%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN076+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 05:22:37 AM UTC 2025
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUN076+2 : TPTP v9.0.0. Released v7.3.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:15:40 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 tff(r2_type, type, (
% 0.22/0.44 r2: ( $i * $i ) > $o)).
% 0.22/0.44 tff(tptp_fun_Y21_1_type, type, (
% 0.22/0.44 tptp_fun_Y21_1: $i > $i)).
% 0.22/0.44 tff(tptp_fun_Y24_0_type, type, (
% 0.22/0.44 tptp_fun_Y24_0: $i)).
% 0.22/0.44 tff(r1_type, type, (
% 0.22/0.44 r1: $i > $o)).
% 0.22/0.44 tff(r4_type, type, (
% 0.22/0.44 r4: ( $i * $i * $i ) > $o)).
% 0.22/0.44 tff(tptp_fun_Y2_7_type, type, (
% 0.22/0.44 tptp_fun_Y2_7: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y6_9_type, type, (
% 0.22/0.44 tptp_fun_Y6_9: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y8_11_type, type, (
% 0.22/0.44 tptp_fun_Y8_11: $i > $i)).
% 0.22/0.44 tff(tptp_fun_Y17_12_type, type, (
% 0.22/0.44 tptp_fun_Y17_12: $i > $i)).
% 0.22/0.44 tff(tptp_fun_Y22_2_type, type, (
% 0.22/0.44 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y16_10_type, type, (
% 0.22/0.44 tptp_fun_Y16_10: $i > $i)).
% 0.22/0.44 tff(r3_type, type, (
% 0.22/0.44 r3: ( $i * $i * $i ) > $o)).
% 0.22/0.44 tff(tptp_fun_Y23_3_type, type, (
% 0.22/0.44 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y14_8_type, type, (
% 0.22/0.44 tptp_fun_Y14_8: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y15_5_type, type, (
% 0.22/0.44 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y7_6_type, type, (
% 0.22/0.44 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.22/0.44 tff(tptp_fun_Y4_4_type, type, (
% 0.22/0.44 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.22/0.44 tff(1,plain,
% 0.22/0.44 (^[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))))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(2,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.22/0.44 tff(3,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(4,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.22/0.44 tff(5,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(rewrite,[status(thm)],[])).
% 0.22/0.44 tff(6,plain,
% 0.22/0.44 (^[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))))),
% 0.22/0.44 inference(bind,[status(th)],[])).
% 0.22/0.44 tff(7,plain,
% 0.22/0.44 (![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))),
% 0.22/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.22/0.44 tff(8,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.22/0.44 tff(9,plain,
% 0.22/0.44 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.22/0.44 tff(10,plain,
% 0.22/0.44 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.22/0.44 tff(11,plain,(
% 0.22/0.44 ![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)))),
% 0.22/0.44 inference(skolemize,[status(sab)],[10])).
% 0.22/0.44 tff(12,plain,
% 0.22/0.44 (![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)))),
% 0.22/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.22/0.44 tff(13,plain,
% 0.22/0.44 (![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)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.22/0.45 tff(14,plain,
% 0.22/0.45 ((~![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(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(15,plain,
% 0.22/0.45 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.22/0.45 tff(16,plain,
% 0.22/0.45 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(17,plain,
% 0.22/0.45 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.22/0.45 tff(18,plain,
% 0.22/0.45 ((r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(19,plain,
% 0.22/0.45 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.22/0.45 tff(20,plain,
% 0.22/0.45 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(21,plain,
% 0.22/0.45 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[20])).
% 0.22/0.45 tff(22,plain,
% 0.22/0.45 (^[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))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(23,plain,
% 0.22/0.45 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[22])).
% 0.22/0.45 tff(24,plain,
% 0.22/0.45 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(25,plain,
% 0.22/0.45 (^[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))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(26,plain,
% 0.22/0.45 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[25])).
% 0.22/0.45 tff(27,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.22/0.45 tff(28,plain,
% 0.22/0.45 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.22/0.45 tff(29,plain,
% 0.22/0.45 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.22/0.45 tff(30,plain,(
% 0.22/0.45 $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)))))),
% 0.22/0.45 inference(transitivity,[status(sab)],[29])).
% 0.22/0.45 tff(31,plain,
% 0.22/0.45 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.22/0.45 tff(32,plain,
% 0.22/0.45 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.22/0.45 tff(33,plain,
% 0.22/0.45 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(34,plain,
% 0.22/0.45 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(35,plain,
% 0.22/0.45 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.22/0.45 tff(36,plain,
% 0.22/0.45 (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.22/0.45 tff(37,plain,
% 0.22/0.45 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(38,plain,
% 0.22/0.45 (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.22/0.45 tff(39,plain,
% 0.22/0.45 (Y24!0 = tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.45 inference(symmetry,[status(thm)],[38])).
% 0.22/0.45 tff(40,plain,
% 0.22/0.45 (^[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)))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(41,plain,
% 0.22/0.45 (![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))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[40])).
% 0.22/0.45 tff(42,plain,
% 0.22/0.45 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(43,plain,
% 0.22/0.45 (^[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))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(44,plain,
% 0.22/0.45 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[43])).
% 0.22/0.45 tff(45,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.22/0.45 tff(46,plain,
% 0.22/0.45 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.22/0.45 tff(47,plain,
% 0.22/0.45 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.22/0.45 tff(48,plain,(
% 0.22/0.45 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.22/0.45 inference(skolemize,[status(sab)],[47])).
% 0.22/0.45 tff(49,plain,
% 0.22/0.45 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.22/0.45 tff(50,plain,
% 0.22/0.45 ((~![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))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(51,plain,
% 0.22/0.45 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.22/0.45 tff(52,plain,
% 0.22/0.45 (((~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)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(53,plain,
% 0.22/0.45 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.22/0.45 tff(54,plain,
% 0.22/0.45 ((r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(55,plain,
% 0.22/0.45 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.22/0.45 tff(56,plain,
% 0.22/0.45 (^[X13: $i, X14: $i, X15: $i] : refl(((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(57,plain,
% 0.22/0.45 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[56])).
% 0.22/0.45 tff(58,plain,
% 0.22/0.45 (^[X13: $i, X14: $i, X15: $i] : rewrite((((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.22/0.45 inference(bind,[status(th)],[])).
% 0.22/0.45 tff(59,plain,
% 0.22/0.45 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.22/0.45 inference(quant_intro,[status(thm)],[58])).
% 0.22/0.45 tff(60,plain,
% 0.22/0.45 (![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.22/0.45 inference(pull_quant,[status(thm)],[])).
% 0.22/0.45 tff(61,plain,
% 0.22/0.45 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22))) <=> ![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(62,axiom,(![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.22/0.45 tff(63,plain,
% 0.22/0.45 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.22/0.45 tff(64,plain,(
% 0.22/0.45 ![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.22/0.45 inference(skolemize,[status(sab)],[63])).
% 0.22/0.45 tff(65,plain,
% 0.22/0.45 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[64, 60])).
% 0.22/0.45 tff(66,plain,
% 0.22/0.45 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.22/0.45 tff(67,plain,
% 0.22/0.45 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[66, 57])).
% 0.22/0.45 tff(68,plain,
% 0.22/0.45 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(69,plain,
% 0.22/0.45 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(70,plain,
% 0.22/0.45 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.22/0.45 tff(71,plain,
% 0.22/0.45 (~((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[70, 67, 55])).
% 0.22/0.45 tff(72,plain,
% 0.22/0.45 (((~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(73,plain,
% 0.22/0.45 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[72, 71])).
% 0.22/0.45 tff(74,plain,
% 0.22/0.45 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 0.22/0.45 inference(symmetry,[status(thm)],[73])).
% 0.22/0.45 tff(75,plain,
% 0.22/0.45 (((~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))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(76,plain,
% 0.22/0.45 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[75, 51])).
% 0.22/0.45 tff(77,plain,
% 0.22/0.45 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(78,plain,
% 0.22/0.45 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.22/0.45 tff(79,plain,
% 0.22/0.45 (((~![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))))),
% 0.22/0.45 inference(rewrite,[status(thm)],[])).
% 0.22/0.45 tff(80,plain,
% 0.22/0.45 ((~![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))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(81,plain,
% 0.22/0.45 ((~![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)))),
% 0.22/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.22/0.45 tff(82,plain,
% 0.22/0.45 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[81, 32, 78])).
% 0.22/0.45 tff(83,plain,
% 0.22/0.45 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(84,plain,
% 0.22/0.45 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.22/0.45 tff(85,plain,
% 0.22/0.45 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 0.22/0.45 inference(symmetry,[status(thm)],[84])).
% 0.22/0.45 tff(86,plain,
% 0.22/0.45 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.22/0.45 inference(monotonicity,[status(thm)],[85])).
% 0.22/0.45 tff(87,plain,
% 0.22/0.45 ((~![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)))))),
% 0.22/0.45 inference(quant_inst,[status(thm)],[])).
% 0.22/0.45 tff(88,plain,
% 0.22/0.45 (~((~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))))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[87, 13])).
% 0.22/0.45 tff(89,plain,
% 0.22/0.45 (((~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))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(90,plain,
% 0.22/0.45 (r1(tptp_fun_Y8_11(Y24!0))),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.22/0.45 tff(91,plain,
% 0.22/0.45 ((r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y8_11(Y24!0)))),
% 0.22/0.45 inference(tautology,[status(thm)],[])).
% 0.22/0.45 tff(92,plain,
% 0.22/0.45 (r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.22/0.45 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.22/0.45 tff(93,plain,
% 0.22/0.45 (((~![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))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(94,plain,
% 0.22/0.46 ((~![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))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(95,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.22/0.46 tff(96,plain,
% 0.22/0.46 (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[95, 32, 92])).
% 0.22/0.46 tff(97,plain,
% 0.22/0.46 (((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0))) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(98,plain,
% 0.22/0.46 (tptp_fun_Y8_11(Y24!0) = Y24!0),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.22/0.46 tff(99,plain,
% 0.22/0.46 (((~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))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(100,plain,
% 0.22/0.46 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[99, 88])).
% 0.22/0.46 tff(101,plain,
% 0.22/0.46 ((r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(102,plain,
% 0.22/0.46 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.22/0.46 tff(103,plain,
% 0.22/0.46 (^[X16: $i, X17: $i, X18: $i] : refl(((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(104,plain,
% 0.22/0.46 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[103])).
% 0.22/0.46 tff(105,plain,
% 0.22/0.46 (^[X16: $i, X17: $i, X18: $i] : trans(monotonicity(rewrite((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) <=> (~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16)))))), rewrite(((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))) <=> (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))), (((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))))), rewrite(((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))), (((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(106,plain,
% 0.22/0.46 (![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[105])).
% 0.22/0.46 tff(107,plain,
% 0.22/0.46 (![X16: $i, X17: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(pull_quant,[status(thm)],[])).
% 0.22/0.46 tff(108,plain,
% 0.22/0.46 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23)))) <=> ![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(109,plain,
% 0.22/0.46 (^[X16: $i, X17: $i] : quant_intro(proof_bind(^[Y23: $i] : quant_intro(proof_bind(^[X18: $i] : rewrite((((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23)))))), (![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))))), (?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(110,plain,
% 0.22/0.46 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[109])).
% 0.22/0.46 tff(111,axiom,(![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_4')).
% 0.22/0.46 tff(112,plain,
% 0.22/0.46 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.22/0.46 tff(113,plain,
% 0.22/0.46 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.22/0.46 tff(114,plain,(
% 0.22/0.46 ![X16: $i, X17: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[113])).
% 0.22/0.46 tff(115,plain,
% 0.22/0.46 (![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.22/0.46 tff(116,plain,
% 0.22/0.46 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[115, 106])).
% 0.22/0.46 tff(117,plain,
% 0.22/0.46 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[116, 104])).
% 0.22/0.46 tff(118,plain,
% 0.22/0.46 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(119,plain,
% 0.22/0.46 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(120,plain,
% 0.22/0.46 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.22/0.46 tff(121,plain,
% 0.22/0.46 (~((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[120, 117, 102])).
% 0.22/0.46 tff(122,plain,
% 0.22/0.46 (((~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(123,plain,
% 0.22/0.46 (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.22/0.46 tff(124,plain,
% 0.22/0.46 (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y8_11(Y24!0)),
% 0.22/0.46 inference(symmetry,[status(thm)],[123])).
% 0.22/0.46 tff(125,plain,
% 0.22/0.46 (((~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))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(126,plain,
% 0.22/0.46 (r1(tptp_fun_Y17_12(Y24!0))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[125, 88])).
% 0.22/0.46 tff(127,plain,
% 0.22/0.46 ((r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_12(Y24!0)))),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(128,plain,
% 0.22/0.46 (r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.22/0.46 tff(129,plain,
% 0.22/0.46 (((~![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))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(130,plain,
% 0.22/0.46 ((~![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))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(131,plain,
% 0.22/0.46 ((~![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)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.22/0.46 tff(132,plain,
% 0.22/0.46 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[131, 32, 128])).
% 0.22/0.46 tff(133,plain,
% 0.22/0.46 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0))) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.22/0.46 inference(tautology,[status(thm)],[])).
% 0.22/0.46 tff(134,plain,
% 0.22/0.46 (tptp_fun_Y17_12(Y24!0) = Y24!0),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.22/0.46 tff(135,plain,
% 0.22/0.46 (Y24!0 = tptp_fun_Y17_12(Y24!0)),
% 0.22/0.46 inference(symmetry,[status(thm)],[134])).
% 0.22/0.46 tff(136,plain,
% 0.22/0.46 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.22/0.46 inference(monotonicity,[status(thm)],[135])).
% 0.22/0.46 tff(137,plain,
% 0.22/0.46 (^[X2: $i, X9: $i] : rewrite((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2))))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(138,plain,
% 0.22/0.46 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> ![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[137])).
% 0.22/0.46 tff(139,plain,
% 0.22/0.46 (^[X2: $i, X9: $i] : rewrite(((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(140,plain,
% 0.22/0.46 (![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> ![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[139])).
% 0.22/0.46 tff(141,plain,
% 0.22/0.46 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(142,plain,
% 0.22/0.46 (^[X2: $i, X9: $i] : quant_intro(proof_bind(^[Y2: $i] : rewrite((?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))))), (?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(143,plain,
% 0.22/0.46 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[142])).
% 0.22/0.46 tff(144,axiom,(![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2a')).
% 0.22/0.46 tff(145,plain,
% 0.22/0.46 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.22/0.47 tff(146,plain,
% 0.22/0.47 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.22/0.47 tff(147,plain,(
% 0.22/0.47 ![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[146])).
% 0.22/0.47 tff(148,plain,
% 0.22/0.47 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[147, 140])).
% 0.22/0.47 tff(149,plain,
% 0.22/0.47 (![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.22/0.47 tff(150,plain,
% 0.22/0.47 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(151,plain,
% 0.22/0.47 (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.22/0.47 tff(152,plain,
% 0.22/0.47 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(153,plain,
% 0.22/0.47 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.22/0.47 tff(154,plain,
% 0.22/0.47 ((r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(155,plain,
% 0.22/0.47 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.22/0.47 tff(156,plain,
% 0.22/0.47 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(157,plain,
% 0.22/0.47 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(158,plain,
% 0.22/0.47 ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) <=> (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(159,plain,
% 0.22/0.47 ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(160,plain,
% 0.22/0.47 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[159, 158])).
% 0.22/0.47 tff(161,plain,
% 0.22/0.47 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[160, 157])).
% 0.22/0.47 tff(162,plain,
% 0.22/0.47 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[161])).
% 0.22/0.47 tff(163,plain,
% 0.22/0.47 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[162, 156])).
% 0.22/0.47 tff(164,plain,
% 0.22/0.47 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(165,plain,
% 0.22/0.47 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.22/0.47 tff(166,plain,
% 0.22/0.47 (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[165, 117, 155])).
% 0.22/0.47 tff(167,plain,
% 0.22/0.47 (((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(168,plain,
% 0.22/0.47 (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.22/0.47 tff(169,plain,
% 0.22/0.47 (tptp_fun_Y6_9(Y24!0, Y24!0) = Y24!0),
% 0.22/0.47 inference(transitivity,[status(thm)],[168, 136, 124, 98])).
% 0.22/0.47 tff(170,plain,
% 0.22/0.47 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.22/0.47 inference(monotonicity,[status(thm)],[169])).
% 0.22/0.47 tff(171,plain,
% 0.22/0.47 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(172,plain,
% 0.22/0.47 (r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[171, 151])).
% 0.22/0.47 tff(173,plain,
% 0.22/0.47 ((r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)))),
% 0.22/0.47 inference(tautology,[status(thm)],[])).
% 0.22/0.47 tff(174,plain,
% 0.22/0.47 (r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.22/0.47 tff(175,plain,
% 0.22/0.47 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(176,plain,
% 0.22/0.47 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(177,plain,
% 0.22/0.47 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0)) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.22/0.48 tff(178,plain,
% 0.22/0.48 (~((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[177, 67, 174])).
% 0.22/0.48 tff(179,plain,
% 0.22/0.48 (((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~(tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(180,plain,
% 0.22/0.48 (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.22/0.48 tff(181,plain,
% 0.22/0.48 (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[180, 170, 86, 74, 39])).
% 0.22/0.48 tff(182,plain,
% 0.22/0.48 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(183,plain,
% 0.22/0.48 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[182, 15])).
% 0.22/0.48 tff(184,plain,
% 0.22/0.48 ((r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(185,plain,
% 0.22/0.48 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.22/0.48 tff(186,plain,
% 0.22/0.48 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(187,plain,
% 0.22/0.48 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(188,plain,
% 0.22/0.48 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.22/0.48 tff(189,plain,
% 0.22/0.48 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[188, 32, 185])).
% 0.22/0.48 tff(190,plain,
% 0.22/0.48 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0)),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(191,plain,
% 0.22/0.48 (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = Y24!0),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.22/0.48 tff(192,plain,
% 0.22/0.48 (Y24!0 = tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(symmetry,[status(thm)],[191])).
% 0.22/0.48 tff(193,plain,
% 0.22/0.48 (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[168, 136, 124, 98, 192])).
% 0.22/0.48 tff(194,plain,
% 0.22/0.48 (r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0)) <=> r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[193, 181])).
% 0.22/0.48 tff(195,plain,
% 0.22/0.48 (r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.22/0.48 inference(symmetry,[status(thm)],[194])).
% 0.22/0.48 tff(196,plain,
% 0.22/0.48 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(tautology,[status(thm)],[])).
% 0.22/0.48 tff(197,plain,
% 0.22/0.48 (r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[196, 15])).
% 0.22/0.48 tff(198,plain,
% 0.22/0.48 (r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[197, 195])).
% 0.22/0.48 tff(199,plain,
% 0.22/0.48 (^[Y1: $i, Y2: $i, Y3: $i] : refl(((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(200,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[199])).
% 0.22/0.48 tff(201,plain,
% 0.22/0.48 (^[Y1: $i, Y2: $i, Y3: $i] : rewrite(((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(202,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[201])).
% 0.22/0.48 tff(203,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[202, 200])).
% 0.22/0.48 tff(204,plain,
% 0.22/0.48 (^[Y1: $i, Y2: $i, Y3: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y6: $i] : rewrite(((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) <=> ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))), (![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) <=> ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))), ((![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1))) <=> (![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1))))), rewrite((![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1))) <=> ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))), ((![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1))) <=> ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(205,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : (![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[204])).
% 0.22/0.48 tff(206,plain,
% 0.22/0.48 ((~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))) <=> (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(207,plain,
% 0.22/0.48 ((~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y4: $i] : ((Y4 = Y1) & ?[Y6: $i] : (r4(Y6, Y2, Y4) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7))))) & ?[Y5: $i] : (r3(Y2, Y3, Y5) & (Y5 = Y1)))) <=> (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(208,axiom,(~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y4: $i] : ((Y4 = Y1) & ?[Y6: $i] : (r4(Y6, Y2, Y4) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7))))) & ?[Y5: $i] : (r3(Y2, Y3, Y5) & (Y5 = Y1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thereexistsanevennumber')).
% 0.22/0.48 tff(209,plain,
% 0.22/0.48 (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.22/0.48 tff(210,plain,
% 0.22/0.48 (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[209, 206])).
% 0.22/0.48 tff(211,plain,
% 0.22/0.48 (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.22/0.48 tff(212,plain,
% 0.22/0.48 (~?[Y1: $i, Y2: $i, Y3: $i] : (?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[211, 206])).
% 0.22/0.48 tff(213,plain,
% 0.22/0.48 (^[Y1: $i, Y2: $i, Y3: $i] : nnf_neg(nnf_neg(proof_bind(^[Y6: $i] : nnf_neg(refl($oeq((~r4(Y6, Y2, Y1)), (~r4(Y6, Y2, Y1)))), nnf_neg(proof_bind(^[Y7: $i] : nnf_neg(refl($oeq((~r2(Y7, Y6)), (~r2(Y7, Y6)))), nnf_neg(proof_bind(^[Y8: $i] : refl($oeq((~(r1(Y8) & r2(Y8, Y7))), (~(r1(Y8) & r2(Y8, Y7)))))), $oeq((~?[Y8: $i] : (r1(Y8) & r2(Y8, Y7))), ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))), $oeq((~(r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))), ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))))), $oeq((~?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))), ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7)))))), $oeq((~(r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7))))), ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7)))))))), $oeq((~?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7))))), ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))))), refl($oeq((~r3(Y2, Y3, Y1)), (~r3(Y2, Y3, Y1)))), $oeq((~(?[Y6: $i] : (r4(Y6, Y2, Y1) & ?[Y7: $i] : (r2(Y7, Y6) & ?[Y8: $i] : (r1(Y8) & r2(Y8, Y7)))) & r3(Y2, Y3, Y1))), (![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(214,plain,(
% 0.22/0.48 ![Y1: $i, Y2: $i, Y3: $i] : (![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : (~(r1(Y8) & r2(Y8, Y7))))) | (~r3(Y2, Y3, Y1)))),
% 0.22/0.48 inference(nnf-neg,[status(sab)],[212, 213])).
% 0.22/0.48 tff(215,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[214, 205])).
% 0.22/0.48 tff(216,plain,
% 0.22/0.48 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[215, 203])).
% 0.22/0.48 tff(217,plain,
% 0.22/0.48 (((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))) | ((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(218,plain,
% 0.22/0.48 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))) | ((~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(219,plain,
% 0.22/0.48 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y2, Y3, Y1)) | ![Y6: $i] : ((~r4(Y6, Y2, Y1)) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.22/0.48 tff(220,plain,
% 0.22/0.48 (![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[219, 216, 172])).
% 0.22/0.48 tff(221,plain,
% 0.22/0.48 (((~![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) | ((~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) <=> ((~![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(222,plain,
% 0.22/0.48 ((~![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) | ((~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(223,plain,
% 0.22/0.48 ((~![Y6: $i] : ((~r4(Y6, tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, Y6)) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.22/0.48 tff(224,plain,
% 0.22/0.48 ((~r4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y6_9(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | ![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[223, 220])).
% 0.22/0.48 tff(225,plain,
% 0.22/0.48 (![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[224, 198])).
% 0.22/0.48 tff(226,plain,
% 0.22/0.48 (^[X11: $i, X12: $i] : refl(((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(227,plain,
% 0.22/0.48 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[226])).
% 0.22/0.48 tff(228,plain,
% 0.22/0.48 (^[X11: $i, X12: $i] : rewrite((((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(229,plain,
% 0.22/0.48 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[228])).
% 0.22/0.48 tff(230,plain,
% 0.22/0.48 (![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.48 inference(pull_quant,[status(thm)],[])).
% 0.22/0.48 tff(231,plain,
% 0.22/0.48 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(232,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.22/0.48 tff(233,plain,
% 0.22/0.48 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.22/0.48 tff(234,plain,(
% 0.22/0.48 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[233])).
% 0.22/0.48 tff(235,plain,
% 0.22/0.48 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.22/0.48 tff(236,plain,
% 0.22/0.48 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[235, 229])).
% 0.22/0.48 tff(237,plain,
% 0.22/0.48 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[236, 227])).
% 0.22/0.48 tff(238,plain,
% 0.22/0.48 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(239,plain,
% 0.22/0.48 (($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(240,plain,
% 0.22/0.48 ((~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(241,plain,
% 0.22/0.48 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(242,plain,
% 0.22/0.48 ((~$true) <=> $false),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(243,plain,
% 0.22/0.48 ((tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) <=> $true),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(244,plain,
% 0.22/0.48 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (~$true)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[243])).
% 0.22/0.48 tff(245,plain,
% 0.22/0.48 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $false),
% 0.22/0.48 inference(transitivity,[status(thm)],[244, 242])).
% 0.22/0.48 tff(246,plain,
% 0.22/0.48 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[245])).
% 0.22/0.48 tff(247,plain,
% 0.22/0.48 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[246, 241])).
% 0.22/0.48 tff(248,plain,
% 0.22/0.48 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> (~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[247])).
% 0.22/0.48 tff(249,plain,
% 0.22/0.48 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[248, 240])).
% 0.22/0.48 tff(250,plain,
% 0.22/0.48 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true) <=> $true),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(251,plain,
% 0.22/0.48 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[243])).
% 0.22/0.48 tff(252,plain,
% 0.22/0.48 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $true),
% 0.22/0.48 inference(transitivity,[status(thm)],[251, 250])).
% 0.22/0.48 tff(253,plain,
% 0.22/0.48 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~$true)),
% 0.22/0.48 inference(monotonicity,[status(thm)],[252])).
% 0.22/0.48 tff(254,plain,
% 0.22/0.48 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> $false),
% 0.22/0.48 inference(transitivity,[status(thm)],[253, 242])).
% 0.22/0.48 tff(255,plain,
% 0.22/0.48 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> ($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[254, 249])).
% 0.22/0.48 tff(256,plain,
% 0.22/0.48 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(transitivity,[status(thm)],[255, 239])).
% 0.22/0.48 tff(257,plain,
% 0.22/0.48 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[256])).
% 0.22/0.48 tff(258,plain,
% 0.22/0.48 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[257, 238])).
% 0.22/0.48 tff(259,plain,
% 0.22/0.48 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(260,plain,
% 0.22/0.48 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.22/0.48 tff(261,plain,
% 0.22/0.48 (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[260, 237])).
% 0.22/0.48 tff(262,plain,
% 0.22/0.49 (((~![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0)))))) <=> ((~![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(263,plain,
% 0.22/0.49 ((~![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(264,plain,
% 0.22/0.49 ((~![Y7: $i] : ((~r2(Y7, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, Y7))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.22/0.49 tff(265,plain,
% 0.22/0.49 (![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[264, 261, 225])).
% 0.22/0.49 tff(266,plain,
% 0.22/0.49 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) <=> r1(Y24!0)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[74])).
% 0.22/0.49 tff(267,plain,
% 0.22/0.49 (r1(Y24!0) <=> r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.22/0.49 inference(symmetry,[status(thm)],[266])).
% 0.22/0.49 tff(268,plain,
% 0.22/0.49 (r1(tptp_fun_Y16_10(Y24!0)) <=> r1(Y24!0)),
% 0.22/0.49 inference(monotonicity,[status(thm)],[84])).
% 0.22/0.49 tff(269,plain,
% 0.22/0.49 (r1(Y24!0)),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[76, 268])).
% 0.22/0.49 tff(270,plain,
% 0.22/0.49 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[269, 267])).
% 0.22/0.49 tff(271,plain,
% 0.22/0.49 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1))))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(272,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[271])).
% 0.22/0.49 tff(273,plain,
% 0.22/0.49 (^[X1: $i, X8: $i] : rewrite(((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(274,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[273])).
% 0.22/0.49 tff(275,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(276,plain,
% 0.22/0.49 (^[X1: $i, X8: $i] : quant_intro(proof_bind(^[Y4: $i] : rewrite((?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))))), (?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))))),
% 0.22/0.49 inference(bind,[status(th)],[])).
% 0.22/0.49 tff(277,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.49 inference(quant_intro,[status(thm)],[276])).
% 0.22/0.49 tff(278,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.22/0.49 tff(279,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.22/0.49 tff(280,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.22/0.49 tff(281,plain,(
% 0.22/0.49 ![X1: $i, X8: $i] : ((r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1))))),
% 0.22/0.49 inference(skolemize,[status(sab)],[280])).
% 0.22/0.49 tff(282,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_5(X8, X1)) & r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_6(X8, X1)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.22/0.49 tff(283,plain,
% 0.22/0.49 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[282, 272])).
% 0.22/0.49 tff(284,plain,
% 0.22/0.49 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_5(X8, X1))) | (~r3(X1, tptp_fun_Y15_5(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_6(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_6(X8, X1)))))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(285,plain,
% 0.22/0.49 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.22/0.49 tff(286,plain,
% 0.22/0.49 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(287,plain,
% 0.22/0.49 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[286, 285])).
% 0.22/0.49 tff(288,plain,
% 0.22/0.49 ((r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(289,plain,
% 0.22/0.49 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.22/0.49 tff(290,plain,
% 0.22/0.49 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(291,plain,
% 0.22/0.49 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(292,plain,
% 0.22/0.49 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.22/0.49 tff(293,plain,
% 0.22/0.49 (~((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[292, 237, 289])).
% 0.22/0.49 tff(294,plain,
% 0.22/0.49 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~(tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.22/0.49 inference(tautology,[status(thm)],[])).
% 0.22/0.49 tff(295,plain,
% 0.22/0.49 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[294, 293])).
% 0.22/0.49 tff(296,plain,
% 0.22/0.49 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.22/0.49 inference(symmetry,[status(thm)],[295])).
% 0.22/0.49 tff(297,plain,
% 0.22/0.49 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.22/0.49 inference(monotonicity,[status(thm)],[74, 296])).
% 0.22/0.49 tff(298,plain,
% 0.22/0.49 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.22/0.49 inference(symmetry,[status(thm)],[297])).
% 0.22/0.49 tff(299,plain,
% 0.22/0.49 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[287, 298])).
% 0.22/0.49 tff(300,plain,
% 0.22/0.49 (((~![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.49 inference(rewrite,[status(thm)],[])).
% 0.22/0.49 tff(301,plain,
% 0.22/0.49 ((~![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.22/0.49 inference(quant_inst,[status(thm)],[])).
% 0.22/0.49 tff(302,plain,
% 0.22/0.49 ((~![Y8: $i] : ((~r1(Y8)) | (~r2(Y8, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.22/0.49 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.22/0.49 tff(303,plain,
% 0.22/0.49 ($false),
% 0.22/0.49 inference(unit_resolution,[status(thm)],[302, 299, 270, 265])).
% 0.22/0.49 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------