TSTP Solution File: GEO082+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Fri Sep 16 20:34:44 EDT 2022
% Result : Theorem 0.63s 0.68s
% Output : Proof 0.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO082+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:20:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.63/0.68 % SZS status Theorem
% 0.63/0.68 % SZS output start Proof
% 0.63/0.68 tff(incident_c_type, type, (
% 0.63/0.68 incident_c: ( $i * $i ) > $o)).
% 0.63/0.68 tff(tptp_fun_C1_13_type, type, (
% 0.63/0.68 tptp_fun_C1_13: $i)).
% 0.63/0.68 tff(tptp_fun_P_11_type, type, (
% 0.63/0.68 tptp_fun_P_11: ( $i * $i ) > $i)).
% 0.63/0.68 tff(tptp_fun_C2_12_type, type, (
% 0.63/0.68 tptp_fun_C2_12: $i)).
% 0.63/0.68 tff(part_of_type, type, (
% 0.63/0.68 part_of: ( $i * $i ) > $o)).
% 0.63/0.68 tff(tptp_fun_P_0_type, type, (
% 0.63/0.68 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.63/0.68 tff(1,assumption,(incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)), introduced(assumption)).
% 0.63/0.68 tff(2,plain,
% 0.63/0.68 ((~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))) <=> (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2)))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(3,plain,
% 0.63/0.68 ((~![C1: $i, C2: $i] : ((part_of(C1, C2) & part_of(C2, C1)) => (C1 = C2))) <=> (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2)))),
% 0.63/0.68 inference(rewrite,[status(thm)],[])).
% 0.63/0.68 tff(4,axiom,(~![C1: $i, C2: $i] : ((part_of(C1, C2) & part_of(C2, C1)) => (C1 = C2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','part_of_antisymmetry')).
% 0.63/0.68 tff(5,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.63/0.68 tff(6,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.63/0.68 tff(7,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.63/0.68 tff(8,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.63/0.68 tff(9,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[8, 2])).
% 0.63/0.68 tff(10,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.68 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.63/0.68 tff(11,plain,
% 0.63/0.68 (~![C1: $i, C2: $i] : ((~(part_of(C1, C2) & part_of(C2, C1))) | (C1 = C2))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.63/0.69 tff(12,plain,(
% 0.63/0.69 ~((~(part_of(C1!13, C2!12) & part_of(C2!12, C1!13))) | (C1!13 = C2!12))),
% 0.63/0.69 inference(skolemize,[status(sab)],[11])).
% 0.63/0.69 tff(13,plain,
% 0.63/0.69 (~(C1!13 = C2!12)),
% 0.63/0.69 inference(or_elim,[status(thm)],[12])).
% 0.63/0.69 tff(14,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : trans(monotonicity(rewrite((~(incident_c(tptp_fun_P_11(C1, C), C) <=> incident_c(tptp_fun_P_11(C1, C), C1))) <=> ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1))), (((~(incident_c(tptp_fun_P_11(C1, C), C) <=> incident_c(tptp_fun_P_11(C1, C), C1))) | (C = C1)) <=> (((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)) | (C = C1)))), rewrite((((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)) | (C = C1)) <=> ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))), (((~(incident_c(tptp_fun_P_11(C1, C), C) <=> incident_c(tptp_fun_P_11(C1, C), C1))) | (C = C1)) <=> ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(15,plain,
% 0.63/0.69 (![C: $i, C1: $i] : ((~(incident_c(tptp_fun_P_11(C1, C), C) <=> incident_c(tptp_fun_P_11(C1, C), C1))) | (C = C1)) <=> ![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[14])).
% 0.63/0.69 tff(16,plain,
% 0.63/0.69 (![C: $i, C1: $i] : ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1)) <=> ![C: $i, C1: $i] : ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(17,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : rewrite((![P: $i] : (incident_c(P, C) <=> incident_c(P, C1)) => (C = C1)) <=> ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1)))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(18,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (![P: $i] : (incident_c(P, C) <=> incident_c(P, C1)) => (C = C1)) <=> ![C: $i, C1: $i] : ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[17])).
% 0.63/0.69 tff(19,axiom,(![C: $i, C1: $i] : (![P: $i] : (incident_c(P, C) <=> incident_c(P, C1)) => (C = C1))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','c9')).
% 0.63/0.69 tff(20,plain,
% 0.63/0.69 (![C: $i, C1: $i] : ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.63/0.69 tff(21,plain,
% 0.63/0.69 (![C: $i, C1: $i] : ((~![P: $i] : (incident_c(P, C) <=> incident_c(P, C1))) | (C = C1))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.63/0.69 tff(22,plain,(
% 0.63/0.69 ![C: $i, C1: $i] : ((~(incident_c(tptp_fun_P_11(C1, C), C) <=> incident_c(tptp_fun_P_11(C1, C), C1))) | (C = C1))),
% 0.63/0.69 inference(skolemize,[status(sab)],[21])).
% 0.63/0.69 tff(23,plain,
% 0.63/0.69 (![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[22, 15])).
% 0.63/0.69 tff(24,plain,
% 0.63/0.69 (((~![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))) | ((C1!13 = C2!12) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)))) <=> ((~![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))) | (C1!13 = C2!12) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(25,plain,
% 0.63/0.69 ((~![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))) | ((C1!13 = C2!12) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(26,plain,
% 0.63/0.69 ((~![C: $i, C1: $i] : ((C = C1) | ((~incident_c(tptp_fun_P_11(C1, C), C)) <=> incident_c(tptp_fun_P_11(C1, C), C1)))) | (C1!13 = C2!12) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.63/0.69 tff(27,plain,
% 0.63/0.69 ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[26, 23, 13])).
% 0.63/0.69 tff(28,plain,
% 0.63/0.69 ((~((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(29,plain,
% 0.63/0.69 ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.63/0.69 tff(30,plain,
% 0.63/0.69 (~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[29, 1])).
% 0.63/0.69 tff(31,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : refl((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(32,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[31])).
% 0.63/0.69 tff(33,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : rewrite((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(34,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[33])).
% 0.63/0.69 tff(35,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(transitivity,[status(thm)],[34, 32])).
% 0.63/0.69 tff(36,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : trans(monotonicity(rewrite(((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))), rewrite((part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))) <=> (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))), rewrite((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(37,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[36])).
% 0.63/0.69 tff(38,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(39,plain,
% 0.63/0.69 (^[C: $i, C1: $i] : rewrite((part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))))),
% 0.63/0.69 inference(bind,[status(th)],[])).
% 0.63/0.69 tff(40,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.69 inference(quant_intro,[status(thm)],[39])).
% 0.63/0.69 tff(41,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.63/0.69 tff(42,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.63/0.69 tff(43,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.63/0.69 tff(44,plain,(
% 0.63/0.69 ![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))),
% 0.63/0.69 inference(skolemize,[status(sab)],[43])).
% 0.63/0.69 tff(45,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.63/0.69 tff(46,plain,
% 0.63/0.69 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.69 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.63/0.69 tff(47,plain,
% 0.63/0.69 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12)))))))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.69 tff(48,plain,
% 0.63/0.69 (~((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12))))))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.63/0.69 tff(49,plain,
% 0.63/0.69 (((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12)))))) | ((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(50,plain,
% 0.63/0.69 ((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.63/0.69 tff(51,plain,
% 0.63/0.69 (part_of(C1!13, C2!12) & part_of(C2!12, C1!13)),
% 0.63/0.69 inference(or_elim,[status(thm)],[12])).
% 0.63/0.69 tff(52,plain,
% 0.63/0.69 (part_of(C1!13, C2!12)),
% 0.63/0.69 inference(and_elim,[status(thm)],[51])).
% 0.63/0.69 tff(53,plain,
% 0.63/0.69 ((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.63/0.69 inference(tautology,[status(thm)],[])).
% 0.63/0.69 tff(54,plain,
% 0.63/0.69 ((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.63/0.69 tff(55,plain,
% 0.63/0.69 (![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.63/0.69 inference(unit_resolution,[status(thm)],[54, 50])).
% 0.63/0.69 tff(56,plain,
% 0.63/0.69 (((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))) <=> ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))),
% 0.63/0.69 inference(rewrite,[status(thm)],[])).
% 0.63/0.69 tff(57,plain,
% 0.63/0.69 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))),
% 0.63/0.69 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(58,plain,
% 0.63/0.70 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.63/0.70 tff(59,plain,
% 0.63/0.70 ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[58, 55])).
% 0.63/0.70 tff(60,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[59, 30, 1])).
% 0.63/0.70 tff(61,plain,(~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.70 tff(62,plain,
% 0.63/0.70 ((~((~incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)) <=> incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12))) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(63,plain,
% 0.63/0.70 (incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13) | incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[62, 27])).
% 0.63/0.70 tff(64,plain,
% 0.63/0.70 (incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[63, 61])).
% 0.63/0.70 tff(65,plain,
% 0.63/0.70 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))) | (~(part_of(C2!12, C1!13) | (~((~incident_c(tptp_fun_P_0(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C1!13), C1!13)))))))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(66,plain,
% 0.63/0.70 (~((~((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))) | (~(part_of(C2!12, C1!13) | (~((~incident_c(tptp_fun_P_0(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C1!13), C1!13))))))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[65, 46])).
% 0.63/0.70 tff(67,plain,
% 0.63/0.70 (((~((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))) | (~(part_of(C2!12, C1!13) | (~((~incident_c(tptp_fun_P_0(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C1!13), C1!13)))))) | ((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(68,plain,
% 0.63/0.70 ((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.63/0.70 tff(69,plain,
% 0.63/0.70 (part_of(C2!12, C1!13)),
% 0.63/0.70 inference(and_elim,[status(thm)],[51])).
% 0.63/0.70 tff(70,plain,
% 0.63/0.70 ((~((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))) | (~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))),
% 0.63/0.70 inference(tautology,[status(thm)],[])).
% 0.63/0.70 tff(71,plain,
% 0.63/0.70 ((~((~part_of(C2!12, C1!13)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13)))) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.63/0.70 tff(72,plain,
% 0.63/0.70 (![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[71, 68])).
% 0.63/0.70 tff(73,plain,
% 0.63/0.70 (((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13))) <=> ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13))),
% 0.63/0.70 inference(rewrite,[status(thm)],[])).
% 0.63/0.70 tff(74,plain,
% 0.63/0.70 ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))) | ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13))),
% 0.63/0.70 inference(quant_inst,[status(thm)],[])).
% 0.63/0.70 tff(75,plain,
% 0.63/0.70 ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C1!13))) | (~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)),
% 0.63/0.70 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.63/0.70 tff(76,plain,
% 0.63/0.70 ((~incident_c(tptp_fun_P_11(C2!12, C1!13), C2!12)) | incident_c(tptp_fun_P_11(C2!12, C1!13), C1!13)),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.63/0.70 tff(77,plain,
% 0.63/0.70 ($false),
% 0.63/0.70 inference(unit_resolution,[status(thm)],[76, 64, 61])).
% 0.63/0.70 % SZS output end Proof
%------------------------------------------------------------------------------