%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN059+2 : TPTP v9.0.0. Bugfixed v7.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:22:35 AM UTC 2025
% Result : Theorem 0.18s 0.36s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : NUN059+2 : TPTP v9.0.0. Bugfixed v7.4.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n004.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 02:10:38 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.18/0.36 % SZS status Theorem
% 0.18/0.36 % SZS output start Proof
% 0.18/0.36 tff(r4_type, type, (
% 0.18/0.36 r4: ( $i * $i * $i ) > $o)).
% 0.18/0.36 tff(tptp_fun_Y24_0_type, type, (
% 0.18/0.36 tptp_fun_Y24_0: $i)).
% 0.18/0.36 tff(tptp_fun_Y8_11_type, type, (
% 0.18/0.36 tptp_fun_Y8_11: $i > $i)).
% 0.18/0.36 tff(tptp_fun_Y17_12_type, type, (
% 0.18/0.36 tptp_fun_Y17_12: $i > $i)).
% 0.18/0.36 tff(r1_type, type, (
% 0.18/0.36 r1: $i > $o)).
% 0.18/0.36 tff(r3_type, type, (
% 0.18/0.36 r3: ( $i * $i * $i ) > $o)).
% 0.18/0.36 tff(tptp_fun_Y16_10_type, type, (
% 0.18/0.36 tptp_fun_Y16_10: $i > $i)).
% 0.18/0.36 tff(1,plain,
% 0.18/0.36 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5))))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(2,plain,
% 0.18/0.36 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.36 tff(3,plain,
% 0.18/0.36 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(4,plain,
% 0.18/0.36 (![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.36 tff(5,plain,
% 0.18/0.36 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.36 inference(rewrite,[status(thm)],[])).
% 0.18/0.36 tff(6,plain,
% 0.18/0.36 (^[X5: $i] : quant_intro(proof_bind(^[Y8: $i] : rewrite((?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)))), (?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))))),
% 0.18/0.36 inference(bind,[status(th)],[])).
% 0.18/0.36 tff(7,plain,
% 0.18/0.36 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.36 tff(8,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.18/0.36 tff(9,plain,
% 0.18/0.36 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.36 tff(10,plain,
% 0.18/0.36 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.36 tff(11,plain,(
% 0.18/0.36 ![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.36 inference(skolemize,[status(sab)],[10])).
% 0.18/0.36 tff(12,plain,
% 0.18/0.36 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.36 tff(13,plain,
% 0.18/0.36 (![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.18/0.36 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.18/0.36 tff(14,plain,
% 0.18/0.36 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))))),
% 0.18/0.36 inference(quant_inst,[status(thm)],[])).
% 0.18/0.36 tff(15,plain,
% 0.18/0.36 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0))))),
% 0.18/0.36 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.18/0.37 tff(16,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(17,plain,
% 0.18/0.37 (r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.18/0.37 tff(18,plain,
% 0.18/0.37 ((r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y8_11(Y24!0)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(19,plain,
% 0.18/0.37 (r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.18/0.37 tff(20,plain,
% 0.18/0.37 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(21,plain,
% 0.18/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.37 tff(22,plain,
% 0.18/0.37 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(23,plain,
% 0.18/0.37 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.37 tff(24,plain,
% 0.18/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(25,plain,
% 0.18/0.37 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(26,plain,
% 0.18/0.37 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.37 tff(27,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.18/0.37 tff(28,plain,
% 0.18/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.37 tff(29,plain,
% 0.18/0.37 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.37 tff(30,plain,(
% 0.18/0.37 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.18/0.37 inference(transitivity,[status(sab)],[29])).
% 0.18/0.37 tff(31,plain,
% 0.18/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.37 tff(32,plain,
% 0.18/0.37 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.18/0.37 tff(33,plain,
% 0.18/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(34,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(35,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.37 tff(36,plain,
% 0.18/0.37 (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.18/0.37 tff(37,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0))) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(38,plain,
% 0.18/0.37 (tptp_fun_Y8_11(Y24!0) = Y24!0),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.37 tff(39,plain,
% 0.18/0.37 (Y24!0 = tptp_fun_Y8_11(Y24!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[38])).
% 0.18/0.37 tff(40,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y17_12(Y24!0))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(41,plain,
% 0.18/0.37 (r1(tptp_fun_Y17_12(Y24!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[40, 15])).
% 0.18/0.37 tff(42,plain,
% 0.18/0.37 ((r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_12(Y24!0)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(43,plain,
% 0.18/0.37 (r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.37 tff(44,plain,
% 0.18/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(45,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(46,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.18/0.37 tff(47,plain,
% 0.18/0.37 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[46, 32, 43])).
% 0.18/0.37 tff(48,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0))) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(49,plain,
% 0.18/0.37 (tptp_fun_Y17_12(Y24!0) = Y24!0),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.37 tff(50,plain,
% 0.18/0.37 (Y24!0 = tptp_fun_Y17_12(Y24!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[49])).
% 0.18/0.37 tff(51,plain,
% 0.18/0.37 (r4(Y24!0, Y24!0, Y24!0) <=> r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.37 inference(monotonicity,[status(thm)],[50, 39])).
% 0.18/0.37 tff(52,plain,
% 0.18/0.37 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) <=> r4(Y24!0, Y24!0, Y24!0)),
% 0.18/0.37 inference(symmetry,[status(thm)],[51])).
% 0.18/0.37 tff(53,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(54,plain,
% 0.18/0.37 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[53, 15])).
% 0.18/0.37 tff(55,plain,
% 0.18/0.37 (r4(Y24!0, Y24!0, Y24!0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[54, 52])).
% 0.18/0.37 tff(56,plain,
% 0.18/0.37 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(57,plain,
% 0.18/0.37 (![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[56])).
% 0.18/0.37 tff(58,plain,
% 0.18/0.37 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(59,plain,
% 0.18/0.37 (^[X4: $i] : trans(der(?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), elim_unused(?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), (?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(60,plain,
% 0.18/0.37 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[59])).
% 0.18/0.37 tff(61,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.18/0.37 tff(62,plain,
% 0.18/0.37 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.18/0.37 tff(63,plain,
% 0.18/0.37 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.18/0.37 tff(64,plain,(
% 0.18/0.37 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.18/0.37 inference(skolemize,[status(sab)],[63])).
% 0.18/0.37 tff(65,plain,
% 0.18/0.37 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.18/0.37 tff(66,plain,
% 0.18/0.37 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(67,plain,
% 0.18/0.37 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.18/0.37 tff(68,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r1(tptp_fun_Y16_10(Y24!0))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(69,plain,
% 0.18/0.37 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.18/0.37 tff(70,plain,
% 0.18/0.37 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(71,plain,
% 0.18/0.37 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.18/0.37 tff(72,plain,
% 0.18/0.37 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(rewrite,[status(thm)],[])).
% 0.18/0.37 tff(73,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.18/0.37 inference(quant_inst,[status(thm)],[])).
% 0.18/0.37 tff(74,plain,
% 0.18/0.37 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.37 tff(75,plain,
% 0.18/0.37 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[74, 32, 71])).
% 0.18/0.37 tff(76,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(77,plain,
% 0.18/0.37 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.18/0.37 tff(78,plain,
% 0.18/0.37 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) <=> r3(Y24!0, Y24!0, Y24!0)),
% 0.18/0.37 inference(monotonicity,[status(thm)],[77])).
% 0.18/0.37 tff(79,plain,
% 0.18/0.37 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.37 inference(tautology,[status(thm)],[])).
% 0.18/0.37 tff(80,plain,
% 0.18/0.37 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.37 inference(unit_resolution,[status(thm)],[79, 67])).
% 0.18/0.37 tff(81,plain,
% 0.18/0.37 (r3(Y24!0, Y24!0, Y24!0)),
% 0.18/0.37 inference(modus_ponens,[status(thm)],[80, 78])).
% 0.18/0.37 tff(82,plain,
% 0.18/0.37 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))), (((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), rewrite(((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)))), (((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6))))), (((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y4)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)))))), rewrite(((~r4(Y2, Y2, Y4)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))), (((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(83,plain,
% 0.18/0.37 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.37 tff(84,plain,
% 0.18/0.37 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : refl(((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.18/0.37 inference(bind,[status(th)],[])).
% 0.18/0.37 tff(85,plain,
% 0.18/0.37 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.37 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.37 tff(86,plain,
% 0.18/0.37 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ![Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.37 inference(pull_quant,[status(thm)],[])).
% 0.18/0.37 tff(87,plain,
% 0.18/0.37 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y6: $i] : pull_quant(((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), (![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i] : ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), pull_quant(![Y6: $i] : ![Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))), (![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), (((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y4)) | ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))), pull_quant(((~r4(Y2, Y2, Y4)) | ![Y6: $i, Y7: $i] : ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))), (((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(88,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ![Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[87])).
% 0.18/0.38 tff(89,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[88, 86])).
% 0.18/0.38 tff(90,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[89, 85])).
% 0.18/0.38 tff(91,plain,
% 0.18/0.38 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : rewrite(((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(92,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[91])).
% 0.18/0.38 tff(93,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(transitivity,[status(thm)],[92, 90])).
% 0.18/0.38 tff(94,plain,
% 0.18/0.38 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : rewrite(((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(95,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(quant_intro,[status(thm)],[94])).
% 0.18/0.38 tff(96,plain,
% 0.18/0.38 ((~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(97,plain,
% 0.18/0.38 ((~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))) <=> (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(98,axiom,(~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (?[Y5: $i] : (r4(Y2, Y2, Y5) & (Y4 = Y5)) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fermattothepoweroftwo')).
% 0.18/0.38 tff(99,plain,
% 0.18/0.38 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.38 tff(100,plain,
% 0.18/0.38 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[99, 96])).
% 0.18/0.38 tff(101,plain,
% 0.18/0.38 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.18/0.38 tff(102,plain,
% 0.18/0.38 (~?[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : (r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[101, 96])).
% 0.18/0.38 tff(103,plain,
% 0.18/0.38 (^[Y1: $i, Y3: $i, Y2: $i, Y4: $i] : nnf_neg(refl($oeq((~r4(Y2, Y2, Y4)), (~r4(Y2, Y2, Y4)))), nnf_neg(proof_bind(^[Y6: $i] : nnf_neg(refl($oeq((~r4(Y3, Y3, Y6)), (~r4(Y3, Y3, Y6)))), nnf_neg(proof_bind(^[Y7: $i] : refl($oeq((~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))), (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))), $oeq((~?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))), ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), $oeq((~(r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))), ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))))), $oeq((~?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))), ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))), $oeq((~(r4(Y2, Y2, Y4) & ?[Y6: $i] : (r4(Y3, Y3, Y6) & ?[Y7: $i] : (r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4))))), ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))))),
% 0.18/0.38 inference(bind,[status(th)],[])).
% 0.18/0.38 tff(104,plain,(
% 0.18/0.38 ![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : (~(r4(Y1, Y1, Y7) & r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(nnf-neg,[status(sab)],[102, 103])).
% 0.18/0.38 tff(105,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y4)) | ![Y6: $i] : ((~r4(Y3, Y3, Y6)) | ![Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[104, 95])).
% 0.18/0.38 tff(106,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y2, Y2, Y4)) | ((~r4(Y3, Y3, Y6)) | ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)))))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[105, 93])).
% 0.18/0.38 tff(107,plain,
% 0.18/0.38 (![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[106, 83])).
% 0.18/0.38 tff(108,plain,
% 0.18/0.38 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(109,plain,
% 0.18/0.38 (((~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))) <=> ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.18/0.38 inference(rewrite,[status(thm)],[])).
% 0.18/0.38 tff(110,plain,
% 0.18/0.38 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | ((~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))))),
% 0.18/0.38 inference(monotonicity,[status(thm)],[109])).
% 0.18/0.38 tff(111,plain,
% 0.18/0.38 (((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))) <=> ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.18/0.38 inference(transitivity,[status(thm)],[110, 108])).
% 0.18/0.38 tff(112,plain,
% 0.18/0.38 ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | ((~r4(Y24!0, Y24!0, Y24!0)) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0)))),
% 0.18/0.38 inference(quant_inst,[status(thm)],[])).
% 0.18/0.38 tff(113,plain,
% 0.18/0.38 ((~![Y1: $i, Y3: $i, Y2: $i, Y4: $i, Y6: $i, Y7: $i] : ((~r4(Y1, Y1, Y7)) | (~r3(Y7, Y6, Y4)) | (~r4(Y3, Y3, Y6)) | (~r4(Y2, Y2, Y4)))) | (~r3(Y24!0, Y24!0, Y24!0)) | (~r4(Y24!0, Y24!0, Y24!0))),
% 0.18/0.38 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.18/0.38 tff(114,plain,
% 0.18/0.38 (~r4(Y24!0, Y24!0, Y24!0)),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[113, 107, 81])).
% 0.18/0.38 tff(115,plain,
% 0.18/0.38 ($false),
% 0.18/0.38 inference(unit_resolution,[status(thm)],[114, 55])).
% 0.18/0.38 % SZS output end Proof
% 0.18/0.38 % E exiting
%------------------------------------------------------------------------------