% 0.57/0.59 (incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) <=> incident_c(ax0_sk1(sk14, sk16), sk16)),
% 0.57/0.59 inference(monotonicity,[status(thm)],[21])).
% 0.57/0.59 tff(29,plain,
% 0.57/0.59 (incident_c(ax0_sk1(sk14, sk16), sk16) <=> incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))),
% 0.57/0.59 inference(symmetry,[status(thm)],[28])).
% 0.57/0.59 tff(30,plain,
% 0.57/0.59 ((~incident_c(ax0_sk1(sk14, sk16), sk16)) <=> (~incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))))),
% 0.57/0.59 inference(monotonicity,[status(thm)],[29])).
% 0.57/0.59 tff(31,plain,
% 0.57/0.59 ((~part_of(sk14, sk16)) <=> (~part_of(sk14, sk16))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(32,axiom,(~part_of(sk14, sk16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_of_transitivity_69')).
% 0.57/0.59 tff(33,plain,
% 0.57/0.59 (~part_of(sk14, sk16)),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.57/0.59 tff(34,plain,
% 0.57/0.59 (^[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)))),
% 0.57/0.59 inference(bind,[status(th)],[])).
% 0.57/0.59 tff(35,plain,
% 0.57/0.59 (![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))),
% 0.57/0.59 inference(quant_intro,[status(thm)],[34])).
% 0.57/0.59 tff(36,plain,
% 0.57/0.59 (![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))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(37,axiom,(![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax','part_of_defn_3')).
% 0.57/0.59 tff(38,plain,
% 0.57/0.59 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.57/0.59 tff(39,plain,(
% 0.57/0.59 ![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.57/0.59 inference(skolemize,[status(sab)],[38])).
% 0.57/0.59 tff(40,plain,
% 0.57/0.59 (![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.57/0.59 tff(41,plain,
% 0.57/0.59 (((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | ((~incident_c(ax0_sk1(sk14, sk16), sk16)) | part_of(sk14, sk16))) <=> ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | (~incident_c(ax0_sk1(sk14, sk16), sk16)) | part_of(sk14, sk16))),
% 0.57/0.59 inference(rewrite,[status(thm)],[])).
% 0.57/0.59 tff(42,plain,
% 0.57/0.59 ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | ((~incident_c(ax0_sk1(sk14, sk16), sk16)) | part_of(sk14, sk16))),
% 0.57/0.59 inference(quant_inst,[status(thm)],[])).
% 0.57/0.59 tff(43,plain,
% 0.57/0.59 ((~![B: $i, A: $i] : ((~incident_c(ax0_sk1(A, B), B)) | part_of(A, B))) | (~incident_c(ax0_sk1(sk14, sk16), sk16)) | part_of(sk14, sk16)),
% 0.57/0.59 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.57/0.59 tff(44,plain,
% 0.57/0.59 (~incident_c(ax0_sk1(sk14, sk16), sk16)),
% 0.57/0.59 inference(unit_resolution,[status(thm)],[43, 40, 33])).
% 0.57/0.60 tff(45,plain,
% 0.57/0.60 (~incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[44, 30])).
% 0.57/0.60 tff(46,assumption,(incident_c(ax0_sk1(sk14, sk16), sk15)), introduced(assumption)).
% 0.57/0.60 tff(47,plain,
% 0.57/0.60 (^[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))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(48,plain,
% 0.57/0.60 (![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)))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[47])).
% 0.57/0.60 tff(49,plain,
% 0.57/0.60 (![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)))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(50,plain,
% 0.57/0.60 (^[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)))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(51,plain,
% 0.57/0.60 (![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)))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[50])).
% 0.57/0.60 tff(52,axiom,(![B: $i, A: $i, C: $i] : (((~part_of(A, B)) | (~incident_c(C, A))) | incident_c(C, B))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax','part_of_defn_1')).
% 0.57/0.60 tff(53,plain,
% 0.57/0.60 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.57/0.60 tff(54,plain,
% 0.57/0.60 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[53, 49])).
% 0.57/0.60 tff(55,plain,(
% 0.57/0.60 ![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.57/0.60 inference(skolemize,[status(sab)],[54])).
% 0.57/0.60 tff(56,plain,
% 0.57/0.60 (![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[55, 48])).
% 0.57/0.60 tff(57,plain,
% 0.57/0.60 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) | (~incident_c(ax0_sk1(sk14, sk16), sk15)) | (~part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) | (~incident_c(ax0_sk1(sk14, sk16), sk15)) | (~part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(58,plain,
% 0.57/0.60 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) | (~incident_c(ax0_sk1(sk14, sk16), sk15)) | (~part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16)))))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(59,plain,
% 0.57/0.60 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | incident_c(ax0_sk1(sk14, sk16), sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))) | (~incident_c(ax0_sk1(sk14, sk16), sk15)) | (~part_of(sk15, sum(ax0_sk9(ax0_sk8(sk16), sk16), ax0_sk10(ax0_sk8(sk16), sk16))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.57/0.60 tff(60,plain,
% 0.57/0.60 ($false),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[59, 56, 46, 45, 27])).
% 0.57/0.60 tff(61,plain,(~incident_c(ax0_sk1(sk14, sk16), sk15)), inference(lemma,lemma(discharge,[]))).
% 0.57/0.60 tff(62,plain,
% 0.57/0.60 (^[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)))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(63,plain,
% 0.57/0.60 (![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))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[62])).
% 0.57/0.60 tff(64,plain,
% 0.57/0.60 (![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))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(65,plain,
% 0.57/0.60 (^[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)))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(66,plain,
% 0.57/0.60 (![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))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[65])).
% 0.57/0.60 tff(67,axiom,(![B: $i, A: $i] : (incident_c(ax0_sk1(A, B), A) | part_of(A, B))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004-0.ax','part_of_defn_2')).
% 0.57/0.60 tff(68,plain,
% 0.57/0.60 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.57/0.60 tff(69,plain,
% 0.57/0.60 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.57/0.60 tff(70,plain,(
% 0.57/0.60 ![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.57/0.60 inference(skolemize,[status(sab)],[69])).
% 0.57/0.60 tff(71,plain,
% 0.57/0.60 (![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.57/0.60 tff(72,plain,
% 0.57/0.60 (((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | (part_of(sk14, sk16) | incident_c(ax0_sk1(sk14, sk16), sk14))) <=> ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | part_of(sk14, sk16) | incident_c(ax0_sk1(sk14, sk16), sk14))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(73,plain,
% 0.57/0.60 ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | (part_of(sk14, sk16) | incident_c(ax0_sk1(sk14, sk16), sk14))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(74,plain,
% 0.57/0.60 ((~![B: $i, A: $i] : (part_of(A, B) | incident_c(ax0_sk1(A, B), A))) | part_of(sk14, sk16) | incident_c(ax0_sk1(sk14, sk16), sk14)),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.57/0.60 tff(75,plain,
% 0.57/0.60 (incident_c(ax0_sk1(sk14, sk16), sk14)),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[74, 71, 33])).
% 0.57/0.60 tff(76,plain,
% 0.57/0.60 (part_of(sk14, sk15) <=> part_of(sk14, sk15)),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(77,axiom,(part_of(sk14, sk15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_of_transitivity_67')).
% 0.57/0.60 tff(78,plain,
% 0.57/0.60 (part_of(sk14, sk15)),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.57/0.60 tff(79,plain,
% 0.57/0.60 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(80,plain,
% 0.57/0.60 ((incident_c(ax0_sk1(sk14, sk16), sk15) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | (~part_of(sk14, sk15))) <=> ((~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(81,plain,
% 0.57/0.60 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sk14, sk16), sk15) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | (~part_of(sk14, sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | ((~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15)))),
% 0.57/0.60 inference(monotonicity,[status(thm)],[80])).
% 0.57/0.60 tff(82,plain,
% 0.57/0.60 (((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sk14, sk16), sk15) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | (~part_of(sk14, sk15)))) <=> ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15))),
% 0.57/0.60 inference(transitivity,[status(thm)],[81, 79])).
% 0.57/0.60 tff(83,plain,
% 0.57/0.60 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (incident_c(ax0_sk1(sk14, sk16), sk15) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | (~part_of(sk14, sk15)))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(84,plain,
% 0.57/0.60 ((~![B: $i, A: $i, C: $i] : (incident_c(C, B) | (~incident_c(C, A)) | (~part_of(A, B)))) | (~part_of(sk14, sk15)) | (~incident_c(ax0_sk1(sk14, sk16), sk14)) | incident_c(ax0_sk1(sk14, sk16), sk15)),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.57/0.60 tff(85,plain,
% 0.57/0.60 ($false),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[84, 56, 78, 75, 61])).
% 0.57/0.60 % SZS output end Proof
%------------------------------------------------------------------------------