TSTP Solution File: GEO084+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:45 EDT 2022
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO084+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 31 05:17:02 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.
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(incident_c_type, type, (
% 0.13/0.41 incident_c: ( $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_C2_14_type, type, (
% 0.13/0.41 tptp_fun_C2_14: $i)).
% 0.13/0.41 tff(tptp_fun_P_0_type, type, (
% 0.13/0.41 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_C3_13_type, type, (
% 0.13/0.41 tptp_fun_C3_13: $i)).
% 0.13/0.41 tff(sum_type, type, (
% 0.13/0.41 sum: ( $i * $i ) > $i)).
% 0.13/0.41 tff(tptp_fun_C1_15_type, type, (
% 0.13/0.41 tptp_fun_C1_15: $i)).
% 0.13/0.41 tff(part_of_type, type, (
% 0.13/0.41 part_of: ( $i * $i ) > $o)).
% 0.13/0.41 tff(meet_type, type, (
% 0.13/0.41 meet: ( $i * $i * $i ) > $o)).
% 0.13/0.41 tff(tptp_fun_P_12_type, type, (
% 0.13/0.41 tptp_fun_P_12: $i)).
% 0.13/0.41 tff(tptp_fun_Q_1_type, type, (
% 0.13/0.41 tptp_fun_Q_1: ( $i * $i * $i ) > $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[1])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[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))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[4, 2])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 (^[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)))))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[6])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 (^[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))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 (![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)))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[9])).
% 0.13/0.41 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.13/0.41 tff(14,plain,(
% 0.13/0.41 ![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)))))),
% 0.13/0.41 inference(skolemize,[status(sab)],[13])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 (![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)))))))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 ((~![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(sum(C1!15, C2!14), C3!13)) | ![P: $i] : ((~incident_c(P, sum(C1!15, C2!14))) | incident_c(P, C3!13)))) | (~(part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)))))))),
% 0.13/0.41 inference(quant_inst,[status(thm)],[])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 (~((~((~part_of(sum(C1!15, C2!14), C3!13)) | ![P: $i] : ((~incident_c(P, sum(C1!15, C2!14))) | incident_c(P, C3!13)))) | (~(part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))))))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 (((~((~part_of(sum(C1!15, C2!14), C3!13)) | ![P: $i] : ((~incident_c(P, sum(C1!15, C2!14))) | incident_c(P, C3!13)))) | (~(part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)))))) | (part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 (part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))) <=> (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 ((~![C1: $i, C2: $i, C3: $i, P: $i] : (((part_of(C1, C3) & part_of(C2, C3)) & meet(P, C1, C2)) => part_of(sum(C1, C2), C3))) <=> (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(23,axiom,(~![C1: $i, C2: $i, C3: $i, P: $i] : (((part_of(C1, C3) & part_of(C2, C3)) & meet(P, C1, C2)) => part_of(sum(C1, C2), C3))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary_2_6_2')).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.13/0.41 tff(28,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.13/0.41 tff(29,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.13/0.41 tff(30,plain,
% 0.13/0.41 (~![C1: $i, C2: $i, C3: $i, P: $i] : ((~(part_of(C1, C3) & part_of(C2, C3) & meet(P, C1, C2))) | part_of(sum(C1, C2), C3))),
% 0.13/0.41 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.13/0.41 tff(31,plain,(
% 0.13/0.41 ~((~(part_of(C1!15, C3!13) & part_of(C2!14, C3!13) & meet(P!12, C1!15, C2!14))) | part_of(sum(C1!15, C2!14), C3!13))),
% 0.13/0.41 inference(skolemize,[status(sab)],[30])).
% 0.13/0.41 tff(32,plain,
% 0.13/0.41 (~part_of(sum(C1!15, C2!14), C3!13)),
% 0.13/0.41 inference(or_elim,[status(thm)],[31])).
% 0.13/0.41 tff(33,plain,
% 0.13/0.41 ((~(part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))))) | part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)))),
% 0.13/0.41 inference(tautology,[status(thm)],[])).
% 0.13/0.41 tff(34,plain,
% 0.13/0.41 ((~(part_of(sum(C1!15, C2!14), C3!13) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))))) | (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)))),
% 0.13/0.41 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.13/0.41 tff(35,plain,
% 0.13/0.41 (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[34, 20])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 (((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 ((~![C: $i, C1: $i] : (~((~((~part_of(C1, C)) | ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))) | (~(part_of(C1, C) | (~((~incident_c(tptp_fun_P_0(C1, C), C1)) | incident_c(tptp_fun_P_0(C1, C), C)))))))) | (~((~((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))) | (~(part_of(C2!14, C3!13) | (~((~incident_c(tptp_fun_P_0(C2!14, C3!13), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C3!13), C3!13)))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 (~((~((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))) | (~(part_of(C2!14, C3!13) | (~((~incident_c(tptp_fun_P_0(C2!14, C3!13), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C3!13), C3!13))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[38, 16])).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 (((~((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))) | (~(part_of(C2!14, C3!13) | (~((~incident_c(tptp_fun_P_0(C2!14, C3!13), C2!14)) | incident_c(tptp_fun_P_0(C2!14, C3!13), C3!13)))))) | ((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(41,plain,
% 0.13/0.42 ((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 (part_of(C1!15, C3!13) & part_of(C2!14, C3!13) & meet(P!12, C1!15, C2!14)),
% 0.13/0.42 inference(or_elim,[status(thm)],[31])).
% 0.13/0.42 tff(43,plain,
% 0.13/0.42 (part_of(C2!14, C3!13)),
% 0.13/0.42 inference(and_elim,[status(thm)],[42])).
% 0.13/0.42 tff(44,plain,
% 0.13/0.42 ((~((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))) | (~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(45,plain,
% 0.13/0.42 ((~((~part_of(C2!14, C3!13)) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13)))) | ![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.13/0.42 tff(46,plain,
% 0.13/0.42 (![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[45, 41])).
% 0.13/0.42 tff(47,plain,
% 0.13/0.42 (((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))) | ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))) <=> ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(48,plain,
% 0.13/0.42 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))) | ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(49,plain,
% 0.13/0.42 ((~![P: $i] : ((~incident_c(P, C2!14)) | incident_c(P, C3!13))) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.13/0.42 tff(50,plain,
% 0.13/0.42 (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[49, 46, 37])).
% 0.13/0.42 tff(51,plain,
% 0.13/0.42 ((~![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!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))) | (~(part_of(C1!15, C3!13) | (~((~incident_c(tptp_fun_P_0(C1!15, C3!13), C1!15)) | incident_c(tptp_fun_P_0(C1!15, C3!13), C3!13)))))))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(52,plain,
% 0.13/0.42 (~((~((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))) | (~(part_of(C1!15, C3!13) | (~((~incident_c(tptp_fun_P_0(C1!15, C3!13), C1!15)) | incident_c(tptp_fun_P_0(C1!15, C3!13), C3!13))))))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[51, 16])).
% 0.13/0.42 tff(53,plain,
% 0.13/0.42 (((~((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))) | (~(part_of(C1!15, C3!13) | (~((~incident_c(tptp_fun_P_0(C1!15, C3!13), C1!15)) | incident_c(tptp_fun_P_0(C1!15, C3!13), C3!13)))))) | ((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(54,plain,
% 0.13/0.42 ((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.13/0.42 tff(55,plain,
% 0.13/0.42 (part_of(C1!15, C3!13)),
% 0.13/0.42 inference(and_elim,[status(thm)],[42])).
% 0.13/0.42 tff(56,plain,
% 0.13/0.42 ((~((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))) | (~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(57,plain,
% 0.13/0.42 ((~((~part_of(C1!15, C3!13)) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13)))) | ![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.13/0.42 tff(58,plain,
% 0.13/0.42 (![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[57, 54])).
% 0.13/0.42 tff(59,plain,
% 0.13/0.42 (((~![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))) | ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))) <=> ((~![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(60,plain,
% 0.13/0.42 ((~![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))) | ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13))),
% 0.13/0.42 inference(quant_inst,[status(thm)],[])).
% 0.13/0.42 tff(61,plain,
% 0.13/0.42 ((~![P: $i] : ((~incident_c(P, C1!15)) | incident_c(P, C3!13))) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)),
% 0.13/0.42 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.13/0.42 tff(62,plain,
% 0.13/0.42 (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15)),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[61, 58, 37])).
% 0.13/0.42 tff(63,plain,
% 0.13/0.42 ((~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(64,plain,
% 0.13/0.42 (~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[63, 62, 50])).
% 0.13/0.42 tff(65,plain,
% 0.13/0.42 (((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C3!13)) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(66,plain,
% 0.13/0.42 (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[65, 35])).
% 0.13/0.42 tff(67,plain,
% 0.13/0.42 ((~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) | (~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))),
% 0.13/0.42 inference(tautology,[status(thm)],[])).
% 0.13/0.42 tff(68,plain,
% 0.13/0.42 (~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.13/0.42 inference(unit_resolution,[status(thm)],[67, 66, 64])).
% 0.13/0.42 tff(69,plain,
% 0.13/0.42 (^[C: $i, C1: $i, C2: $i, Q: $i] : refl((~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(70,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[69])).
% 0.13/0.42 tff(71,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(pull_quant,[status(thm)],[])).
% 0.13/0.42 tff(72,plain,
% 0.13/0.42 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(pull_quant(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> (~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), pull_quant((~![Q: $i] : ((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))))), ((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) <=> ?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), pull_quant((?[Q: $i] : (~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), (((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> ?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> (~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), pull_quant((~?[Q: $i] : ((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), ((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(73,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i] : ![Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[73, 71])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[74, 70])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 (^[C: $i, C1: $i, C2: $i] : rewrite((~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[76])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))) <=> ![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[77, 75])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(rewrite(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), monotonicity(rewrite(((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))) <=> ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))), (((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), rewrite((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(80,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[79])).
% 0.20/0.43 tff(81,plain,
% 0.20/0.43 (^[C: $i, C1: $i, C2: $i] : rewrite((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(82,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> ![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[81])).
% 0.20/0.43 tff(83,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(84,axiom,(![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GEO004+0.ax','sum_defn')).
% 0.20/0.43 tff(85,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.20/0.43 tff(86,plain,(
% 0.20/0.43 ![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))),
% 0.20/0.43 inference(skolemize,[status(sab)],[85])).
% 0.20/0.43 tff(87,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.43 tff(88,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i] : (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[87, 80])).
% 0.20/0.43 tff(89,plain,
% 0.20/0.43 (![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[88, 78])).
% 0.20/0.43 tff(90,plain,
% 0.20/0.43 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(91,plain,
% 0.20/0.43 ((~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(92,plain,
% 0.20/0.43 ((((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))) | $false) <=> ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(93,plain,
% 0.20/0.43 ((~$true) <=> $false),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(94,plain,
% 0.20/0.43 (($true | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(95,plain,
% 0.20/0.43 ((sum(C1!15, C2!14) = sum(C1!15, C2!14)) <=> $true),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(96,plain,
% 0.20/0.43 (((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))) <=> ($true | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.43 tff(97,plain,
% 0.20/0.43 (((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))) <=> $true),
% 0.20/0.43 inference(transitivity,[status(thm)],[96, 94])).
% 0.20/0.43 tff(98,plain,
% 0.20/0.43 ((~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14))))) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[97])).
% 0.20/0.43 tff(99,plain,
% 0.20/0.43 ((~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14))))) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[98, 93])).
% 0.20/0.43 tff(100,plain,
% 0.20/0.43 ((~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(101,plain,
% 0.20/0.43 (($false | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(102,plain,
% 0.20/0.43 ((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) <=> (~$true)),
% 0.20/0.43 inference(monotonicity,[status(thm)],[95])).
% 0.20/0.43 tff(103,plain,
% 0.20/0.43 ((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) <=> $false),
% 0.20/0.43 inference(transitivity,[status(thm)],[102, 93])).
% 0.20/0.43 tff(104,plain,
% 0.20/0.43 (((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> ($false | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[103])).
% 0.20/0.43 tff(105,plain,
% 0.20/0.43 (((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[104, 101])).
% 0.20/0.43 tff(106,plain,
% 0.20/0.43 ((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) <=> (~(incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[105])).
% 0.20/0.43 tff(107,plain,
% 0.20/0.43 ((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) <=> ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.43 inference(transitivity,[status(thm)],[106, 100])).
% 0.20/0.44 tff(108,plain,
% 0.20/0.44 (((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))))) <=> (((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))) | $false)),
% 0.20/0.44 inference(monotonicity,[status(thm)],[107, 99])).
% 0.20/0.44 tff(109,plain,
% 0.20/0.44 (((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))))) <=> ((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[108, 92])).
% 0.20/0.44 tff(110,plain,
% 0.20/0.44 ((~((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14))))))) <=> (~((~incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[109])).
% 0.20/0.44 tff(111,plain,
% 0.20/0.44 ((~((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14))))))) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.44 inference(transitivity,[status(thm)],[110, 91])).
% 0.20/0.44 tff(112,plain,
% 0.20/0.44 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (~((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.44 inference(monotonicity,[status(thm)],[111])).
% 0.20/0.44 tff(113,plain,
% 0.20/0.44 (((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (~((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))),
% 0.20/0.44 inference(transitivity,[status(thm)],[112, 90])).
% 0.20/0.44 tff(114,plain,
% 0.20/0.44 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (~((~((~(sum(C1!15, C2!14) = sum(C1!15, C2!14))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14))))) | (~((sum(C1!15, C2!14) = sum(C1!15, C2!14)) | ((~incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), sum(C1!15, C2!14))) <=> (incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C1!15) | incident_c(tptp_fun_Q_1(C2!14, C1!15, sum(C1!15, C2!14)), C2!14)))))))),
% 0.20/0.44 inference(quant_inst,[status(thm)],[])).
% 0.20/0.44 tff(115,plain,
% 0.20/0.44 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | ((~incident_c(tptp_fun_Q_1(C2, C1, C), C)) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))) | (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), sum(C1!15, C2!14)) <=> (incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C1!15) | incident_c(tptp_fun_P_0(sum(C1!15, C2!14), C3!13), C2!14)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.44 tff(116,plain,
% 0.20/0.44 ($false),
% 0.20/0.44 inference(unit_resolution,[status(thm)],[115, 89, 68])).
% 0.20/0.44 % SZS output end Proof
%------------------------------------------------------------------------------