%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO088+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:05:33 AM UTC 2025
% Result : Theorem 1.45s 1.65s
% Output : Proof 1.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO088+1 : TPTP v9.0.0. Released v2.4.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 14:16:55 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.45/1.65 % SZS status Theorem
% 1.45/1.65 % SZS output start Proof
% 1.45/1.65 tff(incident_c_type, type, (
% 1.45/1.65 incident_c: ( $i * $i ) > $o)).
% 1.45/1.65 tff(tptp_fun_Cpp_12_type, type, (
% 1.45/1.65 tptp_fun_Cpp_12: $i)).
% 1.45/1.65 tff(tptp_fun_P_0_type, type, (
% 1.45/1.65 tptp_fun_P_0: ( $i * $i ) > $i)).
% 1.45/1.65 tff(tptp_fun_C_13_type, type, (
% 1.45/1.65 tptp_fun_C_13: $i)).
% 1.45/1.65 tff(tptp_fun_C2_2_type, type, (
% 1.45/1.65 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 1.45/1.65 tff(tptp_fun_P_11_type, type, (
% 1.45/1.65 tptp_fun_P_11: $i)).
% 1.45/1.65 tff(part_of_type, type, (
% 1.45/1.65 part_of: ( $i * $i ) > $o)).
% 1.45/1.65 tff(tptp_fun_C1_3_type, type, (
% 1.45/1.65 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 1.45/1.65 tff(end_point_type, type, (
% 1.45/1.65 end_point: ( $i * $i ) > $o)).
% 1.45/1.65 tff(1,plain,
% 1.45/1.65 (^[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))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(2,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[1])).
% 1.45/1.65 tff(3,plain,
% 1.45/1.65 (^[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))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(4,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[3])).
% 1.45/1.65 tff(5,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[4, 2])).
% 1.45/1.65 tff(6,plain,
% 1.45/1.65 (^[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)))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(7,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[6])).
% 1.45/1.65 tff(8,plain,
% 1.45/1.65 (![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)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(9,plain,
% 1.45/1.65 (^[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))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(10,plain,
% 1.45/1.65 (![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)))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[9])).
% 1.45/1.65 tff(11,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')).
% 1.45/1.65 tff(12,plain,
% 1.45/1.65 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.45/1.65 tff(13,plain,
% 1.45/1.65 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.45/1.65 tff(14,plain,(
% 1.45/1.65 ![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)))))),
% 1.45/1.65 inference(skolemize,[status(sab)],[13])).
% 1.45/1.65 tff(15,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.45/1.65 tff(16,plain,
% 1.45/1.65 (![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)))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.45/1.65 tff(17,plain,
% 1.45/1.65 ((~![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(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(18,plain,
% 1.45/1.65 (~((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.45/1.65 tff(19,plain,
% 1.45/1.65 (((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)))))) | (part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(20,plain,
% 1.45/1.65 (part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.45/1.65 tff(21,assumption,((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)))))), introduced(assumption)).
% 1.45/1.65 tff(22,plain,
% 1.45/1.65 ((~![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(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(23,plain,
% 1.45/1.65 ($false),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 1.45/1.65 tff(24,plain,(~((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))))))), inference(lemma,lemma(discharge,[]))).
% 1.45/1.65 tff(25,plain,
% 1.45/1.65 (((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, C!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)))))) | (part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(26,plain,
% 1.45/1.65 (part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.45/1.65 tff(27,assumption,(~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))), introduced(assumption)).
% 1.45/1.65 tff(28,plain,
% 1.45/1.65 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(29,plain,
% 1.45/1.65 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.45/1.65 tff(30,plain,
% 1.45/1.65 ((~![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(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))) | (~(part_of(Cpp!12, C!13) | (~((~incident_c(tptp_fun_P_0(Cpp!12, C!13), Cpp!12)) | incident_c(tptp_fun_P_0(Cpp!12, C!13), C!13)))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(31,plain,
% 1.45/1.65 (~((~((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))) | (~(part_of(Cpp!12, C!13) | (~((~incident_c(tptp_fun_P_0(Cpp!12, C!13), Cpp!12)) | incident_c(tptp_fun_P_0(Cpp!12, C!13), C!13))))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[30, 16])).
% 1.45/1.65 tff(32,plain,
% 1.45/1.65 (((~((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))) | (~(part_of(Cpp!12, C!13) | (~((~incident_c(tptp_fun_P_0(Cpp!12, C!13), Cpp!12)) | incident_c(tptp_fun_P_0(Cpp!12, C!13), C!13)))))) | ((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(33,plain,
% 1.45/1.65 ((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.45/1.65 tff(34,plain,
% 1.45/1.65 ((~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))) <=> (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(35,plain,
% 1.45/1.65 ((~![C: $i, Cpp: $i, P: $i] : (((part_of(Cpp, C) & end_point(P, C)) & incident_c(P, Cpp)) => end_point(P, Cpp))) <=> (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp)))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(36,axiom,(~![C: $i, Cpp: $i, P: $i] : (((part_of(Cpp, C) & end_point(P, C)) & incident_c(P, Cpp)) => end_point(P, Cpp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_2_10')).
% 1.45/1.65 tff(37,plain,
% 1.45/1.65 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.45/1.65 tff(38,plain,
% 1.45/1.65 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.45/1.65 tff(39,plain,
% 1.45/1.65 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.45/1.65 tff(40,plain,
% 1.45/1.65 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.45/1.65 tff(41,plain,(
% 1.45/1.65 ~((~(part_of(Cpp!12, C!13) & end_point(P!11, C!13) & incident_c(P!11, Cpp!12))) | end_point(P!11, Cpp!12))),
% 1.45/1.65 inference(skolemize,[status(sab)],[40])).
% 1.45/1.65 tff(42,plain,
% 1.45/1.65 (part_of(Cpp!12, C!13) & end_point(P!11, C!13) & incident_c(P!11, Cpp!12)),
% 1.45/1.65 inference(or_elim,[status(thm)],[41])).
% 1.45/1.65 tff(43,plain,
% 1.45/1.65 (part_of(Cpp!12, C!13)),
% 1.45/1.65 inference(and_elim,[status(thm)],[42])).
% 1.45/1.65 tff(44,plain,
% 1.45/1.65 ((~((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))) | (~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(45,plain,
% 1.45/1.65 ((~((~part_of(Cpp!12, C!13)) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13)))) | ![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.45/1.65 tff(46,plain,
% 1.45/1.65 (![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[45, 33])).
% 1.45/1.65 tff(47,plain,
% 1.45/1.65 (((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(48,plain,
% 1.45/1.65 ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(49,plain,
% 1.45/1.65 ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.45/1.65 tff(50,plain,
% 1.45/1.65 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[49, 46, 29])).
% 1.45/1.65 tff(51,plain,
% 1.45/1.65 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(52,plain,
% 1.45/1.65 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[51, 27])).
% 1.45/1.65 tff(53,plain,
% 1.45/1.65 ((~![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(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), Cpp!12)))))))),
% 1.45/1.65 inference(quant_inst,[status(thm)],[])).
% 1.45/1.65 tff(54,plain,
% 1.45/1.65 (~((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), Cpp!12))))))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[53, 16])).
% 1.45/1.65 tff(55,plain,
% 1.45/1.65 (((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12), Cpp!12)))))) | ((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))),
% 1.45/1.65 inference(tautology,[status(thm)],[])).
% 1.45/1.65 tff(56,plain,
% 1.45/1.65 ((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.65 inference(unit_resolution,[status(thm)],[55, 54])).
% 1.45/1.65 tff(57,plain,
% 1.45/1.65 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(58,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[57])).
% 1.45/1.65 tff(59,plain,
% 1.45/1.65 (^[P: $i, C: $i] : refl((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(60,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[59])).
% 1.45/1.65 tff(61,plain,
% 1.45/1.65 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(62,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[61])).
% 1.45/1.65 tff(63,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(transitivity,[status(thm)],[62, 60])).
% 1.45/1.65 tff(64,plain,
% 1.45/1.65 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))), trans(monotonicity(rewrite((~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), rewrite((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))), rewrite((((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(65,plain,
% 1.45/1.65 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[64])).
% 1.45/1.65 tff(66,plain,
% 1.45/1.65 (^[P: $i, C: $i] : rewrite((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(67,plain,
% 1.45/1.65 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[66])).
% 1.45/1.65 tff(68,plain,
% 1.45/1.65 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.45/1.65 inference(rewrite,[status(thm)],[])).
% 1.45/1.65 tff(69,plain,
% 1.45/1.65 (^[P: $i, C: $i] : rewrite((end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))))),
% 1.45/1.65 inference(bind,[status(th)],[])).
% 1.45/1.65 tff(70,plain,
% 1.45/1.65 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.45/1.65 inference(quant_intro,[status(thm)],[69])).
% 1.45/1.65 tff(71,axiom,(![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1)))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 1.45/1.65 tff(72,plain,
% 1.45/1.65 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.45/1.65 tff(73,plain,
% 1.45/1.65 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.45/1.65 tff(74,plain,(
% 1.45/1.65 ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(skolemize,[status(sab)],[73])).
% 1.45/1.65 tff(75,plain,
% 1.45/1.65 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.45/1.65 tff(76,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.65 inference(modus_ponens,[status(thm)],[75, 65])).
% 1.45/1.65 tff(77,plain,
% 1.45/1.65 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[76, 63])).
% 1.45/1.66 tff(78,plain,
% 1.45/1.66 (![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[77, 58])).
% 1.45/1.66 tff(79,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)))))))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(80,plain,
% 1.45/1.66 ((~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))) <=> (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12))))))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(81,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)))))))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[80])).
% 1.45/1.66 tff(82,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)))))))))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[81, 79])).
% 1.45/1.66 tff(83,plain,
% 1.45/1.66 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(84,plain,
% 1.45/1.66 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12))))))))))),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.45/1.66 tff(85,plain,
% 1.45/1.66 (~((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12)))))))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[84, 78])).
% 1.45/1.66 tff(86,plain,
% 1.45/1.66 (((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~end_point(P!11, Cpp!12)) | (~((~incident_c(P!11, Cpp!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, Cpp!12)) | (~part_of(C2, Cpp!12))))))))) | (end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(87,plain,
% 1.45/1.66 (end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.45/1.66 tff(88,plain,
% 1.45/1.66 (~end_point(P!11, Cpp!12)),
% 1.45/1.66 inference(or_elim,[status(thm)],[41])).
% 1.45/1.66 tff(89,plain,
% 1.45/1.66 (incident_c(P!11, Cpp!12)),
% 1.45/1.66 inference(and_elim,[status(thm)],[42])).
% 1.45/1.66 tff(90,plain,
% 1.45/1.66 ((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(91,plain,
% 1.45/1.66 ((~(end_point(P!11, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))))) | (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[90, 89, 88])).
% 1.45/1.66 tff(92,plain,
% 1.45/1.66 (~((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[91, 87])).
% 1.45/1.66 tff(93,plain,
% 1.45/1.66 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(94,plain,
% 1.45/1.66 (part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[93, 92])).
% 1.45/1.66 tff(95,plain,
% 1.45/1.66 ((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(96,plain,
% 1.45/1.66 ((~((~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[95, 94])).
% 1.45/1.66 tff(97,plain,
% 1.45/1.66 (![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[96, 56])).
% 1.45/1.66 tff(98,plain,
% 1.45/1.66 (((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(99,plain,
% 1.45/1.66 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(100,plain,
% 1.45/1.66 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), Cpp!12)),
% 1.45/1.66 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.45/1.66 tff(101,plain,
% 1.45/1.66 ($false),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[100, 97, 52, 50])).
% 1.45/1.66 tff(102,plain,((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)), inference(lemma,lemma(discharge,[]))).
% 1.45/1.66 tff(103,plain,
% 1.45/1.66 ((~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13)))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(104,plain,
% 1.45/1.66 ((~(part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!12, P!11), C!13), C!13))))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[103, 102])).
% 1.45/1.66 tff(105,plain,
% 1.45/1.66 (part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[104, 26])).
% 1.45/1.66 tff(106,plain,
% 1.45/1.66 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(107,plain,
% 1.45/1.66 (~part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[106, 92])).
% 1.45/1.66 tff(108,plain,
% 1.45/1.66 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(109,plain,
% 1.45/1.66 (~part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[108, 92])).
% 1.45/1.66 tff(110,plain,
% 1.45/1.66 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(111,plain,
% 1.45/1.66 (incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[110, 92])).
% 1.45/1.66 tff(112,plain,
% 1.45/1.66 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))),
% 1.45/1.66 inference(tautology,[status(thm)],[])).
% 1.45/1.66 tff(113,plain,
% 1.45/1.66 (incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))),
% 1.45/1.66 inference(unit_resolution,[status(thm)],[112, 92])).
% 1.45/1.66 tff(114,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(115,plain,
% 1.45/1.66 ((~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~(part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))) <=> (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 1.45/1.66 inference(rewrite,[status(thm)],[])).
% 1.45/1.66 tff(116,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~(part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 1.45/1.66 inference(monotonicity,[status(thm)],[115])).
% 1.45/1.66 tff(117,plain,
% 1.45/1.66 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~(part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 1.45/1.66 inference(transitivity,[status(thm)],[116, 114])).
% 1.45/1.66 tff(118,plain,
% 1.45/1.66 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~(part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 1.45/1.66 inference(quant_inst,[status(thm)],[])).
% 1.45/1.66 tff(119,plain,
% 1.45/1.66 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[118, 117])).
% 1.45/1.67 tff(120,plain,
% 1.45/1.67 (~((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[119, 78])).
% 1.45/1.67 tff(121,plain,
% 1.45/1.67 (((~(end_point(P!11, C!13) | (~incident_c(P!11, C!13)) | (~((~incident_c(P!11, tptp_fun_C2_2(C!13, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!13, P!11))) | (~part_of(tptp_fun_C2_2(C!13, P!11), C!13)) | (~part_of(tptp_fun_C1_3(C!13, P!11), C!13)) | part_of(tptp_fun_C1_3(C!13, P!11), tptp_fun_C2_2(C!13, P!11)) | part_of(tptp_fun_C2_2(C!13, P!11), tptp_fun_C1_3(C!13, P!11)))))) | (~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))) | ((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(122,plain,
% 1.45/1.67 ((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[121, 120])).
% 1.45/1.67 tff(123,plain,
% 1.45/1.67 (end_point(P!11, C!13)),
% 1.45/1.67 inference(and_elim,[status(thm)],[42])).
% 1.45/1.67 tff(124,plain,
% 1.45/1.67 ((~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))) | (~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(125,plain,
% 1.45/1.67 ((~((~end_point(P!11, C!13)) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))) | (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[124, 123])).
% 1.45/1.67 tff(126,plain,
% 1.45/1.67 (~((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[125, 122])).
% 1.45/1.67 tff(127,plain,
% 1.45/1.67 (((~incident_c(P!11, C!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))) | ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(128,plain,
% 1.45/1.67 (![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.45/1.67 tff(129,plain,
% 1.45/1.67 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | ((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(130,plain,
% 1.45/1.67 ((part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11)))) <=> ((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(131,plain,
% 1.45/1.67 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | ((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13))))),
% 1.45/1.67 inference(monotonicity,[status(thm)],[130])).
% 1.45/1.67 tff(132,plain,
% 1.45/1.67 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)))),
% 1.45/1.67 inference(transitivity,[status(thm)],[131, 129])).
% 1.45/1.67 tff(133,plain,
% 1.45/1.67 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13)) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(134,plain,
% 1.45/1.67 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!13)) | (~part_of(C2, C!13)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))) | (~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11)) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13))),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.45/1.67 tff(135,plain,
% 1.45/1.67 ((~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), C!13))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[134, 128, 113, 111, 109, 107])).
% 1.45/1.67 tff(136,plain,
% 1.45/1.67 (~part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[135, 105])).
% 1.45/1.67 tff(137,plain,
% 1.45/1.67 ((~(part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))))) | part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(138,plain,
% 1.45/1.67 ((~(part_of(tptp_fun_C2_2(Cpp!12, P!11), C!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.45/1.67 tff(139,plain,
% 1.45/1.67 (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[138, 20])).
% 1.45/1.67 tff(140,plain,
% 1.45/1.67 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(141,plain,
% 1.45/1.67 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[140, 139])).
% 1.45/1.67 tff(142,plain,
% 1.45/1.67 (((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(143,plain,
% 1.45/1.67 ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(144,plain,
% 1.45/1.67 ((~![P: $i] : ((~incident_c(P, Cpp!12)) | incident_c(P, C!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.45/1.67 tff(145,plain,
% 1.45/1.67 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[144, 46, 141])).
% 1.45/1.67 tff(146,plain,
% 1.45/1.67 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), C!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(147,plain,
% 1.45/1.67 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[146, 139])).
% 1.45/1.67 tff(148,plain,
% 1.45/1.67 ((~![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(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), Cpp!12)))))))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(149,plain,
% 1.45/1.67 (~((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), Cpp!12))))))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[148, 16])).
% 1.45/1.67 tff(150,plain,
% 1.45/1.67 (((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~(part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12), Cpp!12)))))) | ((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(151,plain,
% 1.45/1.67 ((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[150, 149])).
% 1.45/1.67 tff(152,plain,
% 1.45/1.67 (((~incident_c(P!11, tptp_fun_C2_2(Cpp!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(Cpp!12, P!11))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | (~part_of(tptp_fun_C1_3(Cpp!12, P!11), Cpp!12)) | part_of(tptp_fun_C1_3(Cpp!12, P!11), tptp_fun_C2_2(Cpp!12, P!11)) | part_of(tptp_fun_C2_2(Cpp!12, P!11), tptp_fun_C1_3(Cpp!12, P!11))) | part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(153,plain,
% 1.45/1.67 (part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[152, 92])).
% 1.45/1.67 tff(154,plain,
% 1.45/1.67 ((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | (~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.67 inference(tautology,[status(thm)],[])).
% 1.45/1.67 tff(155,plain,
% 1.45/1.67 ((~((~part_of(tptp_fun_C2_2(Cpp!12, P!11), Cpp!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.45/1.67 tff(156,plain,
% 1.45/1.67 (![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[155, 151])).
% 1.45/1.67 tff(157,plain,
% 1.45/1.67 (((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12))),
% 1.45/1.67 inference(rewrite,[status(thm)],[])).
% 1.45/1.67 tff(158,plain,
% 1.45/1.67 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12))),
% 1.45/1.67 inference(quant_inst,[status(thm)],[])).
% 1.45/1.67 tff(159,plain,
% 1.45/1.67 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(P, Cpp!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), tptp_fun_C2_2(Cpp!12, P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!12, P!11), C!13), Cpp!12)),
% 1.45/1.67 inference(modus_ponens,[status(thm)],[158, 157])).
% 1.45/1.67 tff(160,plain,
% 1.45/1.67 ($false),
% 1.45/1.67 inference(unit_resolution,[status(thm)],[159, 156, 147, 145])).
% 1.45/1.67 % SZS output end Proof
% 1.45/1.67 % E exiting
%------------------------------------------------------------------------------