%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN082+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:22:38 AM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN082+2 : TPTP v9.0.0. Released v7.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 02:16:24 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(tptp_fun_Y24_0_type, type, (
% 0.18/0.39 tptp_fun_Y24_0: $i)).
% 0.18/0.39 tff(tptp_fun_Y22_2_type, type, (
% 0.18/0.39 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y6_9_type, type, (
% 0.18/0.39 tptp_fun_Y6_9: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y8_11_type, type, (
% 0.18/0.39 tptp_fun_Y8_11: $i > $i)).
% 0.18/0.39 tff(r1_type, type, (
% 0.18/0.39 r1: $i > $o)).
% 0.18/0.39 tff(r4_type, type, (
% 0.18/0.39 r4: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Y17_12_type, type, (
% 0.18/0.39 tptp_fun_Y17_12: $i > $i)).
% 0.18/0.39 tff(tptp_fun_Y23_3_type, type, (
% 0.18/0.39 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y16_10_type, type, (
% 0.18/0.39 tptp_fun_Y16_10: $i > $i)).
% 0.18/0.39 tff(r3_type, type, (
% 0.18/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Y2_7_type, type, (
% 0.18/0.39 tptp_fun_Y2_7: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y14_8_type, type, (
% 0.18/0.39 tptp_fun_Y14_8: ( $i * $i ) > $i)).
% 0.18/0.39 tff(r2_type, type, (
% 0.18/0.39 r2: ( $i * $i ) > $o)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5))) <=> ![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(6,plain,
% 0.18/0.39 (^[X5: $i] : quant_intro(proof_bind(^[Y8: $i] : rewrite((?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8)))), (?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[6])).
% 0.18/0.39 tff(8,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.18/0.39 tff(11,plain,(
% 0.18/0.39 ![X5: $i] : ((r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.39 inference(skolemize,[status(sab)],[10])).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (![X5: $i] : (r1(tptp_fun_Y17_12(X5)) & r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5)) & r1(tptp_fun_Y8_11(X5)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0))))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 ((r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y8_11(Y24!0)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.39 tff(27,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.18/0.39 tff(29,plain,
% 0.18/0.39 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.18/0.39 tff(30,plain,(
% 0.18/0.39 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.18/0.39 inference(transitivity,[status(sab)],[29])).
% 0.18/0.39 tff(31,plain,
% 0.18/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.18/0.39 tff(32,plain,
% 0.18/0.39 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.18/0.39 tff(33,plain,
% 0.18/0.39 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(34,plain,
% 0.18/0.39 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(35,plain,
% 0.18/0.39 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.18/0.39 tff(36,plain,
% 0.18/0.39 (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[35, 32, 19])).
% 0.18/0.39 tff(37,plain,
% 0.18/0.39 (((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0))) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(38,plain,
% 0.18/0.39 (tptp_fun_Y8_11(Y24!0) = Y24!0),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.18/0.39 tff(39,plain,
% 0.18/0.39 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(40,plain,
% 0.18/0.39 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[39, 15])).
% 0.18/0.39 tff(41,plain,
% 0.18/0.39 ((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)))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(42,plain,
% 0.18/0.39 (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))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.18/0.39 tff(43,plain,
% 0.18/0.39 (^[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))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(44,plain,
% 0.18/0.39 (![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)))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[43])).
% 0.18/0.39 tff(45,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[45])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(pull_quant,[status(thm)],[])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.40 tff(51,axiom,(![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4')).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.18/0.40 tff(54,plain,(
% 0.18/0.40 ![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)))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[53])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[55, 46])).
% 0.18/0.40 tff(57,plain,
% 0.18/0.40 (![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[56, 44])).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (((~![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)))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 ((~![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)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(60,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (~((~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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[60, 57, 42])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (((~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))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y8_11(Y24!0)),
% 0.18/0.40 inference(symmetry,[status(thm)],[63])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[65])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (^[X4: $i] : trans(der(?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), elim_unused(?[Y9: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))), (?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.40 tff(70,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.18/0.40 tff(73,plain,(
% 0.18/0.40 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.18/0.40 inference(skolemize,[status(sab)],[72])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(76,plain,
% 0.18/0.40 (~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[75, 74])).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(78,plain,
% 0.18/0.40 (r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 ((r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[81])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (^[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)))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(pull_quant,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (![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)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(87,axiom,(![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.40 tff(89,plain,(
% 0.18/0.40 ![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))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[88])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[90, 84])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[91, 82])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~![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_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(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_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 ((~![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_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 ((~![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_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (~((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (~((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[95, 92, 80])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (((~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (~(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))) | (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.40 inference(symmetry,[status(thm)],[98])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (Y24!0 = tptp_fun_Y8_11(Y24!0)),
% 0.18/0.40 inference(symmetry,[status(thm)],[38])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 (Y24!0 = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.40 inference(transitivity,[status(thm)],[100, 63])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~r3(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0), tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[102, 76])).
% 0.18/0.41 tff(104,plain,
% 0.18/0.41 ((r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(105,plain,
% 0.18/0.41 (r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (~((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[108, 32, 105])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (((~r1(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(111,plain,
% 0.18/0.41 (tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)) = Y24!0),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (Y24!0 = tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.18/0.41 inference(symmetry,[status(thm)],[111])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)), tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[112, 101])).
% 0.18/0.41 tff(114,plain,
% 0.18/0.41 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))) | (~r1(tptp_fun_Y8_11(Y24!0)))) | r1(tptp_fun_Y17_12(Y24!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (r1(tptp_fun_Y17_12(Y24!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[114, 15])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 ((r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_12(Y24!0)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[120, 32, 117])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0))) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (tptp_fun_Y17_12(Y24!0) = Y24!0),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (Y24!0 = tptp_fun_Y17_12(Y24!0)),
% 0.18/0.41 inference(symmetry,[status(thm)],[123])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[124])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (^[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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[126])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 (^[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)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[131])).
% 0.18/0.41 tff(133,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/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2a')).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[134, 130])).
% 0.18/0.41 tff(136,plain,(
% 0.18/0.41 ![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))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[135])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[136, 129])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[137, 127])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 ((~![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)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 (~((~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))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (((~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))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.18/0.41 tff(143,plain,
% 0.18/0.41 ((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)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 (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))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[143, 142])).
% 0.18/0.41 tff(145,plain,
% 0.18/0.41 (((~![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))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (((~((~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))))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(147,plain,
% 0.18/0.41 ((~(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))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 ((~((~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)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 (((~((~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)))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[148, 147])).
% 0.18/0.41 tff(150,plain,
% 0.18/0.41 (((~((~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))))))),
% 0.18/0.41 inference(transitivity,[status(thm)],[149, 146])).
% 0.18/0.41 tff(151,plain,
% 0.18/0.41 (((~![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)))))))),
% 0.18/0.41 inference(monotonicity,[status(thm)],[150])).
% 0.18/0.41 tff(152,plain,
% 0.18/0.41 (((~![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))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[151, 145])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 ((~![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)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 ((~![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)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (~((~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))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[154, 57, 144])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 (tptp_fun_Y6_9(Y24!0, Y24!0) = Y24!0),
% 0.18/0.42 inference(transitivity,[status(thm)],[157, 125, 64, 38])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[158])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0),
% 0.18/0.42 inference(transitivity,[status(thm)],[159, 113, 99, 64, 38])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 (r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[161, 140])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 ((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)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (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)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.18/0.42 tff(165,plain,
% 0.18/0.42 (((~![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)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 ((~![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)))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 ((~![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))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.18/0.42 tff(168,plain,
% 0.18/0.42 (~((~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)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[167, 92, 164])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 (((~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)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.18/0.42 tff(171,plain,
% 0.18/0.42 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y2_7(Y24!0, Y24!0)),
% 0.18/0.42 inference(symmetry,[status(thm)],[170])).
% 0.18/0.42 tff(172,plain,
% 0.18/0.42 (r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) <=> r1(tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.42 tff(173,plain,
% 0.18/0.42 (r1(tptp_fun_Y2_7(Y24!0, Y24!0)) <=> r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.18/0.42 inference(symmetry,[status(thm)],[172])).
% 0.18/0.42 tff(174,plain,
% 0.18/0.42 ((~r1(tptp_fun_Y2_7(Y24!0, Y24!0))) <=> (~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[173])).
% 0.18/0.42 tff(175,plain,
% 0.18/0.42 (r1(Y24!0) <=> r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[100])).
% 0.18/0.42 tff(176,plain,
% 0.18/0.42 (r1(tptp_fun_Y8_11(Y24!0)) <=> r1(Y24!0)),
% 0.18/0.42 inference(symmetry,[status(thm)],[175])).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 (r1(Y24!0)),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[17, 176])).
% 0.18/0.42 tff(178,plain,
% 0.18/0.42 (((~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, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(179,plain,
% 0.18/0.42 (r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[178, 140])).
% 0.18/0.42 tff(180,plain,
% 0.18/0.42 (((~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)))) | r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(181,plain,
% 0.18/0.42 (r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[180, 140])).
% 0.18/0.42 tff(182,plain,
% 0.18/0.42 (^[Y1: $i, Y2: $i, Y3: $i, Y4: $i] : trans(monotonicity(rewrite(((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))) <=> ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)))), (((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ((~r1(Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)))))), rewrite(((~r1(Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)))) <=> ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))), (((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(183,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[182])).
% 0.18/0.42 tff(184,plain,
% 0.18/0.42 (^[Y1: $i, Y2: $i, Y3: $i, Y4: $i] : refl(((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(185,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[184])).
% 0.18/0.42 tff(186,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i] : ![Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.42 inference(pull_quant,[status(thm)],[])).
% 0.18/0.42 tff(187,plain,
% 0.18/0.42 (^[Y1: $i, Y2: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y3: $i] : pull_quant(((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) <=> ![Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))), (![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) <=> ![Y3: $i] : ![Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))), pull_quant(![Y3: $i] : ![Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))) <=> ![Y3: $i, Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))), (![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))) <=> ![Y3: $i, Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))), (((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ((~r1(Y2)) | ![Y3: $i, Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))))), pull_quant(((~r1(Y2)) | ![Y3: $i, Y4: $i] : ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))), (((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(188,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i] : ![Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[187])).
% 0.18/0.42 tff(189,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[188, 186])).
% 0.18/0.42 tff(190,plain,
% 0.18/0.42 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[189, 185])).
% 0.18/0.43 tff(191,plain,
% 0.18/0.43 (^[Y1: $i, Y2: $i] : rewrite(((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(192,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[191])).
% 0.18/0.43 tff(193,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[192, 190])).
% 0.18/0.43 tff(194,plain,
% 0.18/0.43 (^[Y1: $i, Y2: $i] : rewrite(((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3))))) <=> ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(195,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3))))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[194])).
% 0.18/0.43 tff(196,plain,
% 0.18/0.43 (^[Y1: $i, Y2: $i] : rewrite((![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))) | (~r1(Y2))) <=> ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(197,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : (![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))) | (~r1(Y2))) <=> ![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[196])).
% 0.18/0.43 tff(198,plain,
% 0.18/0.43 ((~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))) <=> (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(199,plain,
% 0.18/0.43 ((~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & ?[Y5: $i] : (r1(Y5) & (Y2 = Y5)))) <=> (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2)))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(200,axiom,(~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & ?[Y5: $i] : (r1(Y5) & (Y2 = Y5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','xtimesoneeqzero')).
% 0.18/0.43 tff(201,plain,
% 0.18/0.43 (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.18/0.43 tff(202,plain,
% 0.18/0.43 (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[201, 198])).
% 0.18/0.43 tff(203,plain,
% 0.18/0.43 (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.18/0.43 tff(204,plain,
% 0.18/0.43 (~?[Y1: $i, Y2: $i] : (?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[203, 198])).
% 0.18/0.43 tff(205,plain,
% 0.18/0.43 (^[Y1: $i, Y2: $i] : nnf_neg(nnf_neg(proof_bind(^[Y3: $i] : nnf_neg(refl($oeq((~r4(Y1, Y3, Y2)), (~r4(Y1, Y3, Y2)))), nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r2(Y4, Y3))), (~(r1(Y4) & r2(Y4, Y3)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))), ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3))))), $oeq((~(r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3)))), ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3))))))), $oeq((~?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3)))), ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))))), refl($oeq((~r1(Y2)), (~r1(Y2)))), $oeq((~(?[Y3: $i] : (r4(Y1, Y3, Y2) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y3))) & r1(Y2))), (![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))) | (~r1(Y2)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(206,plain,(
% 0.18/0.43 ![Y1: $i, Y2: $i] : (![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))) | (~r1(Y2)))),
% 0.18/0.43 inference(nnf-neg,[status(sab)],[204, 205])).
% 0.18/0.43 tff(207,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y3)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[206, 197])).
% 0.18/0.43 tff(208,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i] : ((~r1(Y2)) | ![Y3: $i] : ((~r4(Y1, Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[207, 195])).
% 0.18/0.43 tff(209,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y2)) | ((~r4(Y1, Y3, Y2)) | ((~r1(Y4)) | (~r2(Y4, Y3)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[208, 193])).
% 0.18/0.43 tff(210,plain,
% 0.18/0.43 (![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[209, 183])).
% 0.18/0.43 tff(211,plain,
% 0.18/0.43 (((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | ((~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | (~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(212,plain,
% 0.18/0.43 (((~r1(Y24!0)) | (~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))) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0)))) <=> ((~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(213,plain,
% 0.18/0.43 (((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | ((~r1(Y24!0)) | (~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))) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | ((~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0)))))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[212])).
% 0.18/0.43 tff(214,plain,
% 0.18/0.43 (((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | ((~r1(Y24!0)) | (~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))) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | (~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[213, 211])).
% 0.18/0.43 tff(215,plain,
% 0.18/0.43 ((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | ((~r1(Y24!0)) | (~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))) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(216,plain,
% 0.18/0.43 ((~![Y1: $i, Y2: $i, Y3: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)) | (~r4(Y1, Y3, Y2)) | (~r1(Y2)))) | (~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))) | (~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.18/0.43 tff(217,plain,
% 0.18/0.43 ((~r1(Y24!0)) | (~r1(tptp_fun_Y2_7(Y24!0, Y24!0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[216, 210, 181, 179])).
% 0.18/0.43 tff(218,plain,
% 0.18/0.43 (~r1(tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[217, 177])).
% 0.18/0.43 tff(219,plain,
% 0.18/0.43 (~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[218, 174])).
% 0.18/0.43 tff(220,plain,
% 0.18/0.43 (((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))) | r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(221,plain,
% 0.18/0.43 ((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.18/0.43 tff(222,plain,
% 0.18/0.43 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(223,plain,
% 0.18/0.43 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(224,plain,
% 0.18/0.43 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.18/0.43 tff(225,plain,
% 0.18/0.43 ((~((~r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[224, 32])).
% 0.18/0.43 tff(226,plain,
% 0.18/0.43 (~(r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[225, 221])).
% 0.18/0.43 tff(227,plain,
% 0.18/0.43 ((r1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)) | (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(228,plain,
% 0.18/0.43 (~(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.18/0.43 tff(229,plain,
% 0.18/0.43 ($false),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[228, 160])).
% 0.18/0.43 % SZS output end Proof
% 0.18/0.44 % E exiting
%------------------------------------------------------------------------------