%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO084+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:05:32 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : GEO084+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 14:16:41 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(incident_c_type, type, (
% 0.12/0.37 incident_c: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_C2_13_type, type, (
% 0.12/0.37 tptp_fun_C2_13: $i)).
% 0.12/0.37 tff(tptp_fun_P_0_type, type, (
% 0.12/0.37 tptp_fun_P_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C3_12_type, type, (
% 0.12/0.37 tptp_fun_C3_12: $i)).
% 0.12/0.37 tff(sum_type, type, (
% 0.12/0.37 sum: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_C1_14_type, type, (
% 0.12/0.37 tptp_fun_C1_14: $i)).
% 0.12/0.37 tff(part_of_type, type, (
% 0.12/0.37 part_of: ( $i * $i ) > $o)).
% 0.12/0.37 tff(meet_type, type, (
% 0.12/0.37 meet: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_P_11_type, type, (
% 0.12/0.37 tptp_fun_P_11: $i)).
% 0.12/0.37 tff(tptp_fun_Q_1_type, type, (
% 0.12/0.37 tptp_fun_Q_1: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (^[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))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(4,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.12/0.37 tff(5,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.12/0.37 tff(6,plain,
% 0.12/0.37 (^[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)))))))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(7,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.12/0.37 tff(8,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(9,plain,
% 0.12/0.37 (^[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))))),
% 0.12/0.37 inference(bind,[status(th)],[])).
% 0.12/0.37 tff(10,plain,
% 0.12/0.37 (![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)))),
% 0.12/0.37 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.37 tff(11,axiom,(![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : (incident_c(P, C1) => incident_c(P, C)))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','part_of_defn')).
% 0.12/0.37 tff(12,plain,
% 0.12/0.37 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.12/0.37 tff(13,plain,
% 0.12/0.37 (![C: $i, C1: $i] : (part_of(C1, C) <=> ![P: $i] : ((~incident_c(P, C1)) | incident_c(P, C)))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.12/0.37 tff(14,plain,(
% 0.12/0.37 ![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)))))),
% 0.12/0.37 inference(skolemize,[status(sab)],[13])).
% 0.12/0.37 tff(15,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.12/0.37 tff(16,plain,
% 0.12/0.37 (![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)))))))),
% 0.12/0.37 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.12/0.37 tff(17,plain,
% 0.12/0.37 ((~![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!14, C2!13), C3!12)) | ![P: $i] : ((~incident_c(P, sum(C1!14, C2!13))) | incident_c(P, C3!12)))) | (~(part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)))))))),
% 0.12/0.37 inference(quant_inst,[status(thm)],[])).
% 0.12/0.37 tff(18,plain,
% 0.12/0.37 (~((~((~part_of(sum(C1!14, C2!13), C3!12)) | ![P: $i] : ((~incident_c(P, sum(C1!14, C2!13))) | incident_c(P, C3!12)))) | (~(part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))))))),
% 0.12/0.37 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.37 tff(19,plain,
% 0.12/0.37 (((~((~part_of(sum(C1!14, C2!13), C3!12)) | ![P: $i] : ((~incident_c(P, sum(C1!14, C2!13))) | incident_c(P, C3!12)))) | (~(part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)))))) | (part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 ((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,plain,
% 0.12/0.38 ((~![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)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 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/sandbox/benchmark/theBenchmark.p','corollary_2_6_2')).
% 0.12/0.38 tff(24,plain,
% 0.12/0.38 (~![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))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (~![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))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 (~![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))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (~![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))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.12/0.38 tff(28,plain,(
% 0.12/0.38 ~((~(part_of(C1!14, C3!12) & part_of(C2!13, C3!12) & meet(P!11, C1!14, C2!13))) | part_of(sum(C1!14, C2!13), C3!12))),
% 0.12/0.38 inference(skolemize,[status(sab)],[27])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (~part_of(sum(C1!14, C2!13), C3!12)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 ((~(part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))))) | part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 ((~(part_of(sum(C1!14, C2!13), C3!12) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))))) | (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (~((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[31, 20])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(34,plain,
% 0.12/0.38 (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 ((~![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!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(36,plain,
% 0.12/0.38 (~((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[35, 16])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~(part_of(C2!13, C3!12) | (~((~incident_c(tptp_fun_P_0(C2!13, C3!12), C2!13)) | incident_c(tptp_fun_P_0(C2!13, C3!12), C3!12)))))) | ((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (part_of(C1!14, C3!12) & part_of(C2!13, C3!12) & meet(P!11, C1!14, C2!13)),
% 0.12/0.38 inference(or_elim,[status(thm)],[28])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (part_of(C2!13, C3!12)),
% 0.12/0.38 inference(and_elim,[status(thm)],[39])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 ((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | (~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 ((~((~part_of(C2!13, C3!12)) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12)))) | ![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[42, 38])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 (((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))) <=> ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 ((~![P: $i] : ((~incident_c(P, C2!13)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[46, 43, 34])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 ((~![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!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (~((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12))))))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[48, 16])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~(part_of(C1!14, C3!12) | (~((~incident_c(tptp_fun_P_0(C1!14, C3!12), C1!14)) | incident_c(tptp_fun_P_0(C1!14, C3!12), C3!12)))))) | ((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 ((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (part_of(C1!14, C3!12)),
% 0.12/0.38 inference(and_elim,[status(thm)],[39])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 ((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | (~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(54,plain,
% 0.12/0.38 ((~((~part_of(C1!14, C3!12)) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12)))) | ![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.12/0.38 tff(56,plain,
% 0.12/0.38 (((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))) <=> ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))) | ((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((~![P: $i] : ((~incident_c(P, C1!14)) | incident_c(P, C3!12))) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14)),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 55, 34])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 ((~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[60, 59, 47])).
% 0.12/0.38 tff(62,plain,
% 0.12/0.38 (((~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C3!12)) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(63,plain,
% 0.12/0.38 (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[62, 32])).
% 0.12/0.38 tff(64,plain,
% 0.12/0.38 ((~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) | (~incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))),
% 0.12/0.38 inference(tautology,[status(thm)],[])).
% 0.12/0.38 tff(65,plain,
% 0.12/0.38 (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[64, 63, 61])).
% 0.12/0.38 tff(66,plain,
% 0.12/0.38 (^[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)))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(67,plain,
% 0.12/0.38 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[66])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(pull_quant,[status(thm)],[])).
% 0.12/0.39 tff(69,plain,
% 0.12/0.39 (^[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))))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[69])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[70, 68])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[71, 67])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (^[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)))))))))),
% 0.12/0.39 inference(bind,[status(th)],[])).
% 0.12/0.39 tff(74,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(quant_intro,[status(thm)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 (![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))))))))),
% 0.12/0.39 inference(transitivity,[status(thm)],[74, 72])).
% 0.12/0.39 tff(76,plain,
% 0.12/0.39 (^[C: $i, C1: $i, C2: $i] : trans(monotonicity(rewrite(((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) <=> ((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))), trans(monotonicity(trans(monotonicity(rewrite((incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), rewrite((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))), ((~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))) <=> (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), rewrite(((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))), (((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))) <=> ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))))), rewrite((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))), ((((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2)))) & ((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2)))))) <=> (~((~((~(C = sum(C1, C2))) | ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(77,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[76])).
% 0.19/0.39 tff(78,plain,
% 0.19/0.39 (![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))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(79,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/sandbox/benchmark/Axioms/GEO004+0.ax','sum_defn')).
% 0.19/0.39 tff(80,plain,
% 0.19/0.39 (![C: $i, C1: $i, C2: $i] : ((C = sum(C1, C2)) <=> ![Q: $i] : (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.19/0.39 tff(81,plain,(
% 0.19/0.39 ![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))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[80])).
% 0.19/0.39 tff(82,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.19/0.39 tff(83,plain,
% 0.19/0.39 (![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))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[82, 75])).
% 0.19/0.39 tff(84,plain,
% 0.19/0.39 (((~![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!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(85,plain,
% 0.19/0.39 ((~(~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(86,plain,
% 0.19/0.39 (((~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) | $false) <=> (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(87,plain,
% 0.19/0.39 ((~$true) <=> $false),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(88,plain,
% 0.19/0.39 (($true | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))) <=> $true),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(89,plain,
% 0.19/0.39 ((~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))) <=> (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(90,plain,
% 0.19/0.39 ((sum(C1!14, C2!13) = sum(C1!14, C2!13)) <=> $true),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(91,plain,
% 0.19/0.39 (((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))) <=> ($true | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))))),
% 0.19/0.39 inference(monotonicity,[status(thm)],[90, 89])).
% 0.19/0.39 tff(92,plain,
% 0.19/0.39 (((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))) <=> $true),
% 0.19/0.39 inference(transitivity,[status(thm)],[91, 88])).
% 0.19/0.39 tff(93,plain,
% 0.19/0.39 ((~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[92])).
% 0.19/0.40 tff(94,plain,
% 0.19/0.40 ((~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[93, 87])).
% 0.19/0.40 tff(95,plain,
% 0.19/0.40 ((~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) <=> (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(96,plain,
% 0.19/0.40 (($false | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(97,plain,
% 0.19/0.40 ((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) <=> (~$true)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[90])).
% 0.19/0.40 tff(98,plain,
% 0.19/0.40 ((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) <=> $false),
% 0.19/0.40 inference(transitivity,[status(thm)],[97, 87])).
% 0.19/0.40 tff(99,plain,
% 0.19/0.40 (((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) <=> ($false | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[98])).
% 0.19/0.40 tff(100,plain,
% 0.19/0.40 (((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[99, 96])).
% 0.19/0.40 tff(101,plain,
% 0.19/0.40 ((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) <=> (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[100])).
% 0.19/0.40 tff(102,plain,
% 0.19/0.40 ((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) <=> (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[101, 95])).
% 0.19/0.40 tff(103,plain,
% 0.19/0.40 (((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))))) <=> ((~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))) | $false)),
% 0.19/0.40 inference(monotonicity,[status(thm)],[102, 94])).
% 0.19/0.40 tff(104,plain,
% 0.19/0.40 (((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))))) <=> (~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[103, 86])).
% 0.19/0.40 tff(105,plain,
% 0.19/0.40 ((~((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))))))) <=> (~(~(incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[104])).
% 0.19/0.40 tff(106,plain,
% 0.19/0.40 ((~((~((~(sum(C1!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13)))))))) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.19/0.40 inference(transitivity,[status(thm)],[105, 85])).
% 0.19/0.40 tff(107,plain,
% 0.19/0.40 (((~![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!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[106])).
% 0.19/0.41 tff(108,plain,
% 0.19/0.41 (((~![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!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))))))) <=> ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[107, 84])).
% 0.19/0.41 tff(109,plain,
% 0.19/0.41 ((~![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!14, C2!13) = sum(C1!14, C2!13))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13))))) | (~((sum(C1!14, C2!13) = sum(C1!14, C2!13)) | (~(incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C1!14) | incident_c(tptp_fun_Q_1(C2!13, C1!14, sum(C1!14, C2!13)), C2!13))))))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(110,plain,
% 0.19/0.41 ((~![C: $i, C1: $i, C2: $i, Q: $i] : (~((~((~(C = sum(C1, C2))) | (incident_c(Q, C) <=> (incident_c(Q, C1) | incident_c(Q, C2))))) | (~((C = sum(C1, C2)) | (~(incident_c(tptp_fun_Q_1(C2, C1, C), C) <=> (incident_c(tptp_fun_Q_1(C2, C1, C), C1) | incident_c(tptp_fun_Q_1(C2, C1, C), C2))))))))) | (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), sum(C1!14, C2!13)) <=> (incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C1!14) | incident_c(tptp_fun_P_0(sum(C1!14, C2!13), C3!12), C2!13)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.19/0.41 tff(111,plain,
% 0.19/0.41 ($false),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[110, 83, 65])).
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------