%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO089+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:34 AM UTC 2025
% Result : Theorem 0.63s 0.80s
% Output : Proof 0.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO089+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:16:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.63/0.80 % SZS status Theorem
% 0.63/0.80 % SZS output start Proof
% 0.63/0.80 tff(incident_c_type, type, (
% 0.63/0.80 incident_c: ( $i * $i ) > $o)).
% 0.63/0.80 tff(sum_type, type, (
% 0.63/0.80 sum: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_C2_7_type, type, (
% 0.63/0.80 tptp_fun_C2_7: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_Cpp_13_type, type, (
% 0.63/0.80 tptp_fun_Cpp_13: $i)).
% 0.63/0.80 tff(tptp_fun_P_11_type, type, (
% 0.63/0.80 tptp_fun_P_11: $i)).
% 0.63/0.80 tff(tptp_fun_C1_8_type, type, (
% 0.63/0.80 tptp_fun_C1_8: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_P_0_type, type, (
% 0.63/0.80 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_C_12_type, type, (
% 0.63/0.80 tptp_fun_C_12: $i)).
% 0.63/0.80 tff(tptp_fun_C2_2_type, type, (
% 0.63/0.80 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 0.63/0.80 tff(meet_type, type, (
% 0.63/0.80 meet: ( $i * $i * $i ) > $o)).
% 0.63/0.80 tff(inner_point_type, type, (
% 0.63/0.80 inner_point: ( $i * $i ) > $o)).
% 0.63/0.80 tff(part_of_type, type, (
% 0.63/0.80 part_of: ( $i * $i ) > $o)).
% 0.63/0.80 tff(tptp_fun_C1_3_type, type, (
% 0.63/0.80 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 0.63/0.80 tff(end_point_type, type, (
% 0.63/0.80 end_point: ( $i * $i ) > $o)).
% 0.63/0.80 tff(tptp_fun_Q_1_type, type, (
% 0.63/0.80 tptp_fun_Q_1: ( $i * $i * $i ) > $i)).
% 0.63/0.80 tff(tptp_fun_Q_4_type, type, (
% 0.63/0.80 tptp_fun_Q_4: ( $i * $i ) > $i)).
% 0.63/0.80 tff(1,plain,
% 0.63/0.80 (((part_of(Cpp!13, C!12) & inner_point(P!11, Cpp!13)) & (~inner_point(P!11, C!12))) <=> (part_of(Cpp!13, C!12) & inner_point(P!11, Cpp!13) & (~inner_point(P!11, C!12)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(2,plain,
% 0.63/0.80 ((~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C))) <=> (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(3,plain,
% 0.63/0.80 ((~![C: $i, P: $i] : (?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp)) => inner_point(P, C))) <=> (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C)))),
% 0.63/0.80 inference(rewrite,[status(thm)],[])).
% 0.63/0.80 tff(4,axiom,(~![C: $i, P: $i] : (?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp)) => inner_point(P, C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_11')).
% 0.63/0.80 tff(5,plain,
% 0.63/0.80 (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.63/0.80 tff(6,plain,
% 0.63/0.80 (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.63/0.80 tff(7,plain,
% 0.63/0.80 (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.63/0.80 tff(8,plain,
% 0.63/0.80 (~![C: $i, P: $i] : ((~?[Cpp: $i] : (part_of(Cpp, C) & inner_point(P, Cpp))) | inner_point(P, C))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.63/0.80 tff(9,plain,
% 0.63/0.80 (part_of(Cpp!13, C!12) & inner_point(P!11, Cpp!13) & (~inner_point(P!11, C!12))),
% 0.63/0.80 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.63/0.80 tff(10,plain,
% 0.63/0.80 (inner_point(P!11, Cpp!13)),
% 0.63/0.80 inference(and_elim,[status(thm)],[9])).
% 0.63/0.80 tff(11,plain,
% 0.63/0.80 (^[C: $i, P: $i] : refl(((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(12,plain,
% 0.63/0.80 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.63/0.80 inference(quant_intro,[status(thm)],[11])).
% 0.63/0.80 tff(13,plain,
% 0.63/0.80 (^[C: $i, P: $i] : rewrite(((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))))))),
% 0.63/0.80 inference(bind,[status(th)],[])).
% 0.63/0.80 tff(14,plain,
% 0.63/0.80 (![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[13])).
% 0.63/0.81 tff(15,plain,
% 0.63/0.81 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(16,plain,
% 0.63/0.81 (^[C: $i, P: $i] : rewrite((inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(17,plain,
% 0.63/0.81 (![C: $i, P: $i] : (inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2)))) <=> ![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[16])).
% 0.63/0.81 tff(18,axiom,(![C: $i, P: $i] : (inner_point(P, C) => ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','c4')).
% 0.63/0.81 tff(19,plain,
% 0.63/0.81 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.63/0.81 tff(20,plain,
% 0.63/0.81 (![C: $i, P: $i] : ((~inner_point(P, C)) | ?[C1: $i, C2: $i] : (meet(P, C1, C2) & (C = sum(C1, C2))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[19, 15])).
% 0.63/0.81 tff(21,plain,(
% 0.63/0.81 ![C: $i, P: $i] : ((~inner_point(P, C)) | (meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)) & (C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))),
% 0.63/0.81 inference(skolemize,[status(sab)],[20])).
% 0.63/0.81 tff(22,plain,
% 0.63/0.81 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[21, 14])).
% 0.63/0.81 tff(23,plain,
% 0.63/0.81 (![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[22, 12])).
% 0.63/0.81 tff(24,plain,
% 0.63/0.81 (((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(P!11, Cpp!13)) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))) <=> ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | (~inner_point(P!11, Cpp!13)) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(25,plain,
% 0.63/0.81 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | ((~inner_point(P!11, Cpp!13)) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(26,plain,
% 0.63/0.81 ((~![C: $i, P: $i] : ((~inner_point(P, C)) | (~((~meet(P, tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C))) | (~(C = sum(tptp_fun_C1_8(P, C), tptp_fun_C2_7(P, C)))))))) | (~inner_point(P!11, Cpp!13)) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.63/0.81 tff(27,plain,
% 0.63/0.81 (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[26, 23, 10])).
% 0.63/0.81 tff(28,plain,
% 0.63/0.81 (((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | (Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(29,plain,
% 0.63/0.81 (Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.63/0.81 tff(30,plain,
% 0.63/0.81 (sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = Cpp!13),
% 0.63/0.81 inference(symmetry,[status(thm)],[29])).
% 0.63/0.81 tff(31,plain,
% 0.63/0.81 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[30])).
% 0.63/0.81 tff(32,plain,
% 0.63/0.81 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13) <=> incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.81 inference(symmetry,[status(thm)],[31])).
% 0.63/0.81 tff(33,plain,
% 0.63/0.81 ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) <=> (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[32])).
% 0.63/0.81 tff(34,plain,
% 0.63/0.81 (^[C: $i, C1: $i] : refl((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(35,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[34])).
% 0.63/0.81 tff(36,plain,
% 0.63/0.81 (^[C: $i, C1: $i] : rewrite((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(37,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[36])).
% 0.63/0.81 tff(38,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(transitivity,[status(thm)],[37, 35])).
% 0.63/0.81 tff(39,plain,
% 0.63/0.81 (^[C: $i, C1: $i] : trans(monotonicity(rewrite(((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))), rewrite((part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))) <=> (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))), rewrite((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(40,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[39])).
% 0.63/0.81 tff(41,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(42,plain,
% 0.63/0.81 (^[C: $i, C1: $i] : rewrite((part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(43,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[42])).
% 0.63/0.81 tff(44,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.63/0.81 tff(45,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.63/0.81 tff(46,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.63/0.81 tff(47,plain,(
% 0.63/0.81 ![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))),
% 0.63/0.81 inference(skolemize,[status(sab)],[46])).
% 0.63/0.81 tff(48,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.63/0.81 tff(49,plain,
% 0.63/0.81 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[48, 38])).
% 0.63/0.81 tff(50,plain,
% 0.63/0.81 ((~![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(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(51,plain,
% 0.63/0.81 (~((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.63/0.81 tff(52,plain,
% 0.63/0.81 (((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))))) | (part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(53,plain,
% 0.63/0.81 (part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.63/0.81 tff(54,assumption,((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))))), introduced(assumption)).
% 0.63/0.81 tff(55,plain,
% 0.63/0.81 ((~![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(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(56,plain,
% 0.63/0.81 ($false),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[55, 49, 54])).
% 0.63/0.81 tff(57,plain,(~((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))))), inference(lemma,lemma(discharge,[]))).
% 0.63/0.81 tff(58,plain,
% 0.63/0.81 (((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, C!12)))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))))) | (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(59,plain,
% 0.63/0.81 (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.63/0.81 tff(60,plain,
% 0.63/0.81 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)),
% 0.63/0.81 inference(monotonicity,[status(thm)],[30])).
% 0.63/0.81 tff(61,plain,
% 0.63/0.81 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13) <=> incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.81 inference(symmetry,[status(thm)],[60])).
% 0.63/0.81 tff(62,plain,
% 0.63/0.81 ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) <=> (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.81 inference(monotonicity,[status(thm)],[61])).
% 0.63/0.81 tff(63,assumption,(~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))), introduced(assumption)).
% 0.63/0.81 tff(64,plain,
% 0.63/0.81 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(65,plain,
% 0.63/0.81 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.63/0.81 tff(66,plain,
% 0.63/0.81 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))) | (~(part_of(Cpp!13, C!12) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!12), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!12), C!12)))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(67,plain,
% 0.63/0.81 (~((~((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))) | (~(part_of(Cpp!13, C!12) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!12), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!12), C!12))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[66, 49])).
% 0.63/0.81 tff(68,plain,
% 0.63/0.81 (((~((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))) | (~(part_of(Cpp!13, C!12) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!12), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!12), C!12)))))) | ((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(69,plain,
% 0.63/0.81 ((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.63/0.81 tff(70,plain,
% 0.63/0.81 (part_of(Cpp!13, C!12)),
% 0.63/0.81 inference(and_elim,[status(thm)],[9])).
% 0.63/0.81 tff(71,plain,
% 0.63/0.81 ((~((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))) | (~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(72,plain,
% 0.63/0.81 ((~((~part_of(Cpp!13, C!12)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12)))) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.63/0.81 tff(73,plain,
% 0.63/0.81 (![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.63/0.81 tff(74,plain,
% 0.63/0.81 (((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.63/0.81 inference(rewrite,[status(thm)],[])).
% 0.63/0.81 tff(75,plain,
% 0.63/0.81 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(76,plain,
% 0.63/0.81 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.63/0.81 tff(77,plain,
% 0.63/0.81 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[76, 73, 65])).
% 0.63/0.81 tff(78,plain,
% 0.63/0.81 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.81 inference(modus_ponens,[status(thm)],[77, 62])).
% 0.63/0.81 tff(79,plain,
% 0.63/0.81 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(80,plain,
% 0.63/0.81 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[79, 63])).
% 0.63/0.81 tff(81,plain,
% 0.63/0.81 ((~![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(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))))),
% 0.63/0.81 inference(quant_inst,[status(thm)],[])).
% 0.63/0.81 tff(82,plain,
% 0.63/0.81 (~((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[81, 49])).
% 0.63/0.81 tff(83,plain,
% 0.63/0.81 (((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))) | ((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.81 inference(tautology,[status(thm)],[])).
% 0.63/0.81 tff(84,plain,
% 0.63/0.81 ((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.81 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.63/0.81 tff(85,plain,
% 0.63/0.81 (^[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)))))))))))),
% 0.63/0.81 inference(bind,[status(th)],[])).
% 0.63/0.81 tff(86,plain,
% 0.63/0.81 (![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))))))))))),
% 0.63/0.81 inference(quant_intro,[status(thm)],[85])).
% 0.63/0.81 tff(87,plain,
% 0.63/0.81 (^[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))))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(88,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[87])).
% 0.63/0.82 tff(89,plain,
% 0.63/0.82 (^[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))))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(90,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[89])).
% 0.63/0.82 tff(91,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[90, 88])).
% 0.63/0.82 tff(92,plain,
% 0.63/0.82 (^[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)))))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(93,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[92])).
% 0.63/0.82 tff(94,plain,
% 0.63/0.82 (^[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)))))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(95,plain,
% 0.63/0.82 (![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))))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[94])).
% 0.63/0.82 tff(96,plain,
% 0.63/0.82 (![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))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(97,plain,
% 0.63/0.82 (^[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)))))))),
% 0.63/0.82 inference(bind,[status(th)],[])).
% 0.63/0.82 tff(98,plain,
% 0.63/0.82 (![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))))))),
% 0.63/0.82 inference(quant_intro,[status(thm)],[97])).
% 0.63/0.82 tff(99,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')).
% 0.63/0.82 tff(100,plain,
% 0.63/0.82 (![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))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.63/0.82 tff(101,plain,
% 0.63/0.82 (![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))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.63/0.82 tff(102,plain,(
% 0.63/0.82 ![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)))))))))),
% 0.63/0.82 inference(skolemize,[status(sab)],[101])).
% 0.63/0.82 tff(103,plain,
% 0.63/0.82 (![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))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.63/0.82 tff(104,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.63/0.82 tff(105,plain,
% 0.63/0.82 (![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)))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[104, 91])).
% 0.63/0.82 tff(106,plain,
% 0.63/0.82 (![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))))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[105, 86])).
% 0.63/0.82 tff(107,plain,
% 0.63/0.82 (((~![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(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(108,plain,
% 0.63/0.82 ((~((~(end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))) <=> (~((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 0.63/0.82 inference(rewrite,[status(thm)],[])).
% 0.63/0.82 tff(109,plain,
% 0.63/0.82 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 0.63/0.82 inference(monotonicity,[status(thm)],[108])).
% 0.63/0.82 tff(110,plain,
% 0.63/0.82 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))))),
% 0.63/0.82 inference(transitivity,[status(thm)],[109, 107])).
% 0.63/0.82 tff(111,plain,
% 0.63/0.82 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 0.63/0.82 inference(quant_inst,[status(thm)],[])).
% 0.63/0.82 tff(112,plain,
% 0.63/0.82 ((~![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(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 0.63/0.82 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.63/0.82 tff(113,plain,
% 0.63/0.82 (~((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[112, 106])).
% 0.63/0.83 tff(114,plain,
% 0.63/0.83 (((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~((~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(C2, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))) | ((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))),
% 0.63/0.83 inference(tautology,[status(thm)],[])).
% 0.63/0.83 tff(115,plain,
% 0.63/0.83 ((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))),
% 0.63/0.83 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.63/0.83 tff(116,plain,
% 0.63/0.83 (^[C: $i, C1: $i, C2: $i, Q: $i] : refl((~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(117,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[116])).
% 0.63/0.83 tff(118,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(pull_quant,[status(thm)],[])).
% 0.63/0.83 tff(119,plain,
% 0.63/0.83 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> (~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), pull_quant((~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> (?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), pull_quant((?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))), pull_quant((~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(120,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[119])).
% 0.63/0.83 tff(121,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[120, 118])).
% 0.63/0.83 tff(122,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[121, 117])).
% 0.63/0.83 tff(123,plain,
% 0.63/0.83 (^[C: $i, C1: $i, C2: $i] : rewrite((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(124,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[123])).
% 0.63/0.83 tff(125,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[124, 122])).
% 0.63/0.83 tff(126,plain,
% 0.63/0.83 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(rewrite(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), trans(monotonicity(trans(monotonicity(rewrite((incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), rewrite((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), rewrite(((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), rewrite((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))))),
% 0.63/0.83 inference(bind,[status(th)],[])).
% 0.63/0.83 tff(127,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(quant_intro,[status(thm)],[126])).
% 0.63/0.83 tff(128,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(129,axiom,(![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','sum_defn')).
% 0.63/0.83 tff(130,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.63/0.83 tff(131,plain,(
% 0.63/0.83 ![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))),
% 0.63/0.83 inference(skolemize,[status(sab)],[130])).
% 0.63/0.83 tff(132,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.63/0.83 tff(133,plain,
% 0.63/0.83 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.63/0.83 inference(modus_ponens,[status(thm)],[132, 125])).
% 0.63/0.83 tff(134,plain,
% 0.63/0.83 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(135,plain,
% 0.63/0.83 ((~(~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) <=> (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(136,plain,
% 0.63/0.83 (((~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) | $false) <=> (~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(137,plain,
% 0.63/0.83 ((~$true) <=> $false),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(138,plain,
% 0.63/0.83 (($true | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))) <=> $true),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(139,plain,
% 0.63/0.83 ((~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))) <=> (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(140,plain,
% 0.63/0.83 ((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> $true),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(141,plain,
% 0.63/0.83 (((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))) <=> ($true | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[140, 139])).
% 0.63/0.83 tff(142,plain,
% 0.63/0.83 (((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))) <=> $true),
% 0.63/0.83 inference(transitivity,[status(thm)],[141, 138])).
% 0.63/0.83 tff(143,plain,
% 0.63/0.83 ((~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))))) <=> (~$true)),
% 0.63/0.83 inference(monotonicity,[status(thm)],[142])).
% 0.63/0.83 tff(144,plain,
% 0.63/0.83 ((~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))))) <=> $false),
% 0.63/0.83 inference(transitivity,[status(thm)],[143, 137])).
% 0.63/0.83 tff(145,plain,
% 0.63/0.83 ((~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) <=> (~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(146,plain,
% 0.63/0.83 (($false | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) <=> (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.83 inference(rewrite,[status(thm)],[])).
% 0.63/0.83 tff(147,plain,
% 0.63/0.83 ((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) <=> (~$true)),
% 0.63/0.83 inference(monotonicity,[status(thm)],[140])).
% 0.63/0.83 tff(148,plain,
% 0.63/0.83 ((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) <=> $false),
% 0.63/0.83 inference(transitivity,[status(thm)],[147, 137])).
% 0.63/0.83 tff(149,plain,
% 0.63/0.83 (((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) <=> ($false | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[148])).
% 0.63/0.83 tff(150,plain,
% 0.63/0.83 (((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) <=> (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.83 inference(transitivity,[status(thm)],[149, 146])).
% 0.63/0.83 tff(151,plain,
% 0.63/0.83 ((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) <=> (~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.83 inference(monotonicity,[status(thm)],[150])).
% 0.63/0.83 tff(152,plain,
% 0.63/0.83 ((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) <=> (~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[151, 145])).
% 0.63/0.84 tff(153,plain,
% 0.63/0.84 (((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))))) <=> ((~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) | $false)),
% 0.63/0.84 inference(monotonicity,[status(thm)],[152, 144])).
% 0.63/0.84 tff(154,plain,
% 0.63/0.84 (((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))))) <=> (~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[153, 136])).
% 0.63/0.84 tff(155,plain,
% 0.63/0.84 ((~((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))))))) <=> (~(~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[154])).
% 0.63/0.84 tff(156,plain,
% 0.63/0.84 ((~((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13))))))))) <=> (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[155, 135])).
% 0.63/0.84 tff(157,plain,
% 0.63/0.84 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[156])).
% 0.63/0.84 tff(158,plain,
% 0.63/0.84 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[157, 134])).
% 0.63/0.84 tff(159,plain,
% 0.63/0.84 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (~((~((~(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))))) | (~((sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(tptp_fun_Q_1(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_7(P!11, Cpp!13)))))))))),
% 0.63/0.84 inference(quant_inst,[status(thm)],[])).
% 0.63/0.84 tff(160,plain,
% 0.63/0.84 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.63/0.84 tff(161,plain,
% 0.63/0.84 (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.84 inference(unit_resolution,[status(thm)],[160, 133])).
% 0.63/0.84 tff(162,plain,
% 0.63/0.84 (^[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)))))))))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(163,plain,
% 0.63/0.84 (![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))))))))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[162])).
% 0.63/0.84 tff(164,plain,
% 0.63/0.84 (^[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)))))))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(165,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[164])).
% 0.63/0.84 tff(166,plain,
% 0.63/0.84 (^[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)))))))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(167,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[166])).
% 0.63/0.84 tff(168,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(transitivity,[status(thm)],[167, 165])).
% 0.63/0.84 tff(169,plain,
% 0.63/0.84 (^[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))))))))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(170,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[169])).
% 0.63/0.84 tff(171,plain,
% 0.63/0.84 (^[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)))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(172,plain,
% 0.63/0.84 (![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))))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[171])).
% 0.63/0.84 tff(173,plain,
% 0.63/0.84 (![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)))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(174,plain,
% 0.63/0.84 (^[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))))))),
% 0.63/0.84 inference(bind,[status(th)],[])).
% 0.63/0.84 tff(175,plain,
% 0.63/0.84 (![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)))))),
% 0.63/0.84 inference(quant_intro,[status(thm)],[174])).
% 0.63/0.84 tff(176,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')).
% 0.63/0.84 tff(177,plain,
% 0.63/0.84 (![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)))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.63/0.84 tff(178,plain,
% 0.63/0.84 (![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)))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.63/0.84 tff(179,plain,(
% 0.63/0.84 ![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)))))))),
% 0.63/0.84 inference(skolemize,[status(sab)],[178])).
% 0.63/0.84 tff(180,plain,
% 0.63/0.84 (![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))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.63/0.84 tff(181,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.63/0.84 tff(182,plain,
% 0.63/0.84 (![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))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[181, 168])).
% 0.63/0.84 tff(183,plain,
% 0.63/0.84 (![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))))))))))))),
% 0.63/0.84 inference(modus_ponens,[status(thm)],[182, 163])).
% 0.63/0.84 tff(184,plain,
% 0.63/0.84 (((~![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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(185,plain,
% 0.63/0.84 ((~((~(meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))))) <=> (~((~(meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))))))),
% 0.63/0.84 inference(rewrite,[status(thm)],[])).
% 0.63/0.84 tff(186,plain,
% 0.63/0.84 (((~![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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))))))),
% 0.63/0.84 inference(monotonicity,[status(thm)],[185])).
% 0.63/0.84 tff(187,plain,
% 0.63/0.84 (((~![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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))))))),
% 0.63/0.85 inference(transitivity,[status(thm)],[186, 184])).
% 0.63/0.85 tff(188,plain,
% 0.63/0.85 ((~![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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(189,plain,
% 0.63/0.85 ((~![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, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.63/0.85 tff(190,plain,
% 0.63/0.85 (~((~(meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[189, 183])).
% 0.63/0.85 tff(191,plain,
% 0.63/0.85 (((~(meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C1_8(P!11, Cpp!13))) | (~end_point(tptp_fun_Q_4(tptp_fun_C2_7(P!11, Cpp!13), tptp_fun_C1_8(P!11, Cpp!13)), tptp_fun_C2_7(P!11, Cpp!13))))))))) | (~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))))) | ((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(192,plain,
% 0.63/0.85 ((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[191, 190])).
% 0.63/0.85 tff(193,plain,
% 0.63/0.85 (((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(Cpp!13 = sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(194,plain,
% 0.63/0.85 (meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[193, 27])).
% 0.63/0.85 tff(195,plain,
% 0.63/0.85 ((~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))) | (~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(196,plain,
% 0.63/0.85 ((~((~meet(P!11, tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))))) | (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.63/0.85 tff(197,plain,
% 0.63/0.85 (~((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13))))))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[196, 192])).
% 0.63/0.85 tff(198,plain,
% 0.63/0.85 (((~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~![Q: $i] : ((~incident_c(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(Q, tptp_fun_C1_8(P!11, Cpp!13))) | (~((~end_point(Q, tptp_fun_C2_7(P!11, Cpp!13))) | (~end_point(Q, tptp_fun_C1_8(P!11, Cpp!13)))))))) | incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(199,plain,
% 0.63/0.85 (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.63/0.85 tff(200,plain,
% 0.63/0.85 ((incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))) | (~incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(201,plain,
% 0.63/0.85 (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[200, 199])).
% 0.63/0.85 tff(202,plain,
% 0.63/0.85 ((~(incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> (incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))) | incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~(incident_c(P!11, tptp_fun_C1_8(P!11, Cpp!13)) | incident_c(P!11, tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(203,plain,
% 0.63/0.85 (incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[202, 201, 161])).
% 0.63/0.85 tff(204,plain,
% 0.63/0.85 (end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) <=> end_point(P!11, Cpp!13)),
% 0.63/0.85 inference(monotonicity,[status(thm)],[30])).
% 0.63/0.85 tff(205,plain,
% 0.63/0.85 (end_point(P!11, Cpp!13) <=> end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(symmetry,[status(thm)],[204])).
% 0.63/0.85 tff(206,plain,
% 0.63/0.85 ((~end_point(P!11, Cpp!13)) <=> (~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(monotonicity,[status(thm)],[205])).
% 0.63/0.85 tff(207,plain,
% 0.63/0.85 (^[P: $i, C: $i] : refl((~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(208,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> ![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[207])).
% 0.63/0.85 tff(209,plain,
% 0.63/0.85 (^[P: $i, C: $i] : trans(trans(monotonicity(rewrite((incident_c(P, C) & (~end_point(P, C))) <=> (~((~incident_c(P, C)) | end_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))), rewrite((inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))))), rewrite((~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))), ((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))))),
% 0.63/0.85 inference(bind,[status(th)],[])).
% 0.63/0.85 tff(210,plain,
% 0.63/0.85 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.63/0.85 inference(quant_intro,[status(thm)],[209])).
% 0.63/0.85 tff(211,plain,
% 0.63/0.85 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(212,axiom,(![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','inner_point_defn')).
% 0.63/0.85 tff(213,plain,
% 0.63/0.85 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.63/0.85 tff(214,plain,(
% 0.63/0.85 ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.63/0.85 inference(skolemize,[status(sab)],[213])).
% 0.63/0.85 tff(215,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[214, 210])).
% 0.63/0.85 tff(216,plain,
% 0.63/0.85 (![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.63/0.85 tff(217,plain,
% 0.63/0.85 ((~![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))) | (~(((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) <=> inner_point(P!11, Cpp!13)))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(218,plain,
% 0.63/0.85 (~(((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) <=> inner_point(P!11, Cpp!13))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.63/0.85 tff(219,plain,
% 0.63/0.85 ((((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) <=> inner_point(P!11, Cpp!13)) | (~((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13))) | (~inner_point(P!11, Cpp!13))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(220,plain,
% 0.63/0.85 ((((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) <=> inner_point(P!11, Cpp!13)) | (~((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[219, 10])).
% 0.63/0.85 tff(221,plain,
% 0.63/0.85 (~((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[220, 218])).
% 0.63/0.85 tff(222,plain,
% 0.63/0.85 (((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) | (~end_point(P!11, Cpp!13))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(223,plain,
% 0.63/0.85 (~end_point(P!11, Cpp!13)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.63/0.85 tff(224,plain,
% 0.63/0.85 (~end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[223, 206])).
% 0.63/0.85 tff(225,plain,
% 0.63/0.85 ((~((~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))))) | (~incident_c(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | end_point(P!11, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(226,plain,
% 0.63/0.85 (~((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[225, 224, 203, 115])).
% 0.63/0.85 tff(227,plain,
% 0.63/0.85 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(228,plain,
% 0.63/0.85 (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.63/0.85 tff(229,plain,
% 0.63/0.85 ((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(230,plain,
% 0.63/0.85 ((~((~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.63/0.85 tff(231,plain,
% 0.63/0.85 (![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[230, 84])).
% 0.63/0.85 tff(232,plain,
% 0.63/0.85 (((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(rewrite,[status(thm)],[])).
% 0.63/0.85 tff(233,plain,
% 0.63/0.85 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.63/0.85 inference(quant_inst,[status(thm)],[])).
% 0.63/0.85 tff(234,plain,
% 0.63/0.85 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.63/0.85 tff(235,plain,
% 0.63/0.85 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[234, 231, 80])).
% 0.63/0.85 tff(236,plain,
% 0.63/0.85 ($false),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[235, 78])).
% 0.63/0.85 tff(237,plain,((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)), inference(lemma,lemma(discharge,[]))).
% 0.63/0.85 tff(238,plain,
% 0.63/0.85 ((~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))),
% 0.63/0.85 inference(tautology,[status(thm)],[])).
% 0.63/0.85 tff(239,plain,
% 0.63/0.85 ((~(part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.63/0.85 tff(240,plain,
% 0.63/0.85 (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)),
% 0.63/0.85 inference(unit_resolution,[status(thm)],[239, 59])).
% 0.63/0.85 tff(241,plain,
% 0.63/0.85 (((~![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(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(242,plain,
% 0.63/0.86 ((~((~(end_point(P!11, C!12) | (~incident_c(P!11, C!12)) | (~(part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)))))))))) <=> (~((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))))))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(243,plain,
% 0.63/0.86 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!12) | (~incident_c(P!11, C!12)) | (~(part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))))))),
% 0.63/0.86 inference(monotonicity,[status(thm)],[242])).
% 0.63/0.86 tff(244,plain,
% 0.63/0.86 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!12) | (~incident_c(P!11, C!12)) | (~(part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))))))),
% 0.63/0.86 inference(transitivity,[status(thm)],[243, 241])).
% 0.63/0.86 tff(245,plain,
% 0.63/0.86 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!11, C!12) | (~incident_c(P!11, C!12)) | (~(part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2))))))))))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(246,plain,
% 0.63/0.86 ((~![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(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))))))),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.63/0.86 tff(247,plain,
% 0.63/0.86 (~((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[246, 106])).
% 0.63/0.86 tff(248,plain,
% 0.63/0.86 (((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12) | (~((~incident_c(P!11, tptp_fun_C2_2(C!12, P!11))) | (~incident_c(P!11, tptp_fun_C1_3(C!12, P!11))) | (~part_of(tptp_fun_C2_2(C!12, P!11), C!12)) | (~part_of(tptp_fun_C1_3(C!12, P!11), C!12)) | part_of(tptp_fun_C1_3(C!12, P!11), tptp_fun_C2_2(C!12, P!11)) | part_of(tptp_fun_C2_2(C!12, P!11), tptp_fun_C1_3(C!12, P!11)))))) | (~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))))) | ((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(249,plain,
% 0.63/0.86 ((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.63/0.86 tff(250,plain,
% 0.63/0.86 ((~![P: $i, C: $i] : (~(((~incident_c(P, C)) | end_point(P, C)) <=> inner_point(P, C)))) | (~(((~incident_c(P!11, C!12)) | end_point(P!11, C!12)) <=> inner_point(P!11, C!12)))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(251,plain,
% 0.63/0.86 (~(((~incident_c(P!11, C!12)) | end_point(P!11, C!12)) <=> inner_point(P!11, C!12))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[250, 216])).
% 0.63/0.86 tff(252,plain,
% 0.63/0.86 (~inner_point(P!11, C!12)),
% 0.63/0.86 inference(and_elim,[status(thm)],[9])).
% 0.63/0.86 tff(253,plain,
% 0.63/0.86 ((((~incident_c(P!11, C!12)) | end_point(P!11, C!12)) <=> inner_point(P!11, C!12)) | ((~incident_c(P!11, C!12)) | end_point(P!11, C!12)) | inner_point(P!11, C!12)),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(254,plain,
% 0.63/0.86 ((((~incident_c(P!11, C!12)) | end_point(P!11, C!12)) <=> inner_point(P!11, C!12)) | ((~incident_c(P!11, C!12)) | end_point(P!11, C!12))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[253, 252])).
% 0.63/0.86 tff(255,plain,
% 0.63/0.86 ((~incident_c(P!11, C!12)) | end_point(P!11, C!12)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[254, 251])).
% 0.63/0.86 tff(256,plain,
% 0.63/0.86 (((~incident_c(P!11, Cpp!13)) | end_point(P!11, Cpp!13)) | incident_c(P!11, Cpp!13)),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(257,plain,
% 0.63/0.86 (incident_c(P!11, Cpp!13)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[256, 221])).
% 0.63/0.86 tff(258,plain,
% 0.63/0.86 (((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(P!11, Cpp!13)) | incident_c(P!11, C!12))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(P!11, Cpp!13)) | incident_c(P!11, C!12))),
% 0.63/0.86 inference(rewrite,[status(thm)],[])).
% 0.63/0.86 tff(259,plain,
% 0.63/0.86 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(P!11, Cpp!13)) | incident_c(P!11, C!12))),
% 0.63/0.86 inference(quant_inst,[status(thm)],[])).
% 0.63/0.86 tff(260,plain,
% 0.63/0.86 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(P!11, Cpp!13)) | incident_c(P!11, C!12)),
% 0.63/0.86 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.63/0.86 tff(261,plain,
% 0.63/0.86 (incident_c(P!11, C!12)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[260, 73, 257])).
% 0.63/0.86 tff(262,plain,
% 0.63/0.86 ((~((~incident_c(P!11, C!12)) | end_point(P!11, C!12))) | (~incident_c(P!11, C!12)) | end_point(P!11, C!12)),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(263,plain,
% 0.63/0.86 (end_point(P!11, C!12)),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[262, 261, 255])).
% 0.63/0.86 tff(264,plain,
% 0.63/0.86 ((~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))) | (~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(265,plain,
% 0.63/0.86 ((~((~end_point(P!11, C!12)) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))))) | (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.63/0.86 tff(266,plain,
% 0.63/0.86 (~((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[265, 249])).
% 0.63/0.86 tff(267,plain,
% 0.63/0.86 (((~incident_c(P!11, C!12)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12))))) | ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.63/0.86 tff(268,plain,
% 0.63/0.86 (![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))),
% 0.63/0.86 inference(unit_resolution,[status(thm)],[267, 266])).
% 0.63/0.86 tff(269,plain,
% 0.63/0.86 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))),
% 0.63/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(270,plain,
% 0.71/0.86 (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[269, 226])).
% 0.71/0.86 tff(271,plain,
% 0.71/0.86 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(272,plain,
% 0.71/0.86 (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[271, 226])).
% 0.71/0.86 tff(273,plain,
% 0.71/0.86 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(274,plain,
% 0.71/0.86 (incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[273, 226])).
% 0.71/0.86 tff(275,plain,
% 0.71/0.86 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(276,plain,
% 0.71/0.86 (incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[275, 226])).
% 0.71/0.86 tff(277,plain,
% 0.71/0.86 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | ((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(278,plain,
% 0.71/0.86 ((part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12))) <=> ((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(279,plain,
% 0.71/0.86 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | ((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[278])).
% 0.71/0.86 tff(280,plain,
% 0.71/0.86 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[279, 277])).
% 0.71/0.86 tff(281,plain,
% 0.71/0.86 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(282,plain,
% 0.71/0.87 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!11, C1)) | (~incident_c(P!11, C2)) | (~part_of(C1, C!12)) | (~part_of(C2, C!12)))) | (~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.71/0.87 tff(283,plain,
% 0.71/0.87 ((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[282, 276, 274, 272, 270, 268])).
% 0.71/0.87 tff(284,plain,
% 0.71/0.87 (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[283, 240])).
% 0.71/0.87 tff(285,plain,
% 0.71/0.87 ((~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(286,plain,
% 0.71/0.87 ((~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[285, 284])).
% 0.71/0.87 tff(287,plain,
% 0.71/0.87 (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[286, 53])).
% 0.71/0.87 tff(288,plain,
% 0.71/0.87 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(289,plain,
% 0.71/0.87 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.71/0.87 tff(290,plain,
% 0.71/0.87 (((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(291,plain,
% 0.71/0.87 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(292,plain,
% 0.71/0.87 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!12))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.71/0.87 tff(293,plain,
% 0.71/0.87 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), Cpp!13)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[292, 73, 289])).
% 0.71/0.87 tff(294,plain,
% 0.71/0.87 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[293, 33])).
% 0.71/0.87 tff(295,plain,
% 0.71/0.87 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), C!12)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(296,plain,
% 0.71/0.87 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[295, 287])).
% 0.71/0.87 tff(297,plain,
% 0.71/0.87 ((~![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(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(298,plain,
% 0.71/0.87 (~((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[297, 49])).
% 0.71/0.87 tff(299,plain,
% 0.71/0.87 (((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~(part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))))) | ((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(300,plain,
% 0.71/0.87 ((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.71/0.87 tff(301,plain,
% 0.71/0.87 (((~incident_c(P!11, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~incident_c(P!11, tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | (~part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | part_of(tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11)) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), tptp_fun_C1_3(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.72/0.87 inference(tautology,[status(thm)],[])).
% 0.72/0.87 tff(302,plain,
% 0.72/0.87 (part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[301, 226])).
% 0.72/0.87 tff(303,plain,
% 0.72/0.87 ((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | (~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.72/0.87 inference(tautology,[status(thm)],[])).
% 0.72/0.87 tff(304,plain,
% 0.72/0.87 ((~((~part_of(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.72/0.87 tff(305,plain,
% 0.72/0.87 (![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[304, 300])).
% 0.72/0.87 tff(306,plain,
% 0.72/0.87 (((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.72/0.87 inference(rewrite,[status(thm)],[])).
% 0.72/0.87 tff(307,plain,
% 0.72/0.87 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))),
% 0.72/0.87 inference(quant_inst,[status(thm)],[])).
% 0.72/0.87 tff(308,plain,
% 0.72/0.87 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(P, sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13))))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.72/0.87 inference(modus_ponens,[status(thm)],[307, 306])).
% 0.72/0.87 tff(309,plain,
% 0.72/0.87 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)), P!11), C!12), sum(tptp_fun_C1_8(P!11, Cpp!13), tptp_fun_C2_7(P!11, Cpp!13)))),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[308, 305, 296])).
% 0.72/0.87 tff(310,plain,
% 0.72/0.87 ($false),
% 0.72/0.87 inference(unit_resolution,[status(thm)],[309, 294])).
% 0.72/0.87 % SZS output end Proof
% 0.72/0.87 % E exiting
%------------------------------------------------------------------------------