%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO085+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Sat Jun 21 05:05:33 AM UTC 2025
% Result : Theorem 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO085+1 : TPTP v9.0.0. Released v2.4.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n013.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 14:16:53 EDT 2025
% 0.17/0.32 % CPUTime :
% 0.17/0.37 % SZS status Theorem
% 0.17/0.37 % SZS output start Proof
% 0.17/0.37 tff(tptp_fun_Q_9_type, type, (
% 0.17/0.37 tptp_fun_Q_9: ( $i * $i ) > $i)).
% 0.17/0.37 tff(tptp_fun_C_11_type, type, (
% 0.17/0.37 tptp_fun_C_11: $i)).
% 0.17/0.37 tff(tptp_fun_P_5_type, type, (
% 0.17/0.37 tptp_fun_P_5: $i > $i)).
% 0.17/0.37 tff(end_point_type, type, (
% 0.17/0.37 end_point: ( $i * $i ) > $o)).
% 0.17/0.37 tff(open_type, type, (
% 0.17/0.37 open: $i > $o)).
% 0.17/0.37 tff(1,plain,
% 0.17/0.37 (^[C: $i] : refl((~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))) <=> (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(2,plain,
% 0.17/0.37 (![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))) <=> ![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.37 tff(3,plain,
% 0.17/0.37 (^[C: $i] : rewrite((~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))) <=> (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(4,plain,
% 0.17/0.37 (![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))) <=> ![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.37 tff(5,plain,
% 0.17/0.37 (![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C)))))) <=> ![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(transitivity,[status(thm)],[4, 2])).
% 0.17/0.37 tff(6,plain,
% 0.17/0.37 (^[C: $i] : trans(monotonicity(rewrite((open(C) | ![P: $i] : (~end_point(P, C))) <=> (open(C) | ![P: $i] : (~end_point(P, C)))), ((((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C)))) <=> (((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C)))))), rewrite((((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C)))) <=> (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))), ((((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C)))) <=> (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(7,plain,
% 0.17/0.37 (![C: $i] : (((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C)))) <=> ![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.37 tff(8,plain,
% 0.17/0.37 (![C: $i] : (open(C) <=> ?[P: $i] : end_point(P, C)) <=> ![C: $i] : (open(C) <=> ?[P: $i] : end_point(P, C))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(9,axiom,(![C: $i] : (open(C) <=> ?[P: $i] : end_point(P, C))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','open_defn')).
% 0.17/0.37 tff(10,plain,
% 0.17/0.37 (![C: $i] : (open(C) <=> ?[P: $i] : end_point(P, C))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.17/0.37 tff(11,plain,(
% 0.17/0.37 ![C: $i] : (((~open(C)) | end_point(tptp_fun_P_5(C), C)) & (open(C) | ![P: $i] : (~end_point(P, C))))),
% 0.17/0.37 inference(skolemize,[status(sab)],[10])).
% 0.17/0.37 tff(12,plain,
% 0.17/0.37 (![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.17/0.37 tff(13,plain,
% 0.17/0.37 (![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.17/0.37 tff(14,plain,
% 0.17/0.37 ((~![C: $i] : (~((~((~open(C)) | end_point(tptp_fun_P_5(C), C))) | (~(open(C) | ![P: $i] : (~end_point(P, C))))))) | (~((~((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))) | (~(open(C!11) | ![P: $i] : (~end_point(P, C!11))))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(15,plain,
% 0.17/0.37 (~((~((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))) | (~(open(C!11) | ![P: $i] : (~end_point(P, C!11)))))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.17/0.37 tff(16,plain,
% 0.17/0.37 (((~((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))) | (~(open(C!11) | ![P: $i] : (~end_point(P, C!11))))) | ((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(17,plain,
% 0.17/0.37 ((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11)),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.17/0.37 tff(18,plain,
% 0.17/0.37 ((open(C!11) & ![P: $i, Q: $i] : (~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11)))) <=> (open(C!11) & ![P: $i, Q: $i] : (~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(19,plain,
% 0.17/0.37 ((~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C)))) <=> (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(20,plain,
% 0.17/0.37 ((~![C: $i] : (open(C) => ?[P: $i, Q: $i] : (((~(P = Q)) & end_point(P, C)) & end_point(Q, C)))) <=> (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(21,axiom,(~![C: $i] : (open(C) => ?[P: $i, Q: $i] : (((~(P = Q)) & end_point(P, C)) & end_point(Q, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','theorem_2_7_1')).
% 0.17/0.37 tff(22,plain,
% 0.17/0.37 (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.17/0.37 tff(23,plain,
% 0.17/0.37 (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[22, 19])).
% 0.17/0.37 tff(24,plain,
% 0.17/0.37 (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.17/0.37 tff(25,plain,
% 0.17/0.37 (~![C: $i] : ((~open(C)) | ?[P: $i, Q: $i] : ((~(P = Q)) & end_point(P, C) & end_point(Q, C)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.17/0.37 tff(26,plain,
% 0.17/0.37 (open(C!11) & ![P: $i, Q: $i] : (~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.17/0.37 tff(27,plain,
% 0.17/0.37 (open(C!11)),
% 0.17/0.37 inference(and_elim,[status(thm)],[26])).
% 0.17/0.37 tff(28,plain,
% 0.17/0.37 ((~((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))) | (~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11)),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(29,plain,
% 0.17/0.37 ((~((~open(C!11)) | end_point(tptp_fun_P_5(C!11), C!11))) | end_point(tptp_fun_P_5(C!11), C!11)),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.17/0.37 tff(30,plain,
% 0.17/0.37 (end_point(tptp_fun_P_5(C!11), C!11)),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[29, 17])).
% 0.17/0.37 tff(31,plain,
% 0.17/0.37 (^[C: $i, P: $i] : refl(((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))) <=> ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(32,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[31])).
% 0.17/0.37 tff(33,plain,
% 0.17/0.37 (^[C: $i, P: $i] : rewrite(((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C))))) <=> ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C))))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(34,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C))))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[33])).
% 0.17/0.37 tff(35,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(36,plain,
% 0.17/0.37 (^[C: $i, P: $i] : rewrite((end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(37,plain,
% 0.17/0.37 (![C: $i, P: $i] : (end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q)))) <=> ![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[36])).
% 0.17/0.37 tff(38,axiom,(![C: $i, P: $i] : (end_point(P, C) => ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))), file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax','c6')).
% 0.17/0.37 tff(39,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.17/0.37 tff(40,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | ?[Q: $i] : (end_point(Q, C) & (~(P = Q))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[39, 35])).
% 0.17/0.37 tff(41,plain,(
% 0.17/0.37 ![C: $i, P: $i] : ((~end_point(P, C)) | (end_point(tptp_fun_Q_9(P, C), C) & (~(P = tptp_fun_Q_9(P, C)))))),
% 0.17/0.37 inference(skolemize,[status(sab)],[40])).
% 0.17/0.37 tff(42,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[41, 34])).
% 0.17/0.37 tff(43,plain,
% 0.17/0.37 (![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[42, 32])).
% 0.17/0.37 tff(44,plain,
% 0.17/0.37 (((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | ((~end_point(tptp_fun_P_5(C!11), C!11)) | (~((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)))))) <=> ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)))))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(45,plain,
% 0.17/0.37 ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | ((~end_point(tptp_fun_P_5(C!11), C!11)) | (~((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)))))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(46,plain,
% 0.17/0.37 ((~![C: $i, P: $i] : ((~end_point(P, C)) | (~((~end_point(tptp_fun_Q_9(P, C), C)) | (P = tptp_fun_Q_9(P, C)))))) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11))))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.17/0.37 tff(47,plain,
% 0.17/0.37 (~((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[46, 43, 30])).
% 0.17/0.37 tff(48,plain,
% 0.17/0.37 (((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11))) | (~(tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)))),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(49,plain,
% 0.17/0.37 (~(tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11))),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.17/0.37 tff(50,plain,
% 0.17/0.37 (((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11))) | end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)),
% 0.17/0.37 inference(tautology,[status(thm)],[])).
% 0.17/0.37 tff(51,plain,
% 0.17/0.37 (end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)),
% 0.17/0.37 inference(unit_resolution,[status(thm)],[50, 47])).
% 0.17/0.37 tff(52,plain,
% 0.17/0.37 (^[P: $i, Q: $i] : refl(((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))) <=> ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(53,plain,
% 0.17/0.37 (![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))) <=> ![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[52])).
% 0.17/0.37 tff(54,plain,
% 0.17/0.37 (^[P: $i, Q: $i] : trans(monotonicity(rewrite(((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11)) <=> (~((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))))), ((~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11))) <=> (~(~((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))))))), rewrite((~(~((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11))))) <=> ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))), ((~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11))) <=> ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))))),
% 0.17/0.37 inference(bind,[status(th)],[])).
% 0.17/0.37 tff(55,plain,
% 0.17/0.37 (![P: $i, Q: $i] : (~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11))) <=> ![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))),
% 0.17/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.17/0.37 tff(56,plain,
% 0.17/0.37 (![P: $i, Q: $i] : (~((~(P = Q)) & end_point(P, C!11) & end_point(Q, C!11)))),
% 0.17/0.37 inference(and_elim,[status(thm)],[26])).
% 0.17/0.37 tff(57,plain,
% 0.17/0.37 (![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.17/0.37 tff(58,plain,
% 0.17/0.37 (![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))),
% 0.17/0.37 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.17/0.37 tff(59,plain,
% 0.17/0.37 (((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | ((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)))) <=> ((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(60,plain,
% 0.17/0.37 (((tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11))) <=> ((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)))),
% 0.17/0.37 inference(rewrite,[status(thm)],[])).
% 0.17/0.37 tff(61,plain,
% 0.17/0.37 (((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | ((tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)))) <=> ((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | ((~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11))))),
% 0.17/0.37 inference(monotonicity,[status(thm)],[60])).
% 0.17/0.37 tff(62,plain,
% 0.17/0.37 (((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | ((tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)))) <=> ((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)))),
% 0.17/0.37 inference(transitivity,[status(thm)],[61, 59])).
% 0.17/0.37 tff(63,plain,
% 0.17/0.37 ((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | ((tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)))),
% 0.17/0.37 inference(quant_inst,[status(thm)],[])).
% 0.17/0.37 tff(64,plain,
% 0.17/0.37 ((~![P: $i, Q: $i] : ((P = Q) | (~end_point(P, C!11)) | (~end_point(Q, C!11)))) | (~end_point(tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11), C!11)) | (tptp_fun_P_5(C!11) = tptp_fun_Q_9(tptp_fun_P_5(C!11), C!11)) | (~end_point(tptp_fun_P_5(C!11), C!11))),
% 0.17/0.38 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.17/0.38 tff(65,plain,
% 0.17/0.38 ($false),
% 0.17/0.38 inference(unit_resolution,[status(thm)],[64, 58, 30, 51, 49])).
% 0.17/0.38 % SZS output end Proof
% 0.17/0.38 % E exiting
%------------------------------------------------------------------------------