TSTP Solution File: GEO088+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO088+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 20:34:47 EDT 2022
% Result : Theorem 2.08s 1.55s
% Output : Proof 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO088+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 31 05:19:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 2.08/1.55 % SZS status Theorem
% 2.08/1.55 % SZS output start Proof
% 2.08/1.55 tff(incident_c_type, type, (
% 2.08/1.55 incident_c: ( $i * $i ) > $o)).
% 2.08/1.55 tff(tptp_fun_Cpp_13_type, type, (
% 2.08/1.55 tptp_fun_Cpp_13: $i)).
% 2.08/1.55 tff(tptp_fun_P_0_type, type, (
% 2.08/1.55 tptp_fun_P_0: ( $i * $i ) > $i)).
% 2.08/1.55 tff(tptp_fun_C_14_type, type, (
% 2.08/1.55 tptp_fun_C_14: $i)).
% 2.08/1.55 tff(tptp_fun_C1_3_type, type, (
% 2.08/1.55 tptp_fun_C1_3: ( $i * $i ) > $i)).
% 2.08/1.55 tff(tptp_fun_P_12_type, type, (
% 2.08/1.55 tptp_fun_P_12: $i)).
% 2.08/1.55 tff(part_of_type, type, (
% 2.08/1.55 part_of: ( $i * $i ) > $o)).
% 2.08/1.55 tff(tptp_fun_C2_2_type, type, (
% 2.08/1.55 tptp_fun_C2_2: ( $i * $i ) > $i)).
% 2.08/1.55 tff(end_point_type, type, (
% 2.08/1.55 end_point: ( $i * $i ) > $o)).
% 2.08/1.55 tff(1,plain,
% 2.08/1.55 (^[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))))))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(2,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[1])).
% 2.08/1.55 tff(3,plain,
% 2.08/1.55 (^[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))))))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(4,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[3])).
% 2.08/1.55 tff(5,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(transitivity,[status(thm)],[4, 2])).
% 2.08/1.55 tff(6,plain,
% 2.08/1.55 (^[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)))))))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(7,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[6])).
% 2.08/1.55 tff(8,plain,
% 2.08/1.55 (![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)))),
% 2.08/1.55 inference(rewrite,[status(thm)],[])).
% 2.08/1.55 tff(9,plain,
% 2.08/1.55 (^[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))))),
% 2.08/1.55 inference(bind,[status(th)],[])).
% 2.08/1.55 tff(10,plain,
% 2.08/1.55 (![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)))),
% 2.08/1.55 inference(quant_intro,[status(thm)],[9])).
% 2.08/1.55 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 2.08/1.55 tff(12,plain,
% 2.08/1.55 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[11, 10])).
% 2.08/1.55 tff(13,plain,
% 2.08/1.55 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[12, 8])).
% 2.08/1.55 tff(14,plain,(
% 2.08/1.55 ![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)))))),
% 2.08/1.55 inference(skolemize,[status(sab)],[13])).
% 2.08/1.55 tff(15,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[14, 7])).
% 2.08/1.55 tff(16,plain,
% 2.08/1.55 (![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)))))))),
% 2.08/1.55 inference(modus_ponens,[status(thm)],[15, 5])).
% 2.08/1.55 tff(17,plain,
% 2.08/1.55 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)))))))),
% 2.08/1.55 inference(quant_inst,[status(thm)],[])).
% 2.08/1.55 tff(18,plain,
% 2.08/1.55 (~((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))))))),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[17, 16])).
% 2.08/1.55 tff(19,plain,
% 2.08/1.55 (((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)))))) | (part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))))),
% 2.08/1.55 inference(tautology,[status(thm)],[])).
% 2.08/1.55 tff(20,plain,
% 2.08/1.55 (part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)))),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[19, 18])).
% 2.08/1.55 tff(21,assumption,((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)))))), introduced(assumption)).
% 2.08/1.55 tff(22,plain,
% 2.08/1.55 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)))))))),
% 2.08/1.55 inference(quant_inst,[status(thm)],[])).
% 2.08/1.55 tff(23,plain,
% 2.08/1.55 ($false),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[22, 16, 21])).
% 2.08/1.55 tff(24,plain,(~((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))))))), inference(lemma,lemma(discharge,[]))).
% 2.08/1.55 tff(25,plain,
% 2.08/1.55 (((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, C!14)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)))))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))))),
% 2.08/1.55 inference(tautology,[status(thm)],[])).
% 2.08/1.55 tff(26,plain,
% 2.08/1.55 (part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)))),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[25, 24])).
% 2.08/1.55 tff(27,assumption,(~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))), introduced(assumption)).
% 2.08/1.55 tff(28,plain,
% 2.08/1.55 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))),
% 2.08/1.55 inference(tautology,[status(thm)],[])).
% 2.08/1.55 tff(29,plain,
% 2.08/1.55 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)),
% 2.08/1.55 inference(unit_resolution,[status(thm)],[28, 27])).
% 2.08/1.55 tff(30,plain,
% 2.08/1.55 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))) | (~(part_of(Cpp!13, C!14) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!14), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!14), C!14)))))))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(31,plain,
% 2.08/1.56 (~((~((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))) | (~(part_of(Cpp!13, C!14) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!14), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!14), C!14))))))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[30, 16])).
% 2.08/1.56 tff(32,plain,
% 2.08/1.56 (((~((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))) | (~(part_of(Cpp!13, C!14) | (~((~incident_c(tptp_fun_P_0(Cpp!13, C!14), Cpp!13)) | incident_c(tptp_fun_P_0(Cpp!13, C!14), C!14)))))) | ((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))),
% 2.08/1.56 inference(tautology,[status(thm)],[])).
% 2.08/1.56 tff(33,plain,
% 2.08/1.56 ((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[32, 31])).
% 2.08/1.56 tff(34,plain,
% 2.08/1.56 ((~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))) <=> (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(35,plain,
% 2.08/1.56 ((~![C: $i, Cpp: $i, P: $i] : (((part_of(Cpp, C) & end_point(P, C)) & incident_c(P, Cpp)) => end_point(P, Cpp))) <=> (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp)))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(36,axiom,(~![C: $i, Cpp: $i, P: $i] : (((part_of(Cpp, C) & end_point(P, C)) & incident_c(P, Cpp)) => end_point(P, Cpp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_2_10')).
% 2.08/1.56 tff(37,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[36, 35])).
% 2.08/1.56 tff(38,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[37, 34])).
% 2.08/1.56 tff(39,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[38, 34])).
% 2.08/1.56 tff(40,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[39, 34])).
% 2.08/1.56 tff(41,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[40, 34])).
% 2.08/1.56 tff(42,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[41, 34])).
% 2.08/1.56 tff(43,plain,
% 2.08/1.56 (~![C: $i, Cpp: $i, P: $i] : ((~(part_of(Cpp, C) & end_point(P, C) & incident_c(P, Cpp))) | end_point(P, Cpp))),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[42, 34])).
% 2.08/1.56 tff(44,plain,(
% 2.08/1.56 ~((~(part_of(Cpp!13, C!14) & end_point(P!12, C!14) & incident_c(P!12, Cpp!13))) | end_point(P!12, Cpp!13))),
% 2.08/1.56 inference(skolemize,[status(sab)],[43])).
% 2.08/1.56 tff(45,plain,
% 2.08/1.56 (part_of(Cpp!13, C!14) & end_point(P!12, C!14) & incident_c(P!12, Cpp!13)),
% 2.08/1.56 inference(or_elim,[status(thm)],[44])).
% 2.08/1.56 tff(46,plain,
% 2.08/1.56 (part_of(Cpp!13, C!14)),
% 2.08/1.56 inference(and_elim,[status(thm)],[45])).
% 2.08/1.56 tff(47,plain,
% 2.08/1.56 ((~((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))) | (~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))),
% 2.08/1.56 inference(tautology,[status(thm)],[])).
% 2.08/1.56 tff(48,plain,
% 2.08/1.56 ((~((~part_of(Cpp!13, C!14)) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14)))) | ![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[47, 46])).
% 2.08/1.56 tff(49,plain,
% 2.08/1.56 (![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[48, 33])).
% 2.08/1.56 tff(50,plain,
% 2.08/1.56 (((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))),
% 2.08/1.56 inference(rewrite,[status(thm)],[])).
% 2.08/1.56 tff(51,plain,
% 2.08/1.56 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(52,plain,
% 2.08/1.56 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)),
% 2.08/1.56 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.08/1.56 tff(53,plain,
% 2.08/1.56 (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[52, 49, 29])).
% 2.08/1.56 tff(54,plain,
% 2.08/1.56 (((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))),
% 2.08/1.56 inference(tautology,[status(thm)],[])).
% 2.08/1.56 tff(55,plain,
% 2.08/1.56 (incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[54, 27])).
% 2.08/1.56 tff(56,plain,
% 2.08/1.56 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), Cpp!13)))))))),
% 2.08/1.56 inference(quant_inst,[status(thm)],[])).
% 2.08/1.56 tff(57,plain,
% 2.08/1.56 (~((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), Cpp!13))))))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[56, 16])).
% 2.08/1.56 tff(58,plain,
% 2.08/1.56 (((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13), Cpp!13)))))) | ((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))),
% 2.08/1.56 inference(tautology,[status(thm)],[])).
% 2.08/1.56 tff(59,plain,
% 2.08/1.56 ((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.08/1.56 inference(unit_resolution,[status(thm)],[58, 57])).
% 2.08/1.56 tff(60,plain,
% 2.08/1.56 (^[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)))))))))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(61,plain,
% 2.08/1.56 (![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))))))))))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[60])).
% 2.08/1.56 tff(62,plain,
% 2.08/1.56 (^[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))))))))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(63,plain,
% 2.08/1.56 (![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)))))))))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[62])).
% 2.08/1.56 tff(64,plain,
% 2.08/1.56 (^[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))))))))))),
% 2.08/1.56 inference(bind,[status(th)],[])).
% 2.08/1.56 tff(65,plain,
% 2.08/1.56 (![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)))))))))),
% 2.08/1.56 inference(quant_intro,[status(thm)],[64])).
% 2.08/1.56 tff(66,plain,
% 2.08/1.56 (![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)))))))))),
% 2.08/1.56 inference(transitivity,[status(thm)],[65, 63])).
% 2.08/1.56 tff(67,plain,
% 2.08/1.56 (^[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)))))))))))),
% 2.12/1.56 inference(bind,[status(th)],[])).
% 2.12/1.56 tff(68,plain,
% 2.12/1.56 (![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)))))))))),
% 2.12/1.56 inference(quant_intro,[status(thm)],[67])).
% 2.12/1.56 tff(69,plain,
% 2.12/1.56 (^[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)))))))))),
% 2.12/1.56 inference(bind,[status(th)],[])).
% 2.12/1.56 tff(70,plain,
% 2.12/1.56 (![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))))))))),
% 2.12/1.56 inference(quant_intro,[status(thm)],[69])).
% 2.12/1.56 tff(71,plain,
% 2.12/1.56 (![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))))))),
% 2.12/1.56 inference(rewrite,[status(thm)],[])).
% 2.12/1.56 tff(72,plain,
% 2.12/1.56 (^[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)))))))),
% 2.12/1.57 inference(bind,[status(th)],[])).
% 2.12/1.57 tff(73,plain,
% 2.12/1.57 (![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))))))),
% 2.12/1.57 inference(quant_intro,[status(thm)],[72])).
% 2.12/1.57 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/sandbox/benchmark/Axioms/GEO004+0.ax','end_point_defn')).
% 2.12/1.57 tff(75,plain,
% 2.12/1.57 (![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))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[74, 73])).
% 2.12/1.57 tff(76,plain,
% 2.12/1.57 (![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))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[75, 71])).
% 2.12/1.57 tff(77,plain,(
% 2.12/1.57 ![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)))))))))),
% 2.12/1.57 inference(skolemize,[status(sab)],[76])).
% 2.12/1.57 tff(78,plain,
% 2.12/1.57 (![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))))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[77, 70])).
% 2.12/1.57 tff(79,plain,
% 2.12/1.57 (![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)))))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[78, 68])).
% 2.12/1.57 tff(80,plain,
% 2.12/1.57 (![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)))))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[79, 66])).
% 2.12/1.57 tff(81,plain,
% 2.12/1.57 (![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))))))))))),
% 2.12/1.57 inference(modus_ponens,[status(thm)],[80, 61])).
% 2.12/1.57 tff(82,plain,
% 2.12/1.57 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)))))))))))),
% 2.12/1.57 inference(rewrite,[status(thm)],[])).
% 2.12/1.57 tff(83,plain,
% 2.12/1.57 ((~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))))))) <=> (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13))))))))))),
% 2.12/1.57 inference(rewrite,[status(thm)],[])).
% 2.12/1.57 tff(84,plain,
% 2.12/1.57 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)))))))))))),
% 2.12/1.57 inference(monotonicity,[status(thm)],[83])).
% 2.12/1.57 tff(85,plain,
% 2.12/1.57 (((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))))))) <=> ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)))))))))))),
% 2.12/1.57 inference(transitivity,[status(thm)],[84, 82])).
% 2.12/1.57 tff(86,plain,
% 2.12/1.57 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))))))),
% 2.12/1.57 inference(quant_inst,[status(thm)],[])).
% 2.12/1.57 tff(87,plain,
% 2.12/1.57 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13))))))))))),
% 2.12/1.58 inference(modus_ponens,[status(thm)],[86, 85])).
% 2.12/1.58 tff(88,plain,
% 2.12/1.58 (~((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13)))))))))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[87, 81])).
% 2.12/1.58 tff(89,plain,
% 2.12/1.58 (((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~((~end_point(P!12, Cpp!13)) | (~((~incident_c(P!12, Cpp!13)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)) | (~part_of(C1, Cpp!13)) | (~part_of(C2, Cpp!13))))))))) | (end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))),
% 2.12/1.58 inference(tautology,[status(thm)],[])).
% 2.12/1.58 tff(90,plain,
% 2.12/1.58 (end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[89, 88])).
% 2.12/1.58 tff(91,plain,
% 2.12/1.58 (~end_point(P!12, Cpp!13)),
% 2.12/1.58 inference(or_elim,[status(thm)],[44])).
% 2.12/1.58 tff(92,plain,
% 2.12/1.58 (incident_c(P!12, Cpp!13)),
% 2.12/1.58 inference(and_elim,[status(thm)],[45])).
% 2.12/1.58 tff(93,plain,
% 2.12/1.58 ((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))))),
% 2.12/1.58 inference(tautology,[status(thm)],[])).
% 2.12/1.58 tff(94,plain,
% 2.12/1.58 ((~(end_point(P!12, Cpp!13) | (~incident_c(P!12, Cpp!13)) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))))) | (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[93, 92, 91])).
% 2.12/1.58 tff(95,plain,
% 2.12/1.58 (~(part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[94, 90])).
% 2.12/1.58 tff(96,plain,
% 2.12/1.58 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)),
% 2.12/1.58 inference(tautology,[status(thm)],[])).
% 2.12/1.58 tff(97,plain,
% 2.12/1.58 (part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[96, 95])).
% 2.12/1.58 tff(98,plain,
% 2.12/1.58 ((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.58 inference(tautology,[status(thm)],[])).
% 2.12/1.58 tff(99,plain,
% 2.12/1.58 ((~((~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[98, 97])).
% 2.12/1.58 tff(100,plain,
% 2.12/1.58 (![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[99, 59])).
% 2.12/1.58 tff(101,plain,
% 2.12/1.58 (((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13))),
% 2.12/1.58 inference(rewrite,[status(thm)],[])).
% 2.12/1.58 tff(102,plain,
% 2.12/1.58 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13))),
% 2.12/1.58 inference(quant_inst,[status(thm)],[])).
% 2.12/1.58 tff(103,plain,
% 2.12/1.58 ((~![P: $i] : ((~incident_c(P, tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), Cpp!13)),
% 2.12/1.58 inference(modus_ponens,[status(thm)],[102, 101])).
% 2.12/1.58 tff(104,plain,
% 2.12/1.58 ($false),
% 2.12/1.58 inference(unit_resolution,[status(thm)],[103, 100, 55, 53])).
% 2.12/1.58 tff(105,plain,((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)), inference(lemma,lemma(discharge,[]))).
% 2.12/1.58 tff(106,plain,
% 2.12/1.58 ((~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14)))),
% 2.12/1.58 inference(tautology,[status(thm)],[])).
% 2.12/1.58 tff(107,plain,
% 2.12/1.58 ((~(part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), tptp_fun_C2_2(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C2_2(Cpp!13, P!12), C!14), C!14))))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[106, 105])).
% 2.12/1.59 tff(108,plain,
% 2.12/1.59 (part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[107, 26])).
% 2.12/1.59 tff(109,plain,
% 2.12/1.59 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(110,plain,
% 2.12/1.59 (incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[109, 95])).
% 2.12/1.59 tff(111,plain,
% 2.12/1.59 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(112,plain,
% 2.12/1.59 (incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[111, 95])).
% 2.12/1.59 tff(113,plain,
% 2.12/1.59 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(114,plain,
% 2.12/1.59 (~part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[113, 95])).
% 2.12/1.59 tff(115,plain,
% 2.12/1.59 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(116,plain,
% 2.12/1.59 (~part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[115, 95])).
% 2.12/1.59 tff(117,plain,
% 2.12/1.59 ((~![P: $i, C: $i] : (~((~(end_point(P, C) | (~incident_c(P, C)) | (~(part_of(tptp_fun_C2_2(C, P), tptp_fun_C1_3(C, P)) | part_of(tptp_fun_C1_3(C, P), tptp_fun_C2_2(C, P)) | (~part_of(tptp_fun_C1_3(C, P), C)) | (~part_of(tptp_fun_C2_2(C, P), C)) | (~incident_c(P, tptp_fun_C1_3(C, P))) | (~incident_c(P, tptp_fun_C2_2(C, P))))))) | (~((~end_point(P, C)) | (~((~incident_c(P, C)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C)) | (~part_of(C2, C)) | (~incident_c(P, C1)) | (~incident_c(P, C2))))))))))) | (~((~(end_point(P!12, C!14) | (~incident_c(P!12, C!14)) | (~(part_of(tptp_fun_C2_2(C!14, P!12), tptp_fun_C1_3(C!14, P!12)) | part_of(tptp_fun_C1_3(C!14, P!12), tptp_fun_C2_2(C!14, P!12)) | (~part_of(tptp_fun_C1_3(C!14, P!12), C!14)) | (~part_of(tptp_fun_C2_2(C!14, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(C!14, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(C!14, P!12))))))) | (~((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))))))),
% 2.12/1.59 inference(quant_inst,[status(thm)],[])).
% 2.12/1.59 tff(118,plain,
% 2.12/1.59 (~((~(end_point(P!12, C!14) | (~incident_c(P!12, C!14)) | (~(part_of(tptp_fun_C2_2(C!14, P!12), tptp_fun_C1_3(C!14, P!12)) | part_of(tptp_fun_C1_3(C!14, P!12), tptp_fun_C2_2(C!14, P!12)) | (~part_of(tptp_fun_C1_3(C!14, P!12), C!14)) | (~part_of(tptp_fun_C2_2(C!14, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(C!14, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(C!14, P!12))))))) | (~((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))))))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[117, 81])).
% 2.12/1.59 tff(119,plain,
% 2.12/1.59 (((~(end_point(P!12, C!14) | (~incident_c(P!12, C!14)) | (~(part_of(tptp_fun_C2_2(C!14, P!12), tptp_fun_C1_3(C!14, P!12)) | part_of(tptp_fun_C1_3(C!14, P!12), tptp_fun_C2_2(C!14, P!12)) | (~part_of(tptp_fun_C1_3(C!14, P!12), C!14)) | (~part_of(tptp_fun_C2_2(C!14, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(C!14, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(C!14, P!12))))))) | (~((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))))) | ((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(120,plain,
% 2.12/1.59 ((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[119, 118])).
% 2.12/1.59 tff(121,plain,
% 2.12/1.59 (end_point(P!12, C!14)),
% 2.12/1.59 inference(and_elim,[status(thm)],[45])).
% 2.12/1.59 tff(122,plain,
% 2.12/1.59 ((~((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))))) | (~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(123,plain,
% 2.12/1.59 ((~((~end_point(P!12, C!14)) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))))) | (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[122, 121])).
% 2.12/1.59 tff(124,plain,
% 2.12/1.59 (~((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[123, 120])).
% 2.12/1.59 tff(125,plain,
% 2.12/1.59 (((~incident_c(P!12, C!14)) | (~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2))))) | ![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))),
% 2.12/1.59 inference(tautology,[status(thm)],[])).
% 2.12/1.59 tff(126,plain,
% 2.12/1.59 (![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))),
% 2.12/1.59 inference(unit_resolution,[status(thm)],[125, 124])).
% 2.12/1.59 tff(127,plain,
% 2.12/1.59 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)))),
% 2.12/1.59 inference(rewrite,[status(thm)],[])).
% 2.12/1.59 tff(128,plain,
% 2.12/1.59 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) <=> (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)))),
% 2.12/1.59 inference(rewrite,[status(thm)],[])).
% 2.12/1.59 tff(129,plain,
% 2.12/1.59 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14))))),
% 2.12/1.59 inference(monotonicity,[status(thm)],[128])).
% 2.12/1.59 tff(130,plain,
% 2.12/1.59 (((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))) <=> ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)))),
% 2.12/1.59 inference(transitivity,[status(thm)],[129, 127])).
% 2.12/1.59 tff(131,plain,
% 2.12/1.59 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | (part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))))),
% 2.12/1.60 inference(quant_inst,[status(thm)],[])).
% 2.12/1.60 tff(132,plain,
% 2.12/1.60 ((~![C1: $i, C2: $i] : (part_of(C2, C1) | part_of(C1, C2) | (~part_of(C1, C!14)) | (~part_of(C2, C!14)) | (~incident_c(P!12, C1)) | (~incident_c(P!12, C2)))) | part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14))),
% 2.12/1.60 inference(modus_ponens,[status(thm)],[131, 130])).
% 2.12/1.60 tff(133,plain,
% 2.12/1.60 ((~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), C!14))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[132, 126, 116, 114, 112, 110])).
% 2.12/1.60 tff(134,plain,
% 2.12/1.60 (~part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14)),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[133, 108])).
% 2.12/1.60 tff(135,plain,
% 2.12/1.60 ((~(part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))))) | part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)))),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(136,plain,
% 2.12/1.60 ((~(part_of(tptp_fun_C1_3(Cpp!13, P!12), C!14) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))))) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[135, 134])).
% 2.12/1.60 tff(137,plain,
% 2.12/1.60 (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[136, 20])).
% 2.12/1.60 tff(138,plain,
% 2.12/1.60 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(139,plain,
% 2.12/1.60 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[138, 137])).
% 2.12/1.60 tff(140,plain,
% 2.12/1.60 (((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))) <=> ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))),
% 2.12/1.60 inference(rewrite,[status(thm)],[])).
% 2.12/1.60 tff(141,plain,
% 2.12/1.60 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14))),
% 2.12/1.60 inference(quant_inst,[status(thm)],[])).
% 2.12/1.60 tff(142,plain,
% 2.12/1.60 ((~![P: $i] : ((~incident_c(P, Cpp!13)) | incident_c(P, C!14))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)),
% 2.12/1.60 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.12/1.60 tff(143,plain,
% 2.12/1.60 (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[142, 49, 139])).
% 2.12/1.60 tff(144,plain,
% 2.12/1.60 (((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), C!14)) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(145,plain,
% 2.12/1.60 (incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[144, 137])).
% 2.12/1.60 tff(146,plain,
% 2.12/1.60 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), Cpp!13)))))))),
% 2.12/1.60 inference(quant_inst,[status(thm)],[])).
% 2.12/1.60 tff(147,plain,
% 2.12/1.60 (~((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), Cpp!13))))))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[146, 16])).
% 2.12/1.60 tff(148,plain,
% 2.12/1.60 (((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~(part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13) | (~((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13), Cpp!13)))))) | ((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(149,plain,
% 2.12/1.60 ((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[148, 147])).
% 2.12/1.60 tff(150,plain,
% 2.12/1.60 ((part_of(tptp_fun_C2_2(Cpp!13, P!12), tptp_fun_C1_3(Cpp!13, P!12)) | part_of(tptp_fun_C1_3(Cpp!13, P!12), tptp_fun_C2_2(Cpp!13, P!12)) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | (~part_of(tptp_fun_C2_2(Cpp!13, P!12), Cpp!13)) | (~incident_c(P!12, tptp_fun_C1_3(Cpp!13, P!12))) | (~incident_c(P!12, tptp_fun_C2_2(Cpp!13, P!12)))) | part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(151,plain,
% 2.12/1.60 (part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[150, 95])).
% 2.12/1.60 tff(152,plain,
% 2.12/1.60 ((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | (~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.60 inference(tautology,[status(thm)],[])).
% 2.12/1.60 tff(153,plain,
% 2.12/1.60 ((~((~part_of(tptp_fun_C1_3(Cpp!13, P!12), Cpp!13)) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13)))) | ![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[152, 151])).
% 2.12/1.60 tff(154,plain,
% 2.12/1.60 (![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))),
% 2.12/1.60 inference(unit_resolution,[status(thm)],[153, 149])).
% 2.12/1.60 tff(155,plain,
% 2.12/1.60 (((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13))) <=> ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13))),
% 2.12/1.60 inference(rewrite,[status(thm)],[])).
% 2.12/1.60 tff(156,plain,
% 2.12/1.60 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | ((~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13))),
% 2.12/1.61 inference(quant_inst,[status(thm)],[])).
% 2.12/1.61 tff(157,plain,
% 2.12/1.61 ((~![P: $i] : ((~incident_c(P, tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(P, Cpp!13))) | (~incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), tptp_fun_C1_3(Cpp!13, P!12))) | incident_c(tptp_fun_P_0(tptp_fun_C1_3(Cpp!13, P!12), C!14), Cpp!13)),
% 2.12/1.61 inference(modus_ponens,[status(thm)],[156, 155])).
% 2.12/1.61 tff(158,plain,
% 2.12/1.61 ($false),
% 2.12/1.61 inference(unit_resolution,[status(thm)],[157, 154, 145, 143])).
% 2.12/1.61 % SZS output end Proof
%------------------------------------------------------------------------------