TSTP Solution File: GEO087+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO087+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:47 EDT 2022
% Result : Theorem 0.20s 0.45s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO087+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n001.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 05:43:48 EDT 2022
% 0.13/0.35 % 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.
% 0.20/0.45 % SZS status Theorem
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 tff(incident_c_type, type, (
% 0.20/0.45 incident_c: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_C2_12_type, type, (
% 0.20/0.45 tptp_fun_C2_12: $i)).
% 0.20/0.45 tff(tptp_fun_P_6_type, type, (
% 0.20/0.45 tptp_fun_P_6: $i > $i)).
% 0.20/0.45 tff(tptp_fun_C1_13_type, type, (
% 0.20/0.45 tptp_fun_C1_13: $i)).
% 0.20/0.45 tff(end_point_type, type, (
% 0.20/0.45 end_point: ( $i * $i ) > $o)).
% 0.20/0.45 tff(inner_point_type, type, (
% 0.20/0.45 inner_point: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_P_14_type, type, (
% 0.20/0.45 tptp_fun_P_14: $i)).
% 0.20/0.45 tff(meet_type, type, (
% 0.20/0.45 meet: ( $i * $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_Q_4_type, type, (
% 0.20/0.45 tptp_fun_Q_4: ( $i * $i ) > $i)).
% 0.20/0.45 tff(part_of_type, type, (
% 0.20/0.45 part_of: ( $i * $i ) > $o)).
% 0.20/0.45 tff(tptp_fun_P_0_type, type, (
% 0.20/0.45 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.20/0.45 tff(1,plain,
% 0.20/0.45 (^[P: $i, C: $i] : refl((inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(2,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))) <=> ![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.45 tff(3,plain,
% 0.20/0.45 (^[P: $i, C: $i] : rewrite((inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C)))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(4,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.45 tff(5,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C)))) <=> ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(6,axiom,(![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','inner_point_defn')).
% 0.20/0.45 tff(7,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.45 tff(8,plain,(
% 0.20/0.45 ![P: $i, C: $i] : (inner_point(P, C) <=> (incident_c(P, C) & (~end_point(P, C))))),
% 0.20/0.45 inference(skolemize,[status(sab)],[7])).
% 0.20/0.45 tff(9,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.45 tff(10,plain,
% 0.20/0.45 (![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.45 tff(11,plain,
% 0.20/0.45 ((~![P: $i, C: $i] : (inner_point(P, C) <=> (~((~incident_c(P, C)) | end_point(P, C))))) | (inner_point(tptp_fun_P_6(C1!13), C1!13) <=> (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(12,plain,
% 0.20/0.45 (inner_point(tptp_fun_P_6(C1!13), C1!13) <=> (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.45 tff(13,plain,
% 0.20/0.45 (![C: $i] : ?[P: $i] : inner_point(P, C) <=> ![C: $i] : ?[P: $i] : inner_point(P, C)),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(14,axiom,(![C: $i] : ?[P: $i] : inner_point(P, C)), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','c3')).
% 0.20/0.45 tff(15,plain,
% 0.20/0.45 (![C: $i] : ?[P: $i] : inner_point(P, C)),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.20/0.45 tff(16,plain,(
% 0.20/0.45 ![C: $i] : inner_point(tptp_fun_P_6(C), C)),
% 0.20/0.45 inference(skolemize,[status(sab)],[15])).
% 0.20/0.45 tff(17,plain,
% 0.20/0.45 ((~![C: $i] : inner_point(tptp_fun_P_6(C), C)) | inner_point(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(18,plain,
% 0.20/0.45 (inner_point(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.45 tff(19,plain,
% 0.20/0.45 ((~(inner_point(tptp_fun_P_6(C1!13), C1!13) <=> (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13))))) | (~inner_point(tptp_fun_P_6(C1!13), C1!13)) | (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13)))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(20,plain,
% 0.20/0.45 ((~(inner_point(tptp_fun_P_6(C1!13), C1!13) <=> (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13))))) | (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.20/0.45 tff(21,plain,
% 0.20/0.45 (~((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[20, 12])).
% 0.20/0.45 tff(22,plain,
% 0.20/0.45 (((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C1!13))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(23,plain,
% 0.20/0.45 (~end_point(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.20/0.45 tff(24,plain,
% 0.20/0.45 (((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12))) | end_point(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(25,plain,
% 0.20/0.45 ((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.45 tff(26,plain,
% 0.20/0.45 (((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | end_point(tptp_fun_P_6(C1!13), C1!13)) | incident_c(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(27,plain,
% 0.20/0.45 (incident_c(tptp_fun_P_6(C1!13), C1!13)),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[26, 21])).
% 0.20/0.45 tff(28,plain,
% 0.20/0.45 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(29,plain,
% 0.20/0.45 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.45 tff(30,plain,
% 0.20/0.45 (^[P: $i, C: $i, C1: $i] : refl((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(31,plain,
% 0.20/0.45 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[30])).
% 0.20/0.45 tff(32,plain,
% 0.20/0.45 (^[P: $i, C: $i, C1: $i] : rewrite((~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))))),
% 0.20/0.45 inference(bind,[status(th)],[])).
% 0.20/0.45 tff(33,plain,
% 0.20/0.45 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.45 inference(quant_intro,[status(thm)],[32])).
% 0.20/0.45 tff(34,plain,
% 0.20/0.45 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.45 inference(transitivity,[status(thm)],[33, 31])).
% 0.20/0.45 tff(35,plain,
% 0.20/0.45 (^[P: $i, C: $i, C1: $i] : trans(monotonicity(rewrite(((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))), trans(monotonicity(rewrite((~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))) <=> (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), rewrite((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))), ((meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))) <=> (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))))), rewrite((((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))), ((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(36,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))) <=> ![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.46 tff(37,plain,
% 0.20/0.46 (^[P: $i, C: $i, C1: $i] : rewrite((((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(38,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))) <=> ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.46 tff(39,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(40,plain,
% 0.20/0.46 (^[P: $i, C: $i, C1: $i] : rewrite((meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(41,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> ((incident_c(P, C) & incident_c(P, C1)) & ![Q: $i] : ((incident_c(Q, C) & incident_c(Q, C1)) => (end_point(Q, C) & end_point(Q, C1))))) <=> ![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[40])).
% 0.20/0.46 tff(42,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/sandbox/benchmark/Axioms/GEO004+0.ax','meet_defn')).
% 0.20/0.46 tff(43,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.46 tff(44,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (meet(P, C, C1) <=> (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1)))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.46 tff(45,plain,(
% 0.20/0.46 ![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | ((~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1)))))))),
% 0.20/0.46 inference(skolemize,[status(sab)],[44])).
% 0.20/0.46 tff(46,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (((~meet(P, C, C1)) | (incident_c(P, C) & incident_c(P, C1) & ![Q: $i] : ((~(incident_c(Q, C) & incident_c(Q, C1))) | (end_point(Q, C) & end_point(Q, C1))))) & (meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~(incident_c(tptp_fun_Q_4(C1, C), C) & incident_c(tptp_fun_Q_4(C1, C), C1))) | (end_point(tptp_fun_Q_4(C1, C), C) & end_point(tptp_fun_Q_4(C1, C), C1))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.46 tff(47,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.20/0.46 tff(48,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (~((~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C)))))))))) | (~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[47, 34])).
% 0.20/0.46 tff(49,plain,
% 0.20/0.46 (![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[48, 29])).
% 0.20/0.46 tff(50,plain,
% 0.20/0.46 (((~![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!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(51,plain,
% 0.20/0.46 ((~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C2!12)) | (~incident_c(Q, C1!13)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))))) <=> (~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(52,plain,
% 0.20/0.46 (((~![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!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C2!12)) | (~incident_c(Q, C1!13)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[51])).
% 0.20/0.46 tff(53,plain,
% 0.20/0.46 (((~![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!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C2!12)) | (~incident_c(Q, C1!13)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))) <=> ((~![P: $i, C: $i, C1: $i] : (~((~(meet(P, C, C1) | (~incident_c(P, C)) | (~incident_c(P, C1)) | (~((~incident_c(tptp_fun_Q_4(C1, C), C)) | (~incident_c(tptp_fun_Q_4(C1, C), C1)) | (~((~end_point(tptp_fun_Q_4(C1, C), C)) | (~end_point(tptp_fun_Q_4(C1, C), C1)))))))) | (~((~meet(P, C, C1)) | (~((~incident_c(P, C)) | (~incident_c(P, C1)) | (~![Q: $i] : ((~incident_c(Q, C1)) | (~incident_c(Q, C)) | (~((~end_point(Q, C1)) | (~end_point(Q, C))))))))))))) | (~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))))))),
% 0.20/0.46 inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.46 tff(54,plain,
% 0.20/0.46 ((~![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!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C2!12)) | (~incident_c(Q, C1!13)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(55,plain,
% 0.20/0.46 ((~![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!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (~((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[55, 49])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (((~(meet(P!14, C1!13, C2!12) | (~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~((~incident_c(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~incident_c(tptp_fun_Q_4(C2!12, C1!13), C2!12)) | (~((~end_point(tptp_fun_Q_4(C2!12, C1!13), C1!13)) | (~end_point(tptp_fun_Q_4(C2!12, C1!13), C2!12)))))))) | (~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))))) | ((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 ((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (((~(~part_of(C1!13, C2!12))) & meet(P!14, C1!13, C2!12)) <=> (part_of(C1!13, C2!12) & meet(P!14, C1!13, C2!12))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 ((~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))) <=> (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 ((~![C1: $i, C2: $i] : (part_of(C1, C2) => (~?[P: $i] : meet(P, C1, C2)))) <=> (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(62,axiom,(~![C1: $i, C2: $i] : (part_of(C1, C2) => (~?[P: $i] : meet(P, C1, C2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','corollary_2_9')).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.47 tff(64,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[63, 60])).
% 0.20/0.47 tff(65,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.20/0.47 tff(66,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[65, 60])).
% 0.20/0.47 tff(67,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[66, 60])).
% 0.20/0.47 tff(68,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.47 tff(69,plain,
% 0.20/0.47 (~![C1: $i, C2: $i] : ((~part_of(C1, C2)) | (~?[P: $i] : meet(P, C1, C2)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[68, 60])).
% 0.20/0.47 tff(70,plain,
% 0.20/0.47 (part_of(C1!13, C2!12) & meet(P!14, C1!13, C2!12)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.47 tff(71,plain,
% 0.20/0.47 (meet(P!14, C1!13, C2!12)),
% 0.20/0.47 inference(and_elim,[status(thm)],[70])).
% 0.20/0.47 tff(72,plain,
% 0.20/0.47 ((~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))) | (~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(73,plain,
% 0.20/0.47 ((~((~meet(P!14, C1!13, C2!12)) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))))) | (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.20/0.47 tff(74,plain,
% 0.20/0.47 (~((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[73, 58])).
% 0.20/0.47 tff(75,plain,
% 0.20/0.47 (((~incident_c(P!14, C1!13)) | (~incident_c(P!14, C2!12)) | (~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13))))))) | ![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(76,plain,
% 0.20/0.47 (![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.47 tff(77,plain,
% 0.20/0.47 (((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | (~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(78,plain,
% 0.20/0.47 (((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C2!12)) | (~end_point(tptp_fun_P_6(C1!13), C1!13))))) <=> ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(79,plain,
% 0.20/0.47 (((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C2!12)) | (~end_point(tptp_fun_P_6(C1!13), C1!13)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[78])).
% 0.20/0.47 tff(80,plain,
% 0.20/0.47 (((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C2!12)) | (~end_point(tptp_fun_P_6(C1!13), C1!13)))))) <=> ((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | (~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[79, 77])).
% 0.20/0.47 tff(81,plain,
% 0.20/0.47 ((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C2!12)) | (~end_point(tptp_fun_P_6(C1!13), C1!13)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(82,plain,
% 0.20/0.47 ((~![Q: $i] : ((~incident_c(Q, C1!13)) | (~incident_c(Q, C2!12)) | (~((~end_point(Q, C2!12)) | (~end_point(Q, C1!13)))))) | (~incident_c(tptp_fun_P_6(C1!13), C1!13)) | (~incident_c(tptp_fun_P_6(C1!13), C2!12)) | (~((~end_point(tptp_fun_P_6(C1!13), C1!13)) | (~end_point(tptp_fun_P_6(C1!13), C2!12))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.20/0.47 tff(83,plain,
% 0.20/0.47 (~incident_c(tptp_fun_P_6(C1!13), C2!12)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[82, 76, 27, 25])).
% 0.20/0.47 tff(84,plain,
% 0.20/0.47 (^[C: $i, C1: $i] : refl((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(85,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.47 tff(86,plain,
% 0.20/0.47 (^[C: $i, C1: $i] : rewrite((~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(87,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[86])).
% 0.20/0.47 tff(88,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[87, 85])).
% 0.20/0.47 tff(89,plain,
% 0.20/0.47 (^[C: $i, C1: $i] : trans(monotonicity(rewrite(((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))), rewrite((part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))) <=> (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))))), rewrite((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))), ((((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(90,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C))))) <=> ![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[89])).
% 0.20/0.47 tff(91,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(92,plain,
% 0.20/0.47 (^[C: $i, C1: $i] : rewrite((part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(93,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C))) <=> ![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.47 tff(94,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')).
% 0.20/0.47 tff(95,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.47 tff(96,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.20/0.47 tff(97,plain,(
% 0.20/0.47 ![C: $i, C1: $i] : (((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C))) & (part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))),
% 0.20/0.47 inference(skolemize,[status(sab)],[96])).
% 0.20/0.47 tff(98,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.20/0.47 tff(99,plain,
% 0.20/0.47 (![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 ((~![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(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (~((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~(part_of(C1!13, C2!12) | (~((~incident_c(tptp_fun_P_0(C1!13, C2!12), C1!13)) | incident_c(tptp_fun_P_0(C1!13, C2!12), C2!12)))))) | ((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 ((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (part_of(C1!13, C2!12)),
% 0.20/0.48 inference(and_elim,[status(thm)],[70])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 ((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | (~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 ((~((~part_of(C1!13, C2!12)) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12)))) | ![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[106, 103])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | incident_c(tptp_fun_P_6(C1!13), C2!12))) <=> ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_6(C1!13), C1!13)) | incident_c(tptp_fun_P_6(C1!13), C2!12))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | ((~incident_c(tptp_fun_P_6(C1!13), C1!13)) | incident_c(tptp_fun_P_6(C1!13), C2!12))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 ((~![P: $i] : ((~incident_c(P, C1!13)) | incident_c(P, C2!12))) | (~incident_c(tptp_fun_P_6(C1!13), C1!13)) | incident_c(tptp_fun_P_6(C1!13), C2!12)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 ($false),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[110, 107, 27, 83])).
% 0.20/0.48 % SZS output end Proof
%------------------------------------------------------------------------------