%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO081+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO081+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:15:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(incident_c_type, type, (
% 0.12/0.37 incident_c: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_C2_12_type, type, (
% 0.12/0.37 tptp_fun_C2_12: $i)).
% 0.12/0.37 tff(tptp_fun_P_0_type, type, (
% 0.12/0.37 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C3_11_type, type, (
% 0.12/0.37 tptp_fun_C3_11: $i)).
% 0.12/0.37 tff(tptp_fun_C1_13_type, type, (
% 0.12/0.37 tptp_fun_C1_13: $i)).
% 0.12/0.37 tff(part_of_type, type, (
% 0.12/0.37 part_of: ( $i * $i ) > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (^[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)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.37 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')).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.37 tff(14,plain,(
% 0.12/0.37 ![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)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![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, C3!11)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C3!11)))) | (~(part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~((~((~part_of(C1!13, C3!11)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C3!11)))) | (~(part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~((~part_of(C1!13, C3!11)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C3!11)))) | (~(part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)))))) | (part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(20,plain,
% 0.12/0.37 (part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.37 tff(21,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(22,plain,
% 0.12/0.37 ((~![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 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')).
% 0.12/0.37 tff(24,plain,
% 0.12/0.37 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.37 tff(25,plain,
% 0.12/0.37 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.37 tff(26,plain,
% 0.12/0.37 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.37 tff(27,plain,
% 0.12/0.37 (~![C1: $i, C2: $i, C3: $i] : ((~(part_of(C1, C2) & part_of(C2, C3))) | part_of(C1, C3))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.37 tff(28,plain,(
% 0.12/0.37 ~((~(part_of(C1!13, C2!12) & part_of(C2!12, C3!11))) | part_of(C1!13, C3!11))),
% 0.12/0.37 inference(skolemize,[status(sab)],[27])).
% 0.12/0.37 tff(29,plain,
% 0.12/0.37 (~part_of(C1!13, C3!11)),
% 0.12/0.37 inference(or_elim,[status(thm)],[28])).
% 0.12/0.37 tff(30,plain,
% 0.12/0.37 ((~(part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))))) | part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(31,plain,
% 0.12/0.37 ((~(part_of(C1!13, C3!11) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))))) | (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.37 tff(32,plain,
% 0.12/0.37 (~((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.12/0.37 tff(33,plain,
% 0.12/0.37 (((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)) | (~incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(34,plain,
% 0.12/0.37 (~incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.37 tff(35,plain,
% 0.12/0.37 ((~![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, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))) | (~(part_of(C2!12, C3!11) | (~((~incident_c(tptp_fun_P_0(C2!12, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C3!11), C3!11)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(36,plain,
% 0.12/0.37 (~((~((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))) | (~(part_of(C2!12, C3!11) | (~((~incident_c(tptp_fun_P_0(C2!12, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C3!11), C3!11))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[35, 16])).
% 0.12/0.37 tff(37,plain,
% 0.12/0.37 (((~((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))) | (~(part_of(C2!12, C3!11) | (~((~incident_c(tptp_fun_P_0(C2!12, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C2!12, C3!11), C3!11)))))) | ((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(38,plain,
% 0.12/0.37 ((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.37 tff(39,plain,
% 0.12/0.37 (part_of(C1!13, C2!12) & part_of(C2!12, C3!11)),
% 0.12/0.37 inference(or_elim,[status(thm)],[28])).
% 0.12/0.37 tff(40,plain,
% 0.12/0.37 (part_of(C2!12, C3!11)),
% 0.12/0.37 inference(and_elim,[status(thm)],[39])).
% 0.12/0.37 tff(41,plain,
% 0.12/0.37 ((~((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))) | (~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(42,plain,
% 0.12/0.37 ((~((~part_of(C2!12, C3!11)) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11)))) | ![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.37 tff(43,plain,
% 0.12/0.37 (![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.12/0.37 tff(44,plain,
% 0.12/0.37 (((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))) | ((~incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))) <=> ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))) | (~incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(45,plain,
% 0.12/0.37 ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))) | ((~incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(46,plain,
% 0.12/0.37 ((~![P: $i] : ((~incident_c(P, C2!12)) | incident_c(P, C3!11))) | (~incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.37 tff(47,plain,
% 0.12/0.37 (~incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[46, 43, 34])).
% 0.12/0.37 tff(48,plain,
% 0.12/0.37 (((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C3!11)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(49,plain,
% 0.12/0.37 (incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[48, 32])).
% 0.12/0.37 tff(50,plain,
% 0.12/0.37 ((~![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)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(51,plain,
% 0.12/0.37 (~((~((~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))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[50, 16])).
% 0.12/0.37 tff(52,plain,
% 0.12/0.37 (((~((~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)))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(53,plain,
% 0.12/0.37 ((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.12/0.37 tff(54,plain,
% 0.12/0.37 (part_of(C1!13, C2!12)),
% 0.12/0.37 inference(and_elim,[status(thm)],[39])).
% 0.12/0.37 tff(55,plain,
% 0.12/0.37 ((~((~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))),
% 0.12/0.37 inference(tautology,[status(thm)],[])).
% 0.12/0.37 tff(56,plain,
% 0.12/0.37 ((~((~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))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.12/0.37 tff(57,plain,
% 0.12/0.37 (![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[56, 53])).
% 0.12/0.37 tff(58,plain,
% 0.12/0.37 (((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12))) <=> ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(59,plain,
% 0.12/0.37 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(60,plain,
% 0.12/0.37 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_0(C1!13, C3!11), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C3!11), C2!12)),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.12/0.37 tff(61,plain,
% 0.12/0.37 ($false),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[60, 57, 49, 47])).
% 0.12/0.37 % SZS output end Proof
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------