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 : n013.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 0.13s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GEO081+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 05:16:02 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.36 Usage: tptp [options] [-file:]file
% 0.13/0.36 -h, -? prints this message.
% 0.13/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.36 -m, -model generate model.
% 0.13/0.36 -p, -proof generate proof.
% 0.13/0.36 -c, -core generate unsat core of named formulas.
% 0.13/0.36 -st, -statistics display statistics.
% 0.13/0.36 -t:timeout set timeout (in second).
% 0.13/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.36 -<param>:<value> configuration parameter and value.
% 0.13/0.36 -o:<output-file> file to place output in.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(incident_c_type, type, (
% 0.13/0.41 incident_c: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_C2_13_type, type, (
% 0.13/0.41 tptp_fun_C2_13: $i)).
% 0.13/0.41 tff(tptp_fun_P_0_type, type, (
% 0.13/0.41 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_C3_12_type, type, (
% 0.13/0.41 tptp_fun_C3_12: $i)).
% 0.13/0.41 tff(tptp_fun_C1_14_type, type, (
% 0.13/0.41 tptp_fun_C1_14: $i)).
% 0.13/0.41 tff(part_of_type, type, (
% 0.13/0.41 part_of: ( $i * $i ) > $o)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.41 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.41 tff(14,plain,(
% 0.13/0.41 ![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)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[13])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 ((~![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!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))))) | (part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(20,plain,
% 0.20/0.42 (part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.42 tff(21,plain,
% 0.20/0.42 ((~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))) <=> (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(22,plain,
% 0.20/0.42 ((~![C1: $i, C2: $i, C3: $i] : ((part_of(C1, C2) & part_of(C2, C3)) => part_of(C1, C3))) <=> (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(23,axiom,(~![C1: $i, C2: $i, C3: $i] : ((part_of(C1, C2) & part_of(C2, C3)) => part_of(C1, C3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','part_of_transitivity')).
% 0.20/0.42 tff(24,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.42 tff(25,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.42 tff(26,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.42 tff(27,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.42 tff(28,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.42 tff(29,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.42 tff(30,plain,
% 0.20/0.42 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.42 tff(31,plain,(
% 0.20/0.42 ~((~(part_of(C1!14, C2!13) & part_of(C2!13, C3!12))) | part_of(C1!14, C3!12))),
% 0.20/0.42 inference(skolemize,[status(sab)],[30])).
% 0.20/0.42 tff(32,plain,
% 0.20/0.42 (~part_of(C1!14, C3!12)),
% 0.20/0.42 inference(or_elim,[status(thm)],[31])).
% 0.20/0.42 tff(33,plain,
% 0.20/0.42 ((~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))))) | part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(34,plain,
% 0.20/0.42 ((~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))))) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.42 tff(35,plain,
% 0.20/0.42 (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.20/0.42 tff(36,plain,
% 0.20/0.42 (((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)) | (~incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(37,plain,
% 0.20/0.42 (~incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.42 tff(38,plain,
% 0.20/0.42 ((~![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!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(39,plain,
% 0.20/0.42 (~((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.20/0.42 tff(40,plain,
% 0.20/0.42 (((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12)))))) | ((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(41,plain,
% 0.20/0.42 ((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.20/0.42 tff(42,plain,
% 0.20/0.42 (part_of(C1!14, C2!13) & part_of(C2!13, C3!12)),
% 0.20/0.42 inference(or_elim,[status(thm)],[31])).
% 0.20/0.42 tff(43,plain,
% 0.20/0.42 (part_of(C2!13, C3!12)),
% 0.20/0.42 inference(and_elim,[status(thm)],[42])).
% 0.20/0.42 tff(44,plain,
% 0.20/0.42 ((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(45,plain,
% 0.20/0.42 ((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.20/0.42 tff(46,plain,
% 0.20/0.42 (![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.20/0.42 tff(47,plain,
% 0.20/0.42 (((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))) <=> ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(48,plain,
% 0.20/0.42 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(49,plain,
% 0.20/0.42 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.42 tff(50,plain,
% 0.20/0.42 (~incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[49, 46, 37])).
% 0.20/0.42 tff(51,plain,
% 0.20/0.42 (((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(52,plain,
% 0.20/0.42 (incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[51, 35])).
% 0.20/0.42 tff(53,plain,
% 0.20/0.42 ((~![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!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))) | (~(part_of(C1!14, C2!13) | (~((~incident_c(tptp_fun_P_0(C1!14, C2!13), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C2!13), C2!13)))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(54,plain,
% 0.20/0.42 (~((~((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))) | (~(part_of(C1!14, C2!13) | (~((~incident_c(tptp_fun_P_0(C1!14, C2!13), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C2!13), C2!13))))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[53, 16])).
% 0.20/0.42 tff(55,plain,
% 0.20/0.42 (((~((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))) | (~(part_of(C1!14, C2!13) | (~((~incident_c(tptp_fun_P_0(C1!14, C2!13), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C2!13), C2!13)))))) | ((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(56,plain,
% 0.20/0.42 ((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.20/0.42 tff(57,plain,
% 0.20/0.42 (part_of(C1!14, C2!13)),
% 0.20/0.42 inference(and_elim,[status(thm)],[42])).
% 0.20/0.42 tff(58,plain,
% 0.20/0.42 ((~((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))) | (~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(59,plain,
% 0.20/0.42 ((~((~part_of(C1!14, C2!13)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13)))) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.20/0.42 tff(60,plain,
% 0.20/0.42 (![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.20/0.42 tff(61,plain,
% 0.20/0.42 (((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13))) <=> ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(62,plain,
% 0.20/0.42 ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(63,plain,
% 0.20/0.42 ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C2!13)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.42 tff(64,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[63, 60, 52, 50])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------