TSTP Solution File: GEO090+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO090+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:48 EDT 2022
% Result : Theorem 1.61s 1.25s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO090+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n015.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Aug 31 05:34:51 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.34 Usage: tptp [options] [-file:]file
% 0.11/0.34 -h, -? prints this message.
% 0.11/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.34 -m, -model generate model.
% 0.11/0.34 -p, -proof generate proof.
% 0.11/0.34 -c, -core generate unsat core of named formulas.
% 0.11/0.34 -st, -statistics display statistics.
% 0.11/0.34 -t:timeout set timeout (in second).
% 0.11/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.34 -<param>:<value> configuration parameter and value.
% 0.11/0.34 -o:<output-file> file to place output in.
% 1.61/1.25 % SZS status Theorem
% 1.61/1.25 % SZS output start Proof
% 1.61/1.25 tff(incident_c_type, type, (
% 1.61/1.25 incident_c: ( $i * $i ) > $o)).
% 1.61/1.25 tff(tptp_fun_C2_14_type, type, (
% 1.61/1.25 tptp_fun_C2_14: $i)).
% 1.61/1.25 tff(tptp_fun_P_0_type, type, (
% 1.61/1.25 tptp_fun_P_0: ( $i * $i ) > $i)).
% 1.61/1.25 tff(tptp_fun_C1_15_type, type, (
% 1.61/1.25 tptp_fun_C1_15: $i)).
% 1.61/1.25 tff(tptp_fun_C1_3_type, type, (
% 1.61/1.25 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 1.61/1.25 tff(tptp_fun_Q_4_type, type, (
% 1.61/1.25 tptp_fun_Q_4: ( $i * $i ) > $i)).
% 1.61/1.25 tff(tptp_fun_Cpp_13_type, type, (
% 1.61/1.25 tptp_fun_Cpp_13: $i)).
% 1.61/1.25 tff(part_of_type, type, (
% 1.61/1.25 part_of: ( $i * $i ) > $o)).
% 1.61/1.25 tff(tptp_fun_C2_2_type, type, (
% 1.61/1.25 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 1.61/1.25 tff(meet_type, type, (
% 1.61/1.25 meet: ( $i * $i * $i ) > $o)).
% 1.61/1.25 tff(tptp_fun_P_12_type, type, (
% 1.61/1.25 tptp_fun_P_12: $i)).
% 1.61/1.25 tff(end_point_type, type, (
% 1.61/1.25 end_point: ( $i * $i ) > $o)).
% 1.61/1.25 tff(1,plain,
% 1.61/1.25 (^[C: $i, C1: $i] : refl((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(2,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[1])).
% 1.61/1.25 tff(3,plain,
% 1.61/1.25 (^[C: $i, C1: $i] : rewrite((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(4,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[3])).
% 1.61/1.25 tff(5,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(transitivity,[status(thm)],[4, 2])).
% 1.61/1.25 tff(6,plain,
% 1.61/1.25 (^[C: $i, C1: $i] : trans(monotonicity(rewrite(((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))), rewrite((part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))) <=> (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))), rewrite((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(7,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[6])).
% 1.61/1.25 tff(8,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.61/1.25 inference(rewrite,[status(thm)],[])).
% 1.61/1.25 tff(9,plain,
% 1.61/1.25 (^[C: $i, C1: $i] : rewrite((part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))))),
% 1.61/1.25 inference(bind,[status(th)],[])).
% 1.61/1.25 tff(10,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.61/1.25 inference(quant_intro,[status(thm)],[9])).
% 1.61/1.25 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 1.61/1.25 tff(12,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[11, 10])).
% 1.61/1.25 tff(13,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[12, 8])).
% 1.61/1.25 tff(14,plain,(
% 1.61/1.25 ![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))),
% 1.61/1.25 inference(skolemize,[status(sab)],[13])).
% 1.61/1.25 tff(15,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[14, 7])).
% 1.61/1.25 tff(16,plain,
% 1.61/1.25 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 1.61/1.25 inference(modus_ponens,[status(thm)],[15, 5])).
% 1.61/1.25 tff(17,plain,
% 1.61/1.25 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))))))),
% 1.61/1.25 inference(quant_inst,[status(thm)],[])).
% 1.61/1.25 tff(18,plain,
% 1.61/1.25 (~((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[17, 16])).
% 1.61/1.26 tff(19,plain,
% 1.61/1.26 (((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))))) | (part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(20,plain,
% 1.61/1.26 (part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[19, 18])).
% 1.61/1.26 tff(21,assumption,((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))))), introduced(assumption)).
% 1.61/1.26 tff(22,plain,
% 1.61/1.26 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))))))),
% 1.61/1.26 inference(quant_inst,[status(thm)],[])).
% 1.61/1.26 tff(23,plain,
% 1.61/1.26 ($false),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 1.61/1.26 tff(24,plain,(~((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))))), inference(lemma,lemma(discharge,[]))).
% 1.61/1.26 tff(25,plain,
% 1.61/1.26 (((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C1!15)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(26,plain,
% 1.61/1.26 (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[25, 24])).
% 1.61/1.26 tff(27,assumption,(~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))), introduced(assumption)).
% 1.61/1.26 tff(28,plain,
% 1.61/1.26 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(29,plain,
% 1.61/1.26 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.61/1.26 tff(30,plain,
% 1.61/1.26 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))) | (~(part_of(C2!14, C1!15) | (~((~incident_c(tptp_fun_P_0(C2!14, C1!15), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C1!15), C1!15)))))))),
% 1.61/1.26 inference(quant_inst,[status(thm)],[])).
% 1.61/1.26 tff(31,plain,
% 1.61/1.26 (~((~((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))) | (~(part_of(C2!14, C1!15) | (~((~incident_c(tptp_fun_P_0(C2!14, C1!15), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C1!15), C1!15))))))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[30, 16])).
% 1.61/1.26 tff(32,plain,
% 1.61/1.26 (((~((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))) | (~(part_of(C2!14, C1!15) | (~((~incident_c(tptp_fun_P_0(C2!14, C1!15), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C1!15), C1!15)))))) | ((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(33,plain,
% 1.61/1.26 ((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.61/1.26 tff(34,plain,
% 1.61/1.26 ((~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))) <=> (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp)))),
% 1.61/1.26 inference(rewrite,[status(thm)],[])).
% 1.61/1.26 tff(35,plain,
% 1.61/1.26 ((~![C1: $i, C2: $i, Cpp: $i, P: $i] : (((part_of(C2, C1) & incident_c(P, C2)) & meet(P, C1, Cpp)) => meet(P, C2, Cpp))) <=> (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp)))),
% 1.61/1.26 inference(rewrite,[status(thm)],[])).
% 1.61/1.26 tff(36,axiom,(~![C1: $i, C2: $i, Cpp: $i, P: $i] : (((part_of(C2, C1) & incident_c(P, C2)) & meet(P, C1, Cpp)) => meet(P, C2, Cpp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_12')).
% 1.61/1.26 tff(37,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.61/1.26 tff(38,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[37, 34])).
% 1.61/1.26 tff(39,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[38, 34])).
% 1.61/1.26 tff(40,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[39, 34])).
% 1.61/1.26 tff(41,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[40, 34])).
% 1.61/1.26 tff(42,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.61/1.26 tff(43,plain,
% 1.61/1.26 (~![C1: $i, C2: $i, Cpp: $i, P: $i] : ((~(part_of(C2, C1) & incident_c(P, C2) & meet(P, C1, Cpp))) | meet(P, C2, Cpp))),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[42, 34])).
% 1.61/1.26 tff(44,plain,(
% 1.61/1.26 ~((~(part_of(C2!14, C1!15) & incident_c(P!12, C2!14) & meet(P!12, C1!15, Cpp!13))) | meet(P!12, C2!14, Cpp!13))),
% 1.61/1.26 inference(skolemize,[status(sab)],[43])).
% 1.61/1.26 tff(45,plain,
% 1.61/1.26 (part_of(C2!14, C1!15) & incident_c(P!12, C2!14) & meet(P!12, C1!15, Cpp!13)),
% 1.61/1.26 inference(or_elim,[status(thm)],[44])).
% 1.61/1.26 tff(46,plain,
% 1.61/1.26 (part_of(C2!14, C1!15)),
% 1.61/1.26 inference(and_elim,[status(thm)],[45])).
% 1.61/1.26 tff(47,plain,
% 1.61/1.26 ((~((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))) | (~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(48,plain,
% 1.61/1.26 ((~((~part_of(C2!14, C1!15)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15)))) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[47, 46])).
% 1.61/1.26 tff(49,plain,
% 1.61/1.26 (![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[48, 33])).
% 1.61/1.26 tff(50,plain,
% 1.61/1.26 (((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))) <=> ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.61/1.26 inference(rewrite,[status(thm)],[])).
% 1.61/1.26 tff(51,plain,
% 1.61/1.26 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.61/1.26 inference(quant_inst,[status(thm)],[])).
% 1.61/1.26 tff(52,plain,
% 1.61/1.26 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)),
% 1.61/1.26 inference(modus_ponens,[status(thm)],[51, 50])).
% 1.61/1.26 tff(53,plain,
% 1.61/1.26 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[52, 49, 29])).
% 1.61/1.26 tff(54,plain,
% 1.61/1.26 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.61/1.26 inference(tautology,[status(thm)],[])).
% 1.61/1.26 tff(55,plain,
% 1.61/1.26 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.61/1.26 inference(unit_resolution,[status(thm)],[54, 27])).
% 1.61/1.27 tff(56,plain,
% 1.61/1.27 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14)))))))),
% 1.61/1.27 inference(quant_inst,[status(thm)],[])).
% 1.61/1.27 tff(57,plain,
% 1.61/1.27 (~((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14))))))),
% 1.61/1.27 inference(unit_resolution,[status(thm)],[56, 16])).
% 1.61/1.27 tff(58,plain,
% 1.61/1.27 (((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14)))))) | ((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))),
% 1.61/1.27 inference(tautology,[status(thm)],[])).
% 1.61/1.27 tff(59,plain,
% 1.61/1.27 ((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.61/1.27 inference(unit_resolution,[status(thm)],[58, 57])).
% 1.61/1.27 tff(60,plain,
% 1.61/1.27 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(61,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[60])).
% 1.61/1.27 tff(62,plain,
% 1.61/1.27 (^[P: $i, C: $i] : refl((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(63,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[62])).
% 1.61/1.27 tff(64,plain,
% 1.61/1.27 (^[P: $i, C: $i] : rewrite((~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(65,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[64])).
% 1.61/1.27 tff(66,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(transitivity,[status(thm)],[65, 63])).
% 1.61/1.27 tff(67,plain,
% 1.61/1.27 (^[P: $i, C: $i] : trans(monotonicity(rewrite(((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))), trans(monotonicity(rewrite((~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), rewrite((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))), ((end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))))), rewrite((((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))), ((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(68,plain,
% 1.61/1.27 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))) <=> ![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[67])).
% 1.61/1.27 tff(69,plain,
% 1.61/1.27 (^[P: $i, C: $i] : rewrite((((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(70,plain,
% 1.61/1.27 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))) <=> ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[69])).
% 1.61/1.27 tff(71,plain,
% 1.61/1.27 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.61/1.27 inference(rewrite,[status(thm)],[])).
% 1.61/1.27 tff(72,plain,
% 1.61/1.27 (^[P: $i, C: $i] : rewrite((end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))))),
% 1.61/1.27 inference(bind,[status(th)],[])).
% 1.61/1.27 tff(73,plain,
% 1.61/1.27 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1))))) <=> ![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.61/1.27 inference(quant_intro,[status(thm)],[72])).
% 1.61/1.27 tff(74,axiom,(![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : ((((part_of(C1, C) & part_of(C2, C)) & incident_c(P, C1)) & incident_c(P, C2)) => (part_of(C1, C2) | part_of(C2, C1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 1.61/1.27 tff(75,plain,
% 1.61/1.27 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[74, 73])).
% 1.61/1.27 tff(76,plain,
% 1.61/1.27 (![P: $i, C: $i] : (end_point(P, C) <=> (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[75, 71])).
% 1.61/1.27 tff(77,plain,(
% 1.61/1.27 ![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | ((~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(skolemize,[status(sab)],[76])).
% 1.61/1.27 tff(78,plain,
% 1.61/1.27 (![P: $i, C: $i] : (((~end_point(P, C)) | (incident_c(P, C) & ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~(part_of(C1, C) & part_of(C2, C) & incident_c(P, C1) & incident_c(P, C2)))))) & (end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~(part_of(tptp_fun_C1_3(C, P), C) & part_of(tptp_fun_C2_2(C, P), C) & incident_c(P, tptp_fun_C1_3(C, P)) & incident_c(P, tptp_fun_C2_2(C, P))))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[77, 70])).
% 1.61/1.27 tff(79,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[78, 68])).
% 1.61/1.27 tff(80,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2)))))))) | (~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P)))))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[79, 66])).
% 1.61/1.27 tff(81,plain,
% 1.61/1.27 (![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))),
% 1.61/1.27 inference(modus_ponens,[status(thm)],[80, 61])).
% 1.61/1.27 tff(82,plain,
% 1.61/1.27 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.61/1.27 inference(rewrite,[status(thm)],[])).
% 1.61/1.27 tff(83,plain,
% 1.61/1.27 ((~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))) <=> (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.61/1.28 inference(rewrite,[status(thm)],[])).
% 1.61/1.28 tff(84,plain,
% 1.61/1.28 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.61/1.28 inference(monotonicity,[status(thm)],[83])).
% 1.61/1.28 tff(85,plain,
% 1.61/1.28 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.61/1.28 inference(transitivity,[status(thm)],[84, 82])).
% 1.61/1.28 tff(86,plain,
% 1.61/1.28 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.61/1.28 inference(quant_inst,[status(thm)],[])).
% 1.61/1.28 tff(87,plain,
% 1.61/1.28 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.61/1.28 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.61/1.28 tff(88,plain,
% 1.61/1.28 (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))),
% 1.61/1.28 inference(unit_resolution,[status(thm)],[87, 81])).
% 1.61/1.28 tff(89,plain,
% 1.61/1.28 (((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C2!14)) | (~part_of(C2, C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))) | ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))),
% 1.61/1.29 inference(tautology,[status(thm)],[])).
% 1.61/1.29 tff(90,plain,
% 1.61/1.29 ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))))),
% 1.61/1.29 inference(unit_resolution,[status(thm)],[89, 88])).
% 1.61/1.29 tff(91,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(92,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[91])).
% 1.61/1.29 tff(93,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : refl((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(94,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[93])).
% 1.61/1.29 tff(95,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(96,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[95])).
% 1.61/1.29 tff(97,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(transitivity,[status(thm)],[96, 94])).
% 1.61/1.29 tff(98,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : trans(monotonicity(rewrite(((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))), trans(monotonicity(rewrite((~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))) <=> (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), rewrite((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))), rewrite((((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(99,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[98])).
% 1.61/1.29 tff(100,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : rewrite((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(101,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[100])).
% 1.61/1.29 tff(102,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.61/1.29 inference(rewrite,[status(thm)],[])).
% 1.61/1.29 tff(103,plain,
% 1.61/1.29 (^[P: $i, C: $i, C1: $i] : rewrite((meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))))),
% 1.61/1.29 inference(bind,[status(th)],[])).
% 1.61/1.29 tff(104,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.61/1.29 inference(quant_intro,[status(thm)],[103])).
% 1.61/1.29 tff(105,axiom,(![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','meet_defn')).
% 1.61/1.29 tff(106,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.61/1.29 tff(107,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.61/1.29 tff(108,plain,(
% 1.61/1.29 ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 1.61/1.29 inference(skolemize,[status(sab)],[107])).
% 1.61/1.29 tff(109,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.61/1.29 tff(110,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[109, 99])).
% 1.61/1.29 tff(111,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[110, 97])).
% 1.61/1.29 tff(112,plain,
% 1.61/1.29 (![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 1.61/1.29 inference(modus_ponens,[status(thm)],[111, 92])).
% 1.61/1.29 tff(113,plain,
% 1.61/1.29 (((~![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!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14)))))))))))))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(114,plain,
% 1.61/1.30 ((~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C2!14)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14)))))))))))) <=> (~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))),
% 1.61/1.30 inference(rewrite,[status(thm)],[])).
% 1.61/1.30 tff(115,plain,
% 1.61/1.30 (((~![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!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C2!14)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14)))))))))))))),
% 1.61/1.30 inference(monotonicity,[status(thm)],[114])).
% 1.61/1.30 tff(116,plain,
% 1.61/1.30 (((~![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!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C2!14)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14)))))))))))))),
% 1.61/1.30 inference(transitivity,[status(thm)],[115, 113])).
% 1.61/1.30 tff(117,plain,
% 1.61/1.30 ((~![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!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C2!14)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))),
% 1.61/1.30 inference(quant_inst,[status(thm)],[])).
% 1.61/1.30 tff(118,plain,
% 1.61/1.30 ((~![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!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))))),
% 1.61/1.30 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.61/1.30 tff(119,plain,
% 1.61/1.30 (~((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14)))))))))))),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[118, 112])).
% 1.61/1.30 tff(120,plain,
% 1.61/1.30 (((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~((~meet(P!12, C2!14, Cpp!13)) | (~((~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, C2!14)) | (~incident_c(Q, Cpp!13)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C2!14))))))))))) | (meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))),
% 1.61/1.30 inference(tautology,[status(thm)],[])).
% 1.61/1.30 tff(121,plain,
% 1.61/1.30 (meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))))),
% 1.61/1.30 inference(unit_resolution,[status(thm)],[120, 119])).
% 1.61/1.30 tff(122,plain,
% 1.61/1.30 ((~![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!12, C1!15, Cpp!13) | (~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~end_point(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)))))))) | (~((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))))))))),
% 1.69/1.31 inference(quant_inst,[status(thm)],[])).
% 1.69/1.31 tff(123,plain,
% 1.69/1.31 (~((~(meet(P!12, C1!15, Cpp!13) | (~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~end_point(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)))))))) | (~((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))))))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[122, 112])).
% 1.69/1.31 tff(124,plain,
% 1.69/1.31 (((~(meet(P!12, C1!15, Cpp!13) | (~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C1!15), C1!15)) | (~end_point(tptp_fun_Q_4(Cpp!13, C1!15), Cpp!13)))))))) | (~((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))))))) | ((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))))))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(125,plain,
% 1.69/1.31 ((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[124, 123])).
% 1.69/1.31 tff(126,plain,
% 1.69/1.31 (meet(P!12, C1!15, Cpp!13)),
% 1.69/1.31 inference(and_elim,[status(thm)],[45])).
% 1.69/1.31 tff(127,plain,
% 1.69/1.31 ((~((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))))))) | (~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(128,plain,
% 1.69/1.31 ((~((~meet(P!12, C1!15, Cpp!13)) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))))))) | (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[127, 126])).
% 1.69/1.31 tff(129,plain,
% 1.69/1.31 (~((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[128, 125])).
% 1.69/1.31 tff(130,plain,
% 1.69/1.31 (((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))) | incident_c(P!12, Cpp!13)),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(131,plain,
% 1.69/1.31 (incident_c(P!12, Cpp!13)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[130, 129])).
% 1.69/1.31 tff(132,plain,
% 1.69/1.31 (~meet(P!12, C2!14, Cpp!13)),
% 1.69/1.31 inference(or_elim,[status(thm)],[44])).
% 1.69/1.31 tff(133,plain,
% 1.69/1.31 (incident_c(P!12, C2!14)),
% 1.69/1.31 inference(and_elim,[status(thm)],[45])).
% 1.69/1.31 tff(134,plain,
% 1.69/1.31 ((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(135,plain,
% 1.69/1.31 ((~(meet(P!12, C2!14, Cpp!13) | (~incident_c(P!12, C2!14)) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))))) | (~incident_c(P!12, Cpp!13)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[134, 133, 132])).
% 1.69/1.31 tff(136,plain,
% 1.69/1.31 (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[135, 131, 121])).
% 1.69/1.31 tff(137,plain,
% 1.69/1.31 (((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))) | ((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(138,plain,
% 1.69/1.31 ((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[137, 136])).
% 1.69/1.31 tff(139,plain,
% 1.69/1.31 (((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(140,plain,
% 1.69/1.31 (incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[139, 136])).
% 1.69/1.31 tff(141,plain,
% 1.69/1.31 (((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))) <=> ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))),
% 1.69/1.31 inference(rewrite,[status(thm)],[])).
% 1.69/1.31 tff(142,plain,
% 1.69/1.31 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))),
% 1.69/1.31 inference(quant_inst,[status(thm)],[])).
% 1.69/1.31 tff(143,plain,
% 1.69/1.31 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)),
% 1.69/1.31 inference(modus_ponens,[status(thm)],[142, 141])).
% 1.69/1.31 tff(144,plain,
% 1.69/1.31 (incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[143, 49, 140])).
% 1.69/1.31 tff(145,plain,
% 1.69/1.31 (((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))))) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(146,plain,
% 1.69/1.31 (incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[145, 136])).
% 1.69/1.31 tff(147,plain,
% 1.69/1.31 (((~incident_c(P!12, C1!15)) | (~incident_c(P!12, Cpp!13)) | (~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15))))))) | ![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(148,plain,
% 1.69/1.31 (![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[147, 129])).
% 1.69/1.31 tff(149,plain,
% 1.69/1.31 (((~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))) | ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)))))) <=> ((~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)))))),
% 1.69/1.31 inference(rewrite,[status(thm)],[])).
% 1.69/1.31 tff(150,plain,
% 1.69/1.31 ((~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))) | ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)))))),
% 1.69/1.31 inference(quant_inst,[status(thm)],[])).
% 1.69/1.31 tff(151,plain,
% 1.69/1.31 ((~![Q: $i] : ((~incident_c(Q, Cpp!13)) | (~incident_c(Q, C1!15)) | (~((~end_point(Q, Cpp!13)) | (~end_point(Q, C1!15)))))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))))),
% 1.69/1.31 inference(modus_ponens,[status(thm)],[150, 149])).
% 1.69/1.31 tff(152,plain,
% 1.69/1.31 ((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[151, 148, 146])).
% 1.69/1.31 tff(153,plain,
% 1.69/1.31 (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)))),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[152, 144])).
% 1.69/1.31 tff(154,plain,
% 1.69/1.31 (((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(155,plain,
% 1.69/1.31 (end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[154, 153])).
% 1.69/1.31 tff(156,plain,
% 1.69/1.31 ((~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)))) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13))),
% 1.69/1.31 inference(tautology,[status(thm)],[])).
% 1.69/1.31 tff(157,plain,
% 1.69/1.31 (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)),
% 1.69/1.31 inference(unit_resolution,[status(thm)],[156, 155, 138])).
% 1.69/1.31 tff(158,plain,
% 1.69/1.31 ((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))))),
% 1.69/1.32 inference(tautology,[status(thm)],[])).
% 1.69/1.32 tff(159,plain,
% 1.69/1.32 ((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2!14)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C2!14) | (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))))),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[158, 140])).
% 1.69/1.32 tff(160,plain,
% 1.69/1.32 (~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[159, 157, 90])).
% 1.69/1.32 tff(161,plain,
% 1.69/1.32 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)),
% 1.69/1.32 inference(tautology,[status(thm)],[])).
% 1.69/1.32 tff(162,plain,
% 1.69/1.32 (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[161, 160])).
% 1.69/1.32 tff(163,plain,
% 1.69/1.32 ((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.32 inference(tautology,[status(thm)],[])).
% 1.69/1.32 tff(164,plain,
% 1.69/1.32 ((~((~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[163, 162])).
% 1.69/1.32 tff(165,plain,
% 1.69/1.32 (![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[164, 59])).
% 1.69/1.32 tff(166,plain,
% 1.69/1.32 (((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))),
% 1.69/1.32 inference(rewrite,[status(thm)],[])).
% 1.69/1.32 tff(167,plain,
% 1.69/1.32 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))),
% 1.69/1.32 inference(quant_inst,[status(thm)],[])).
% 1.69/1.32 tff(168,plain,
% 1.69/1.32 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)),
% 1.69/1.32 inference(modus_ponens,[status(thm)],[167, 166])).
% 1.69/1.32 tff(169,plain,
% 1.69/1.32 ($false),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[168, 165, 55, 53])).
% 1.69/1.32 tff(170,plain,((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)), inference(lemma,lemma(discharge,[]))).
% 1.69/1.32 tff(171,plain,
% 1.69/1.32 ((~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))),
% 1.69/1.32 inference(tautology,[status(thm)],[])).
% 1.69/1.32 tff(172,plain,
% 1.69/1.32 ((~(part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[171, 170])).
% 1.69/1.32 tff(173,plain,
% 1.69/1.32 (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)),
% 1.69/1.32 inference(unit_resolution,[status(thm)],[172, 26])).
% 1.69/1.32 tff(174,plain,
% 1.69/1.32 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.69/1.32 inference(rewrite,[status(thm)],[])).
% 1.69/1.32 tff(175,plain,
% 1.69/1.32 ((~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))) <=> (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.69/1.33 inference(rewrite,[status(thm)],[])).
% 1.69/1.33 tff(176,plain,
% 1.69/1.33 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.69/1.33 inference(monotonicity,[status(thm)],[175])).
% 1.69/1.33 tff(177,plain,
% 1.69/1.33 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))))),
% 1.69/1.33 inference(transitivity,[status(thm)],[176, 174])).
% 1.69/1.33 tff(178,plain,
% 1.69/1.33 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.69/1.33 inference(quant_inst,[status(thm)],[])).
% 1.69/1.33 tff(179,plain,
% 1.69/1.33 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))))),
% 1.69/1.33 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.69/1.33 tff(180,plain,
% 1.69/1.33 (~((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))))),
% 1.69/1.33 inference(unit_resolution,[status(thm)],[179, 81])).
% 1.69/1.33 tff(181,plain,
% 1.69/1.33 (((~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15) | (~(part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C1!15, tptp_fun_Q_4(Cpp!13, C2!14)))))))) | (~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))))) | ((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))),
% 1.69/1.33 inference(tautology,[status(thm)],[])).
% 1.69/1.33 tff(182,plain,
% 1.69/1.33 ((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))),
% 1.69/1.33 inference(unit_resolution,[status(thm)],[181, 180])).
% 1.69/1.33 tff(183,plain,
% 1.69/1.33 (((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), Cpp!13)) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15))) | end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)),
% 1.69/1.33 inference(tautology,[status(thm)],[])).
% 1.69/1.33 tff(184,plain,
% 1.69/1.33 (end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)),
% 1.69/1.33 inference(unit_resolution,[status(thm)],[183, 153])).
% 1.69/1.33 tff(185,plain,
% 1.69/1.33 ((~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))) | (~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(186,plain,
% 1.69/1.34 ((~((~end_point(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))))) | (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[185, 184])).
% 1.69/1.34 tff(187,plain,
% 1.69/1.34 (~((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[186, 182])).
% 1.69/1.34 tff(188,plain,
% 1.69/1.34 (((~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1!15)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2))))) | ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(189,plain,
% 1.69/1.34 (![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[188, 187])).
% 1.69/1.34 tff(190,plain,
% 1.69/1.34 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(191,plain,
% 1.69/1.34 (incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[190, 160])).
% 1.69/1.34 tff(192,plain,
% 1.69/1.34 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(193,plain,
% 1.69/1.34 (incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[192, 160])).
% 1.69/1.34 tff(194,plain,
% 1.69/1.34 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(195,plain,
% 1.69/1.34 (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[194, 160])).
% 1.69/1.34 tff(196,plain,
% 1.69/1.34 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))),
% 1.69/1.34 inference(tautology,[status(thm)],[])).
% 1.69/1.34 tff(197,plain,
% 1.69/1.34 (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.34 inference(unit_resolution,[status(thm)],[196, 160])).
% 1.69/1.34 tff(198,plain,
% 1.69/1.34 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)))),
% 1.69/1.34 inference(rewrite,[status(thm)],[])).
% 1.69/1.34 tff(199,plain,
% 1.69/1.34 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) <=> (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)))),
% 1.69/1.34 inference(rewrite,[status(thm)],[])).
% 1.69/1.34 tff(200,plain,
% 1.69/1.34 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15))))),
% 1.69/1.34 inference(monotonicity,[status(thm)],[199])).
% 1.69/1.34 tff(201,plain,
% 1.69/1.34 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)))),
% 1.69/1.35 inference(transitivity,[status(thm)],[200, 198])).
% 1.69/1.35 tff(202,plain,
% 1.69/1.35 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | (part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))))),
% 1.69/1.35 inference(quant_inst,[status(thm)],[])).
% 1.69/1.35 tff(203,plain,
% 1.69/1.35 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C1!15)) | (~part_of(C2, C1!15)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C1)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), C2)))) | part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15))),
% 1.69/1.35 inference(modus_ponens,[status(thm)],[202, 201])).
% 1.69/1.35 tff(204,plain,
% 1.69/1.35 ((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[203, 197, 195, 193, 191, 189])).
% 1.69/1.35 tff(205,plain,
% 1.69/1.35 (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15)),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[204, 173])).
% 1.69/1.35 tff(206,plain,
% 1.69/1.35 ((~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(207,plain,
% 1.69/1.35 ((~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[206, 205])).
% 1.69/1.35 tff(208,plain,
% 1.69/1.35 (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[207, 20])).
% 1.69/1.35 tff(209,plain,
% 1.69/1.35 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(210,plain,
% 1.69/1.35 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[209, 208])).
% 1.69/1.35 tff(211,plain,
% 1.69/1.35 (((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))) <=> ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.69/1.35 inference(rewrite,[status(thm)],[])).
% 1.69/1.35 tff(212,plain,
% 1.69/1.35 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15))),
% 1.69/1.35 inference(quant_inst,[status(thm)],[])).
% 1.69/1.35 tff(213,plain,
% 1.69/1.35 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C1!15))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)),
% 1.69/1.35 inference(modus_ponens,[status(thm)],[212, 211])).
% 1.69/1.35 tff(214,plain,
% 1.69/1.35 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[213, 49, 210])).
% 1.69/1.35 tff(215,plain,
% 1.69/1.35 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C1!15)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(216,plain,
% 1.69/1.35 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[215, 208])).
% 1.69/1.35 tff(217,plain,
% 1.69/1.35 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14)))))))),
% 1.69/1.35 inference(quant_inst,[status(thm)],[])).
% 1.69/1.35 tff(218,plain,
% 1.69/1.35 (~((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14))))))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[217, 16])).
% 1.69/1.35 tff(219,plain,
% 1.69/1.35 (((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~(part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14), C2!14)))))) | ((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(220,plain,
% 1.69/1.35 ((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[219, 218])).
% 1.69/1.35 tff(221,plain,
% 1.69/1.35 ((part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~part_of(tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | (~incident_c(tptp_fun_Q_4(Cpp!13, C2!14), tptp_fun_C2_2(C2!14, tptp_fun_Q_4(Cpp!13, C2!14))))) | part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(222,plain,
% 1.69/1.35 (part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[221, 160])).
% 1.69/1.35 tff(223,plain,
% 1.69/1.35 ((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | (~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.35 inference(tautology,[status(thm)],[])).
% 1.69/1.35 tff(224,plain,
% 1.69/1.35 ((~((~part_of(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C2!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[223, 222])).
% 1.69/1.35 tff(225,plain,
% 1.69/1.35 (![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))),
% 1.69/1.35 inference(unit_resolution,[status(thm)],[224, 220])).
% 1.69/1.35 tff(226,plain,
% 1.69/1.35 (((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))),
% 1.69/1.35 inference(rewrite,[status(thm)],[])).
% 1.69/1.35 tff(227,plain,
% 1.69/1.35 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14))),
% 1.69/1.35 inference(quant_inst,[status(thm)],[])).
% 1.69/1.35 tff(228,plain,
% 1.69/1.35 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(P, C2!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(C2!14, tptp_fun_Q_4(Cpp!13, C2!14)), C1!15), C2!14)),
% 1.69/1.36 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.69/1.36 tff(229,plain,
% 1.69/1.36 ($false),
% 1.69/1.36 inference(unit_resolution,[status(thm)],[228, 225, 216, 214])).
% 1.69/1.36 % SZS output end Proof
%------------------------------------------------------------------------------