%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO090+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:05:34 AM UTC 2025
% Result : Theorem 1.75s 1.91s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO090+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 14:20:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 1.75/1.91 % SZS status Theorem
% 1.75/1.91 % SZS output start Proof
% 1.75/1.91 tff(incident_c_type, type, (
% 1.75/1.91 incident_c: ( $i * $i ) > $o)).
% 1.75/1.91 tff(tptp_fun_C2_13_type, type, (
% 1.75/1.91 tptp_fun_C2_13: $i)).
% 1.75/1.91 tff(tptp_fun_P_0_type, type, (
% 1.75/1.91 tptp_fun_P_0: ( $i * $i ) > $i)).
% 1.75/1.91 tff(tptp_fun_C1_14_type, type, (
% 1.75/1.91 tptp_fun_C1_14: $i)).
% 1.75/1.91 tff(tptp_fun_C2_2_type, type, (
% 1.75/1.91 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 1.75/1.91 tff(tptp_fun_Q_4_type, type, (
% 1.75/1.91 tptp_fun_Q_4: ( $i * $i ) > $i)).
% 1.75/1.91 tff(tptp_fun_Cpp_12_type, type, (
% 1.75/1.91 tptp_fun_Cpp_12: $i)).
% 1.75/1.91 tff(part_of_type, type, (
% 1.75/1.91 part_of: ( $i * $i ) > $o)).
% 1.75/1.91 tff(tptp_fun_C1_3_type, type, (
% 1.75/1.91 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 1.75/1.91 tff(meet_type, type, (
% 1.75/1.91 meet: ( $i * $i * $i ) > $o)).
% 1.75/1.91 tff(tptp_fun_P_11_type, type, (
% 1.75/1.91 tptp_fun_P_11: $i)).
% 1.75/1.91 tff(end_point_type, type, (
% 1.75/1.91 end_point: ( $i * $i ) > $o)).
% 1.75/1.91 tff(1,plain,
% 1.75/1.91 (^[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))))))))),
% 1.75/1.91 inference(bind,[status(th)],[])).
% 1.75/1.91 tff(2,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(quant_intro,[status(thm)],[1])).
% 1.75/1.91 tff(3,plain,
% 1.75/1.91 (^[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))))))))),
% 1.75/1.91 inference(bind,[status(th)],[])).
% 1.75/1.91 tff(4,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(quant_intro,[status(thm)],[3])).
% 1.75/1.91 tff(5,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(transitivity,[status(thm)],[4, 2])).
% 1.75/1.91 tff(6,plain,
% 1.75/1.91 (^[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)))))))))),
% 1.75/1.91 inference(bind,[status(th)],[])).
% 1.75/1.91 tff(7,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(quant_intro,[status(thm)],[6])).
% 1.75/1.91 tff(8,plain,
% 1.75/1.91 (![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)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(9,plain,
% 1.75/1.91 (^[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))))),
% 1.75/1.91 inference(bind,[status(th)],[])).
% 1.75/1.91 tff(10,plain,
% 1.75/1.91 (![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)))),
% 1.75/1.91 inference(quant_intro,[status(thm)],[9])).
% 1.75/1.91 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 1.75/1.91 tff(12,plain,
% 1.75/1.91 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.75/1.91 tff(13,plain,
% 1.75/1.91 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.75/1.91 tff(14,plain,(
% 1.75/1.91 ![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)))))),
% 1.75/1.91 inference(skolemize,[status(sab)],[13])).
% 1.75/1.91 tff(15,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.75/1.91 tff(16,plain,
% 1.75/1.91 (![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)))))))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.75/1.91 tff(17,plain,
% 1.75/1.91 ((~![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(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(18,plain,
% 1.75/1.91 (~((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.75/1.91 tff(19,plain,
% 1.75/1.91 (((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))))) | (part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(20,plain,
% 1.75/1.91 (part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.75/1.91 tff(21,assumption,((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))))), introduced(assumption)).
% 1.75/1.91 tff(22,plain,
% 1.75/1.91 ((~![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(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(23,plain,
% 1.75/1.91 ($false),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 1.75/1.91 tff(24,plain,(~((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))))), inference(lemma,lemma(discharge,[]))).
% 1.75/1.91 tff(25,plain,
% 1.75/1.91 (((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C1!14)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))))) | (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(26,plain,
% 1.75/1.91 (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.75/1.91 tff(27,assumption,(~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))), introduced(assumption)).
% 1.75/1.91 tff(28,plain,
% 1.75/1.91 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(29,plain,
% 1.75/1.91 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.75/1.91 tff(30,plain,
% 1.75/1.91 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))) | (~(part_of(C2!13, C1!14) | (~((~incident_c(tptp_fun_P_0(C2!13, C1!14), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C1!14), C1!14)))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(31,plain,
% 1.75/1.91 (~((~((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))) | (~(part_of(C2!13, C1!14) | (~((~incident_c(tptp_fun_P_0(C2!13, C1!14), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C1!14), C1!14))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[30, 16])).
% 1.75/1.91 tff(32,plain,
% 1.75/1.91 (((~((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))) | (~(part_of(C2!13, C1!14) | (~((~incident_c(tptp_fun_P_0(C2!13, C1!14), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C1!14), C1!14)))))) | ((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(33,plain,
% 1.75/1.91 ((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.75/1.91 tff(34,plain,
% 1.75/1.91 ((~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))) <=> (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(35,plain,
% 1.75/1.91 ((~![C1: $i, C2: $i, Cpp: $i, P: $i] : (((part_of(C2, C1) & incident_c(P, C2)) & meet(P, C1, Cpp)) => meet(P, C2, Cpp))) <=> (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp)))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(36,axiom,(~![C1: $i, C2: $i, Cpp: $i, P: $i] : (((part_of(C2, C1) & incident_c(P, C2)) & meet(P, C1, Cpp)) => meet(P, C2, Cpp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_12')).
% 1.75/1.91 tff(37,plain,
% 1.75/1.91 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.75/1.91 tff(38,plain,
% 1.75/1.91 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.75/1.91 tff(39,plain,
% 1.75/1.91 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.75/1.91 tff(40,plain,
% 1.75/1.91 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.75/1.91 tff(41,plain,(
% 1.75/1.91 ~((~(part_of(C2!13, C1!14) & incident_c(P!11, C2!13) & meet(P!11, C1!14, Cpp!12))) | meet(P!11, C2!13, Cpp!12))),
% 1.75/1.91 inference(skolemize,[status(sab)],[40])).
% 1.75/1.91 tff(42,plain,
% 1.75/1.91 (part_of(C2!13, C1!14) & incident_c(P!11, C2!13) & meet(P!11, C1!14, Cpp!12)),
% 1.75/1.91 inference(or_elim,[status(thm)],[41])).
% 1.75/1.91 tff(43,plain,
% 1.75/1.91 (part_of(C2!13, C1!14)),
% 1.75/1.91 inference(and_elim,[status(thm)],[42])).
% 1.75/1.91 tff(44,plain,
% 1.75/1.91 ((~((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))) | (~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(45,plain,
% 1.75/1.91 ((~((~part_of(C2!13, C1!14)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14)))) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[44, 43])).
% 1.75/1.91 tff(46,plain,
% 1.75/1.91 (![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[45, 33])).
% 1.75/1.91 tff(47,plain,
% 1.75/1.91 (((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))) <=> ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.91 inference(rewrite,[status(thm)],[])).
% 1.75/1.91 tff(48,plain,
% 1.75/1.91 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(49,plain,
% 1.75/1.91 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)),
% 1.75/1.91 inference(modus_ponens,[status(thm)],[48, 47])).
% 1.75/1.91 tff(50,plain,
% 1.75/1.91 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[49, 46, 29])).
% 1.75/1.91 tff(51,plain,
% 1.75/1.91 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(52,plain,
% 1.75/1.91 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[51, 27])).
% 1.75/1.91 tff(53,plain,
% 1.75/1.91 ((~![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(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13)))))))),
% 1.75/1.91 inference(quant_inst,[status(thm)],[])).
% 1.75/1.91 tff(54,plain,
% 1.75/1.91 (~((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13))))))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[53, 16])).
% 1.75/1.91 tff(55,plain,
% 1.75/1.91 (((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13)))))) | ((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))),
% 1.75/1.91 inference(tautology,[status(thm)],[])).
% 1.75/1.91 tff(56,plain,
% 1.75/1.91 ((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.91 inference(unit_resolution,[status(thm)],[55, 54])).
% 1.75/1.91 tff(57,plain,
% 1.75/1.91 (^[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)))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(58,plain,
% 1.75/1.92 (![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))))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[57])).
% 1.75/1.92 tff(59,plain,
% 1.75/1.92 (^[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))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(60,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[59])).
% 1.75/1.92 tff(61,plain,
% 1.75/1.92 (^[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))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(62,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[61])).
% 1.75/1.92 tff(63,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[62, 60])).
% 1.75/1.92 tff(64,plain,
% 1.75/1.92 (^[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)))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(65,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[64])).
% 1.75/1.92 tff(66,plain,
% 1.75/1.92 (^[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)))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(67,plain,
% 1.75/1.92 (![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))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[66])).
% 1.75/1.92 tff(68,plain,
% 1.75/1.92 (![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))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(69,plain,
% 1.75/1.92 (^[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)))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(70,plain,
% 1.75/1.92 (![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))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[69])).
% 1.75/1.92 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/sandbox2/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 1.75/1.92 tff(72,plain,
% 1.75/1.92 (![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))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[71, 70])).
% 1.75/1.92 tff(73,plain,
% 1.75/1.92 (![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))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[72, 68])).
% 1.75/1.92 tff(74,plain,(
% 1.75/1.92 ![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)))))))))),
% 1.75/1.92 inference(skolemize,[status(sab)],[73])).
% 1.75/1.92 tff(75,plain,
% 1.75/1.92 (![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))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[74, 67])).
% 1.75/1.92 tff(76,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[75, 65])).
% 1.75/1.92 tff(77,plain,
% 1.75/1.92 (![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)))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[76, 63])).
% 1.75/1.92 tff(78,plain,
% 1.75/1.92 (![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))))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[77, 58])).
% 1.75/1.92 tff(79,plain,
% 1.75/1.92 (((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(80,plain,
% 1.75/1.92 ((~((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))) <=> (~((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.92 inference(rewrite,[status(thm)],[])).
% 1.75/1.92 tff(81,plain,
% 1.75/1.92 (((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.92 inference(monotonicity,[status(thm)],[80])).
% 1.75/1.92 tff(82,plain,
% 1.75/1.92 (((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.92 inference(transitivity,[status(thm)],[81, 79])).
% 1.75/1.92 tff(83,plain,
% 1.75/1.92 ((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.92 inference(quant_inst,[status(thm)],[])).
% 1.75/1.92 tff(84,plain,
% 1.75/1.92 ((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.92 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.75/1.92 tff(85,plain,
% 1.75/1.92 (~((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[84, 78])).
% 1.75/1.92 tff(86,plain,
% 1.75/1.92 (((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!13)) | (~part_of(C2, C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))) | (end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))),
% 1.75/1.92 inference(tautology,[status(thm)],[])).
% 1.75/1.92 tff(87,plain,
% 1.75/1.92 (end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))),
% 1.75/1.92 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.75/1.92 tff(88,plain,
% 1.75/1.92 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(89,plain,
% 1.75/1.92 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 1.75/1.92 inference(quant_intro,[status(thm)],[88])).
% 1.75/1.92 tff(90,plain,
% 1.75/1.92 (^[P: $i, C: $i, C1: $i] : refl((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 1.75/1.92 inference(bind,[status(th)],[])).
% 1.75/1.92 tff(91,plain,
% 1.75/1.92 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[90])).
% 1.75/1.93 tff(92,plain,
% 1.75/1.93 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(93,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[92])).
% 1.75/1.93 tff(94,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[93, 91])).
% 1.75/1.93 tff(95,plain,
% 1.75/1.93 (^[P: $i, C: $i, C1: $i] : trans(monotonicity(rewrite(((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))), trans(monotonicity(rewrite((~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))) <=> (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), rewrite((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))), rewrite((((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(96,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[95])).
% 1.75/1.93 tff(97,plain,
% 1.75/1.93 (^[P: $i, C: $i, C1: $i] : rewrite((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(98,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[97])).
% 1.75/1.93 tff(99,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(100,plain,
% 1.75/1.93 (^[P: $i, C: $i, C1: $i] : rewrite((meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))))),
% 1.75/1.93 inference(bind,[status(th)],[])).
% 1.75/1.93 tff(101,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.75/1.93 inference(quant_intro,[status(thm)],[100])).
% 1.75/1.93 tff(102,axiom,(![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','meet_defn')).
% 1.75/1.93 tff(103,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.75/1.93 tff(104,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[103, 99])).
% 1.75/1.93 tff(105,plain,(
% 1.75/1.93 ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 1.75/1.93 inference(skolemize,[status(sab)],[104])).
% 1.75/1.93 tff(106,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[105, 98])).
% 1.75/1.93 tff(107,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[106, 96])).
% 1.75/1.93 tff(108,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[107, 94])).
% 1.75/1.93 tff(109,plain,
% 1.75/1.93 (![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[108, 89])).
% 1.75/1.93 tff(110,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13)))))))))))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(111,plain,
% 1.75/1.93 ((~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C2!13)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13)))))))))))) <=> (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(112,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C2!13)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13)))))))))))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[111])).
% 1.75/1.93 tff(113,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C2!13)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13)))))))))))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[112, 110])).
% 1.75/1.93 tff(114,plain,
% 1.75/1.93 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C2!13)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(115,plain,
% 1.75/1.93 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.75/1.93 tff(116,plain,
% 1.75/1.93 (~((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13)))))))))))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[115, 109])).
% 1.75/1.93 tff(117,plain,
% 1.75/1.93 (((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~((~meet(P!11, C2!13, Cpp!12)) | (~((~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, C2!13)) | (~incident_c(Q, Cpp!12)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C2!13))))))))))) | (meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))),
% 1.75/1.93 inference(tautology,[status(thm)],[])).
% 1.75/1.93 tff(118,plain,
% 1.75/1.93 (meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))))),
% 1.75/1.93 inference(unit_resolution,[status(thm)],[117, 116])).
% 1.75/1.93 tff(119,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(120,plain,
% 1.75/1.93 ((~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))))) <=> (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))),
% 1.75/1.93 inference(rewrite,[status(thm)],[])).
% 1.75/1.93 tff(121,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))))))),
% 1.75/1.93 inference(monotonicity,[status(thm)],[120])).
% 1.75/1.93 tff(122,plain,
% 1.75/1.93 (((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))))))),
% 1.75/1.93 inference(transitivity,[status(thm)],[121, 119])).
% 1.75/1.93 tff(123,plain,
% 1.75/1.93 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))),
% 1.75/1.93 inference(quant_inst,[status(thm)],[])).
% 1.75/1.93 tff(124,plain,
% 1.75/1.93 ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))))),
% 1.75/1.93 inference(modus_ponens,[status(thm)],[123, 122])).
% 1.75/1.93 tff(125,plain,
% 1.75/1.93 (~((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[124, 109])).
% 1.75/1.94 tff(126,plain,
% 1.75/1.94 (((~(meet(P!11, C1!14, Cpp!12) | (~incident_c(P!11, Cpp!12)) | (~incident_c(P!11, C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C1!14), C1!14)) | (~end_point(tptp_fun_Q_4(Cpp!12, C1!14), Cpp!12)))))))) | (~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))))) | ((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(127,plain,
% 1.75/1.94 ((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[126, 125])).
% 1.75/1.94 tff(128,plain,
% 1.75/1.94 (meet(P!11, C1!14, Cpp!12)),
% 1.75/1.94 inference(and_elim,[status(thm)],[42])).
% 1.75/1.94 tff(129,plain,
% 1.75/1.94 ((~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))) | (~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(130,plain,
% 1.75/1.94 ((~((~meet(P!11, C1!14, Cpp!12)) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))))) | (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[129, 128])).
% 1.75/1.94 tff(131,plain,
% 1.75/1.94 (~((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[130, 127])).
% 1.75/1.94 tff(132,plain,
% 1.75/1.94 (((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))) | incident_c(P!11, Cpp!12)),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(133,plain,
% 1.75/1.94 (incident_c(P!11, Cpp!12)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[132, 131])).
% 1.75/1.94 tff(134,plain,
% 1.75/1.94 (~meet(P!11, C2!13, Cpp!12)),
% 1.75/1.94 inference(or_elim,[status(thm)],[41])).
% 1.75/1.94 tff(135,plain,
% 1.75/1.94 (incident_c(P!11, C2!13)),
% 1.75/1.94 inference(and_elim,[status(thm)],[42])).
% 1.75/1.94 tff(136,plain,
% 1.75/1.94 ((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(137,plain,
% 1.75/1.94 ((~(meet(P!11, C2!13, Cpp!12) | (~incident_c(P!11, C2!13)) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))))) | (~incident_c(P!11, Cpp!12)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[136, 135, 134])).
% 1.75/1.94 tff(138,plain,
% 1.75/1.94 (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[137, 133, 118])).
% 1.75/1.94 tff(139,plain,
% 1.75/1.94 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))) | ((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(140,plain,
% 1.75/1.94 ((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[139, 138])).
% 1.75/1.94 tff(141,plain,
% 1.75/1.94 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(142,plain,
% 1.75/1.94 (incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[141, 138])).
% 1.75/1.94 tff(143,plain,
% 1.75/1.94 (((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))) <=> ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(144,plain,
% 1.75/1.94 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(145,plain,
% 1.75/1.94 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[144, 143])).
% 1.75/1.94 tff(146,plain,
% 1.75/1.94 (incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[145, 46, 142])).
% 1.75/1.94 tff(147,plain,
% 1.75/1.94 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))))) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(148,plain,
% 1.75/1.94 (incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[147, 138])).
% 1.75/1.94 tff(149,plain,
% 1.75/1.94 (((~incident_c(P!11, C1!14)) | (~incident_c(P!11, Cpp!12)) | (~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14))))))) | ![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(150,plain,
% 1.75/1.94 (![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[149, 131])).
% 1.75/1.94 tff(151,plain,
% 1.75/1.94 (((~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)))))) <=> ((~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(152,plain,
% 1.75/1.94 ((~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)))))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(153,plain,
% 1.75/1.94 ((~![Q: $i] : ((~incident_c(Q, Cpp!12)) | (~incident_c(Q, C1!14)) | (~((~end_point(Q, Cpp!12)) | (~end_point(Q, C1!14)))))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))))),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[152, 151])).
% 1.75/1.94 tff(154,plain,
% 1.75/1.94 ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[153, 150, 148])).
% 1.75/1.94 tff(155,plain,
% 1.75/1.94 (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[154, 146])).
% 1.75/1.94 tff(156,plain,
% 1.75/1.94 (((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(157,plain,
% 1.75/1.94 (end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[156, 155])).
% 1.75/1.94 tff(158,plain,
% 1.75/1.94 ((~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)))) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(159,plain,
% 1.75/1.94 (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[158, 157, 140])).
% 1.75/1.94 tff(160,plain,
% 1.75/1.94 ((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(161,plain,
% 1.75/1.94 ((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))))) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C2!13) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[160, 142])).
% 1.75/1.94 tff(162,plain,
% 1.75/1.94 (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[161, 159, 87])).
% 1.75/1.94 tff(163,plain,
% 1.75/1.94 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(164,plain,
% 1.75/1.94 (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[163, 162])).
% 1.75/1.94 tff(165,plain,
% 1.75/1.94 ((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(166,plain,
% 1.75/1.94 ((~((~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[165, 164])).
% 1.75/1.94 tff(167,plain,
% 1.75/1.94 (![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[166, 56])).
% 1.75/1.94 tff(168,plain,
% 1.75/1.94 (((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(169,plain,
% 1.75/1.94 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))),
% 1.75/1.94 inference(quant_inst,[status(thm)],[])).
% 1.75/1.94 tff(170,plain,
% 1.75/1.94 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)),
% 1.75/1.94 inference(modus_ponens,[status(thm)],[169, 168])).
% 1.75/1.94 tff(171,plain,
% 1.75/1.94 ($false),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[170, 167, 52, 50])).
% 1.75/1.94 tff(172,plain,((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)), inference(lemma,lemma(discharge,[]))).
% 1.75/1.94 tff(173,plain,
% 1.75/1.94 ((~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))),
% 1.75/1.94 inference(tautology,[status(thm)],[])).
% 1.75/1.94 tff(174,plain,
% 1.75/1.94 ((~(part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[173, 172])).
% 1.75/1.94 tff(175,plain,
% 1.75/1.94 (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)),
% 1.75/1.94 inference(unit_resolution,[status(thm)],[174, 26])).
% 1.75/1.94 tff(176,plain,
% 1.75/1.94 (((~![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))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(177,plain,
% 1.75/1.94 ((~((~(end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~(part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))) <=> (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.94 inference(rewrite,[status(thm)],[])).
% 1.75/1.94 tff(178,plain,
% 1.75/1.94 (((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~(part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.94 inference(monotonicity,[status(thm)],[177])).
% 1.75/1.94 tff(179,plain,
% 1.75/1.94 (((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~(part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), 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))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))))),
% 1.75/1.95 inference(transitivity,[status(thm)],[178, 176])).
% 1.75/1.95 tff(180,plain,
% 1.75/1.95 ((~![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(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~(part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(181,plain,
% 1.75/1.95 ((~![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))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[180, 179])).
% 1.75/1.95 tff(182,plain,
% 1.75/1.95 (~((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[181, 78])).
% 1.75/1.95 tff(183,plain,
% 1.75/1.95 (((~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | part_of(tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C1!14, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C1!14, tptp_fun_Q_4(Cpp!12, C2!13))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))))) | ((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(184,plain,
% 1.75/1.95 ((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[183, 182])).
% 1.75/1.95 tff(185,plain,
% 1.75/1.95 (((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), Cpp!12)) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14))) | end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(186,plain,
% 1.75/1.95 (end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[185, 155])).
% 1.75/1.95 tff(187,plain,
% 1.75/1.95 ((~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))) | (~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(188,plain,
% 1.75/1.95 ((~((~end_point(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))))) | (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[187, 186])).
% 1.75/1.95 tff(189,plain,
% 1.75/1.95 (~((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[188, 184])).
% 1.75/1.95 tff(190,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2))))) | ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(191,plain,
% 1.75/1.95 (![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[190, 189])).
% 1.75/1.95 tff(192,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(193,plain,
% 1.75/1.95 (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[192, 162])).
% 1.75/1.95 tff(194,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(195,plain,
% 1.75/1.95 (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[194, 162])).
% 1.75/1.95 tff(196,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(197,plain,
% 1.75/1.95 (incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[196, 162])).
% 1.75/1.95 tff(198,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(199,plain,
% 1.75/1.95 (incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[198, 162])).
% 1.75/1.95 tff(200,plain,
% 1.75/1.95 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(201,plain,
% 1.75/1.95 ((part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))))) <=> ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(202,plain,
% 1.75/1.95 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | ((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14))))),
% 1.75/1.95 inference(monotonicity,[status(thm)],[201])).
% 1.75/1.95 tff(203,plain,
% 1.75/1.95 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)))),
% 1.75/1.95 inference(transitivity,[status(thm)],[202, 200])).
% 1.75/1.95 tff(204,plain,
% 1.75/1.95 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(205,plain,
% 1.75/1.95 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!14)) | (~part_of(C2, C1!14)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), C2)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14))),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[204, 203])).
% 1.75/1.95 tff(206,plain,
% 1.75/1.95 ((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[205, 199, 197, 195, 193, 191])).
% 1.75/1.95 tff(207,plain,
% 1.75/1.95 (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[206, 175])).
% 1.75/1.95 tff(208,plain,
% 1.75/1.95 ((~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(209,plain,
% 1.75/1.95 ((~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[208, 207])).
% 1.75/1.95 tff(210,plain,
% 1.75/1.95 (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[209, 20])).
% 1.75/1.95 tff(211,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(212,plain,
% 1.75/1.95 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[211, 210])).
% 1.75/1.95 tff(213,plain,
% 1.75/1.95 (((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))) <=> ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.95 inference(rewrite,[status(thm)],[])).
% 1.75/1.95 tff(214,plain,
% 1.75/1.95 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(215,plain,
% 1.75/1.95 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C1!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)),
% 1.75/1.95 inference(modus_ponens,[status(thm)],[214, 213])).
% 1.75/1.95 tff(216,plain,
% 1.75/1.95 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[215, 46, 212])).
% 1.75/1.95 tff(217,plain,
% 1.75/1.95 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C1!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(tautology,[status(thm)],[])).
% 1.75/1.95 tff(218,plain,
% 1.75/1.95 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[217, 210])).
% 1.75/1.95 tff(219,plain,
% 1.75/1.95 ((~![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(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13)))))))),
% 1.75/1.95 inference(quant_inst,[status(thm)],[])).
% 1.75/1.95 tff(220,plain,
% 1.75/1.95 (~((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13))))))),
% 1.75/1.95 inference(unit_resolution,[status(thm)],[219, 16])).
% 1.75/1.95 tff(221,plain,
% 1.75/1.95 (((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~(part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13), C2!13)))))) | ((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))),
% 1.75/1.96 inference(tautology,[status(thm)],[])).
% 1.75/1.96 tff(222,plain,
% 1.75/1.96 ((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[221, 220])).
% 1.75/1.96 tff(223,plain,
% 1.75/1.96 (((~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~incident_c(tptp_fun_Q_4(Cpp!12, C2!13), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | (~part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | part_of(tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), tptp_fun_C1_3(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)),
% 1.75/1.96 inference(tautology,[status(thm)],[])).
% 1.75/1.96 tff(224,plain,
% 1.75/1.96 (part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[223, 162])).
% 1.75/1.96 tff(225,plain,
% 1.75/1.96 ((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | (~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.96 inference(tautology,[status(thm)],[])).
% 1.75/1.96 tff(226,plain,
% 1.75/1.96 ((~((~part_of(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C2!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[225, 224])).
% 1.75/1.96 tff(227,plain,
% 1.75/1.96 (![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[226, 222])).
% 1.75/1.96 tff(228,plain,
% 1.75/1.96 (((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))),
% 1.75/1.96 inference(rewrite,[status(thm)],[])).
% 1.75/1.96 tff(229,plain,
% 1.75/1.96 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13))),
% 1.75/1.96 inference(quant_inst,[status(thm)],[])).
% 1.75/1.96 tff(230,plain,
% 1.75/1.96 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(P, C2!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!13, tptp_fun_Q_4(Cpp!12, C2!13)), C1!14), C2!13)),
% 1.75/1.96 inference(modus_ponens,[status(thm)],[229, 228])).
% 1.75/1.96 tff(231,plain,
% 1.75/1.96 ($false),
% 1.75/1.96 inference(unit_resolution,[status(thm)],[230, 227, 218, 216])).
% 1.75/1.96 % SZS output end Proof
% 1.75/1.96 % E exiting
%------------------------------------------------------------------------------