%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN086+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:39 AM UTC 2025
% Result : Theorem 0.11s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUN086+2 : TPTP v9.0.0. Released v7.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n004.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 02:16:08 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.39 % SZS status Theorem
% 0.11/0.39 % SZS output start Proof
% 0.11/0.39 tff(r2_type, type, (
% 0.11/0.39 r2: ( $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_Y21_1_type, type, (
% 0.11/0.39 tptp_fun_Y21_1: $i > $i)).
% 0.11/0.39 tff(tptp_fun_Y24_0_type, type, (
% 0.11/0.39 tptp_fun_Y24_0: $i)).
% 0.11/0.39 tff(tptp_fun_Y15_5_type, type, (
% 0.11/0.39 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.11/0.39 tff(r3_type, type, (
% 0.11/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_Y7_6_type, type, (
% 0.11/0.39 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y4_4_type, type, (
% 0.11/0.39 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.11/0.39 tff(r4_type, type, (
% 0.11/0.39 r4: ( $i * $i * $i ) > $o)).
% 0.11/0.39 tff(tptp_fun_Y2_7_type, type, (
% 0.11/0.39 tptp_fun_Y2_7: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y14_8_type, type, (
% 0.11/0.39 tptp_fun_Y14_8: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y22_2_type, type, (
% 0.11/0.39 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y6_9_type, type, (
% 0.11/0.39 tptp_fun_Y6_9: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y8_11_type, type, (
% 0.11/0.39 tptp_fun_Y8_11: $i > $i)).
% 0.11/0.39 tff(r1_type, type, (
% 0.11/0.39 r1: $i > $o)).
% 0.11/0.39 tff(tptp_fun_Y17_12_type, type, (
% 0.11/0.39 tptp_fun_Y17_12: $i > $i)).
% 0.11/0.39 tff(tptp_fun_Y23_3_type, type, (
% 0.11/0.39 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 0.11/0.39 tff(tptp_fun_Y16_10_type, type, (
% 0.11/0.39 tptp_fun_Y16_10: $i > $i)).
% 0.11/0.39 tff(1,plain,
% 0.11/0.39 (^[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))))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(2,plain,
% 0.11/0.39 (![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)))))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.11/0.39 tff(3,plain,
% 0.11/0.39 (^[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))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(4,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.11/0.39 tff(5,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.39 inference(rewrite,[status(thm)],[])).
% 0.11/0.39 tff(6,plain,
% 0.11/0.39 (^[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)))))),
% 0.11/0.39 inference(bind,[status(th)],[])).
% 0.11/0.39 tff(7,plain,
% 0.11/0.39 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[6])).
% 0.11/0.40 tff(8,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')).
% 0.11/0.40 tff(9,plain,
% 0.11/0.40 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.11/0.40 tff(10,plain,
% 0.11/0.40 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.11/0.40 tff(11,plain,(
% 0.11/0.40 ![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))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[10])).
% 0.11/0.40 tff(12,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.11/0.40 tff(13,plain,
% 0.11/0.40 (![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)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.11/0.40 tff(14,plain,
% 0.11/0.40 ((~![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)))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(15,plain,
% 0.11/0.40 (~((~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))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.11/0.40 tff(16,plain,
% 0.11/0.40 (((~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))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(17,plain,
% 0.11/0.40 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.11/0.40 tff(18,plain,
% 0.11/0.40 ((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)))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(19,plain,
% 0.11/0.40 (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))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.11/0.40 tff(20,plain,
% 0.11/0.40 (^[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)))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(21,plain,
% 0.11/0.40 (![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))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[20])).
% 0.11/0.40 tff(22,plain,
% 0.11/0.40 (^[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)))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(23,plain,
% 0.11/0.40 (![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))))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[22])).
% 0.11/0.40 tff(24,plain,
% 0.11/0.40 (![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))))),
% 0.11/0.40 inference(pull_quant,[status(thm)],[])).
% 0.11/0.40 tff(25,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(26,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')).
% 0.11/0.40 tff(27,plain,
% 0.11/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.11/0.40 tff(28,plain,(
% 0.11/0.40 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.11/0.40 inference(skolemize,[status(sab)],[27])).
% 0.11/0.40 tff(29,plain,
% 0.11/0.40 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.11/0.40 tff(30,plain,
% 0.11/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.11/0.40 tff(31,plain,
% 0.11/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.11/0.40 tff(32,plain,
% 0.11/0.40 (((~![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))))))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(33,plain,
% 0.11/0.40 ((~![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))))))),
% 0.11/0.40 inference(quant_inst,[status(thm)],[])).
% 0.11/0.40 tff(34,plain,
% 0.11/0.40 ((~![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)))))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.11/0.40 tff(35,plain,
% 0.11/0.40 (~((~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))))),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[34, 31, 19])).
% 0.11/0.40 tff(36,plain,
% 0.11/0.40 (((~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))),
% 0.11/0.40 inference(tautology,[status(thm)],[])).
% 0.11/0.40 tff(37,plain,
% 0.11/0.40 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.11/0.40 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.11/0.40 tff(38,plain,
% 0.11/0.40 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.11/0.40 inference(symmetry,[status(thm)],[37])).
% 0.11/0.40 tff(39,plain,
% 0.11/0.40 (r2(Y24!0, tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.11/0.40 inference(monotonicity,[status(thm)],[38])).
% 0.11/0.40 tff(40,plain,
% 0.11/0.40 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.11/0.40 inference(symmetry,[status(thm)],[39])).
% 0.11/0.40 tff(41,plain,
% 0.11/0.40 (r2(Y24!0, tptp_fun_Y21_1(Y24!0))),
% 0.11/0.40 inference(modus_ponens,[status(thm)],[17, 40])).
% 0.11/0.40 tff(42,plain,
% 0.11/0.40 (^[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))))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(43,plain,
% 0.11/0.40 (![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)))))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[42])).
% 0.11/0.40 tff(44,plain,
% 0.11/0.40 (^[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))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(45,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[44])).
% 0.11/0.40 tff(46,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(rewrite,[status(thm)],[])).
% 0.11/0.40 tff(47,plain,
% 0.11/0.40 (^[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)))))),
% 0.11/0.40 inference(bind,[status(th)],[])).
% 0.11/0.40 tff(48,plain,
% 0.11/0.40 (![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)))),
% 0.11/0.40 inference(quant_intro,[status(thm)],[47])).
% 0.11/0.40 tff(49,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')).
% 0.11/0.41 tff(50,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.11/0.41 tff(51,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.11/0.41 tff(52,plain,(
% 0.11/0.41 ![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))))),
% 0.11/0.41 inference(skolemize,[status(sab)],[51])).
% 0.11/0.41 tff(53,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.11/0.41 tff(54,plain,
% 0.11/0.41 (![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)))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[53, 43])).
% 0.11/0.41 tff(55,plain,
% 0.11/0.41 ((~![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)))))),
% 0.11/0.41 inference(quant_inst,[status(thm)],[])).
% 0.11/0.41 tff(56,plain,
% 0.11/0.41 (~((~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))))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[55, 54])).
% 0.11/0.41 tff(57,plain,
% 0.11/0.41 (((~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)))) | r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.11/0.41 inference(tautology,[status(thm)],[])).
% 0.11/0.41 tff(58,plain,
% 0.11/0.41 (r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[57, 56])).
% 0.11/0.41 tff(59,plain,
% 0.11/0.41 ((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)))),
% 0.11/0.41 inference(tautology,[status(thm)],[])).
% 0.11/0.41 tff(60,plain,
% 0.11/0.41 (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)))),
% 0.11/0.41 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.11/0.41 tff(61,plain,
% 0.11/0.41 (^[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)))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(62,plain,
% 0.11/0.41 (![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))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[61])).
% 0.11/0.41 tff(63,plain,
% 0.11/0.41 (^[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)))))))),
% 0.11/0.41 inference(bind,[status(th)],[])).
% 0.11/0.41 tff(64,plain,
% 0.11/0.41 (![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))))))),
% 0.11/0.41 inference(quant_intro,[status(thm)],[63])).
% 0.11/0.41 tff(65,plain,
% 0.11/0.41 (![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))))),
% 0.11/0.41 inference(pull_quant,[status(thm)],[])).
% 0.11/0.41 tff(66,plain,
% 0.11/0.41 (![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)))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(67,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')).
% 0.11/0.41 tff(68,plain,
% 0.11/0.41 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.11/0.41 tff(69,plain,(
% 0.11/0.41 ![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))))),
% 0.11/0.41 inference(skolemize,[status(sab)],[68])).
% 0.11/0.41 tff(70,plain,
% 0.11/0.41 (![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))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[69, 65])).
% 0.11/0.41 tff(71,plain,
% 0.11/0.41 (![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))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[70, 64])).
% 0.11/0.41 tff(72,plain,
% 0.11/0.41 (![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))))))),
% 0.11/0.41 inference(modus_ponens,[status(thm)],[71, 62])).
% 0.11/0.41 tff(73,plain,
% 0.11/0.41 (((~![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)))))))),
% 0.11/0.41 inference(rewrite,[status(thm)],[])).
% 0.11/0.41 tff(74,plain,
% 0.11/0.41 ((~![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)))))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(75,plain,
% 0.18/0.41 ((~![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))))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.18/0.41 tff(76,plain,
% 0.18/0.41 (~((~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)))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[75, 72, 60])).
% 0.18/0.41 tff(77,plain,
% 0.18/0.41 (((~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)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(78,plain,
% 0.18/0.41 (tptp_fun_Y2_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.18/0.41 tff(79,plain,
% 0.18/0.41 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y2_7(Y24!0, Y24!0)),
% 0.18/0.41 inference(symmetry,[status(thm)],[78])).
% 0.18/0.41 tff(80,plain,
% 0.18/0.41 (^[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))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(81,plain,
% 0.18/0.41 (![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)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.41 tff(82,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(83,plain,
% 0.18/0.41 (![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)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[82])).
% 0.18/0.41 tff(84,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(85,plain,
% 0.18/0.41 (^[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))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(86,plain,
% 0.18/0.41 (![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))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[85])).
% 0.18/0.41 tff(87,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')).
% 0.18/0.41 tff(88,plain,
% 0.18/0.41 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.18/0.41 tff(89,plain,
% 0.18/0.41 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.18/0.41 tff(90,plain,(
% 0.18/0.41 ![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)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[89])).
% 0.18/0.42 tff(91,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.18/0.42 tff(92,plain,
% 0.18/0.42 (![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)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.18/0.42 tff(93,plain,
% 0.18/0.42 ((~![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)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(94,plain,
% 0.18/0.42 (~((~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))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.18/0.42 tff(95,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(96,plain,
% 0.18/0.42 (r1(tptp_fun_Y8_11(Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.18/0.42 tff(97,plain,
% 0.18/0.42 ((r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y8_11(Y24!0)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(98,plain,
% 0.18/0.42 (r1(tptp_fun_Y8_11(Y24!0)) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.18/0.42 tff(99,plain,
% 0.18/0.42 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(100,plain,
% 0.18/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[99])).
% 0.18/0.42 tff(101,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(102,plain,
% 0.18/0.42 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[101])).
% 0.18/0.42 tff(103,plain,
% 0.18/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(104,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(105,plain,
% 0.18/0.42 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[104])).
% 0.18/0.42 tff(106,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.18/0.42 tff(107,plain,
% 0.18/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.18/0.42 tff(108,plain,
% 0.18/0.42 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.18/0.42 tff(109,plain,(
% 0.18/0.42 $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)))))),
% 0.18/0.42 inference(transitivity,[status(sab)],[108])).
% 0.18/0.42 tff(110,plain,
% 0.18/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.18/0.42 tff(111,plain,
% 0.18/0.42 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[110, 100])).
% 0.18/0.42 tff(112,plain,
% 0.18/0.42 (((~![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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(113,plain,
% 0.18/0.42 ((~![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))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(114,plain,
% 0.18/0.42 ((~![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)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.18/0.42 tff(115,plain,
% 0.18/0.42 (~((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[114, 111, 98])).
% 0.18/0.42 tff(116,plain,
% 0.18/0.42 (((~r1(tptp_fun_Y8_11(Y24!0))) | (~(tptp_fun_Y8_11(Y24!0) = Y24!0))) | (tptp_fun_Y8_11(Y24!0) = Y24!0)),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(117,plain,
% 0.18/0.42 (tptp_fun_Y8_11(Y24!0) = Y24!0),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.18/0.42 tff(118,plain,
% 0.18/0.42 (((~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))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(119,plain,
% 0.18/0.42 (r4(Y24!0, tptp_fun_Y17_12(Y24!0), tptp_fun_Y8_11(Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[118, 94])).
% 0.18/0.42 tff(120,plain,
% 0.18/0.42 ((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)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(121,plain,
% 0.18/0.42 (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))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.18/0.42 tff(122,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(123,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))))) <=> ![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)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[122])).
% 0.18/0.42 tff(124,plain,
% 0.18/0.42 (^[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)))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(125,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))))) <=> ![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)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[124])).
% 0.18/0.42 tff(126,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))))) <=> ![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)))))),
% 0.18/0.42 inference(pull_quant,[status(thm)],[])).
% 0.18/0.42 tff(127,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(128,plain,
% 0.18/0.42 (^[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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(129,plain,
% 0.18/0.42 (![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))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[128])).
% 0.18/0.42 tff(130,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')).
% 0.18/0.42 tff(131,plain,
% 0.18/0.42 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.18/0.42 tff(132,plain,
% 0.18/0.42 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[131, 127])).
% 0.18/0.42 tff(133,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)))))),
% 0.18/0.42 inference(skolemize,[status(sab)],[132])).
% 0.18/0.42 tff(134,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)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[133, 126])).
% 0.18/0.43 tff(135,plain,
% 0.18/0.43 (![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)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[134, 125])).
% 0.18/0.43 tff(136,plain,
% 0.18/0.43 (![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)))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[135, 123])).
% 0.18/0.43 tff(137,plain,
% 0.18/0.43 (((~![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)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(138,plain,
% 0.18/0.43 ((~![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)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(139,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.18/0.43 tff(140,plain,
% 0.18/0.43 (~((~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))))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[139, 136, 121])).
% 0.18/0.43 tff(141,plain,
% 0.18/0.43 (((~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))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(142,plain,
% 0.18/0.43 (tptp_fun_Y8_11(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.18/0.43 tff(143,plain,
% 0.18/0.43 (tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0) = tptp_fun_Y8_11(Y24!0)),
% 0.18/0.43 inference(symmetry,[status(thm)],[142])).
% 0.18/0.43 tff(144,plain,
% 0.18/0.43 (((~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))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(145,plain,
% 0.18/0.43 (r1(tptp_fun_Y17_12(Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[144, 94])).
% 0.18/0.43 tff(146,plain,
% 0.18/0.43 ((r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_12(Y24!0)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(147,plain,
% 0.18/0.43 (r1(tptp_fun_Y17_12(Y24!0)) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.18/0.43 tff(148,plain,
% 0.18/0.43 (((~![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))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(149,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(150,plain,
% 0.18/0.43 ((~![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)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.18/0.43 tff(151,plain,
% 0.18/0.43 (~((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0)))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[150, 111, 147])).
% 0.18/0.43 tff(152,plain,
% 0.18/0.43 (((~r1(tptp_fun_Y17_12(Y24!0))) | (~(tptp_fun_Y17_12(Y24!0) = Y24!0))) | (tptp_fun_Y17_12(Y24!0) = Y24!0)),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(153,plain,
% 0.18/0.43 (tptp_fun_Y17_12(Y24!0) = Y24!0),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.18/0.43 tff(154,plain,
% 0.18/0.43 (Y24!0 = tptp_fun_Y17_12(Y24!0)),
% 0.18/0.43 inference(symmetry,[status(thm)],[153])).
% 0.18/0.43 tff(155,plain,
% 0.18/0.43 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(Y24!0), Y24!0)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[154])).
% 0.18/0.43 tff(156,plain,
% 0.18/0.43 (((~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))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(157,plain,
% 0.18/0.43 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[156, 56])).
% 0.18/0.43 tff(158,plain,
% 0.18/0.43 ((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)))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(159,plain,
% 0.18/0.43 (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))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[158, 157])).
% 0.18/0.43 tff(160,plain,
% 0.18/0.43 (((~![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)))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(161,plain,
% 0.18/0.43 ((~![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)))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(162,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.18/0.44 tff(163,plain,
% 0.18/0.44 (~((~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))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[162, 136, 159])).
% 0.18/0.44 tff(164,plain,
% 0.18/0.44 (((~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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(165,plain,
% 0.18/0.44 (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.18/0.44 tff(166,plain,
% 0.18/0.44 (tptp_fun_Y6_9(Y24!0, Y24!0) = Y24!0),
% 0.18/0.44 inference(transitivity,[status(thm)],[165, 155, 143, 117])).
% 0.18/0.44 tff(167,plain,
% 0.18/0.44 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[166])).
% 0.18/0.44 tff(168,plain,
% 0.18/0.44 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 0.18/0.44 inference(symmetry,[status(thm)],[167])).
% 0.18/0.44 tff(169,plain,
% 0.18/0.44 (^[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)))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(170,plain,
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[169])).
% 0.18/0.44 tff(171,plain,
% 0.18/0.44 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(172,plain,
% 0.18/0.44 (^[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))))),
% 0.18/0.44 inference(bind,[status(th)],[])).
% 0.18/0.44 tff(173,plain,
% 0.18/0.44 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.44 inference(quant_intro,[status(thm)],[172])).
% 0.18/0.44 tff(174,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')).
% 0.18/0.44 tff(175,plain,
% 0.18/0.44 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.44 tff(176,plain,
% 0.18/0.44 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.18/0.44 tff(177,plain,(
% 0.18/0.44 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.18/0.44 inference(skolemize,[status(sab)],[176])).
% 0.18/0.44 tff(178,plain,
% 0.18/0.44 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.18/0.44 tff(179,plain,
% 0.18/0.44 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(180,plain,
% 0.18/0.44 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.18/0.44 tff(181,plain,
% 0.18/0.44 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r1(tptp_fun_Y16_10(Y24!0))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(182,plain,
% 0.18/0.44 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[181, 180])).
% 0.18/0.44 tff(183,plain,
% 0.18/0.44 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(184,plain,
% 0.18/0.44 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.18/0.44 tff(185,plain,
% 0.18/0.44 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(186,plain,
% 0.18/0.44 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(187,plain,
% 0.18/0.44 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.18/0.44 tff(188,plain,
% 0.18/0.44 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[187, 111, 184])).
% 0.18/0.44 tff(189,plain,
% 0.18/0.44 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(190,plain,
% 0.18/0.44 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.18/0.44 tff(191,plain,
% 0.18/0.44 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 0.18/0.44 inference(symmetry,[status(thm)],[190])).
% 0.18/0.44 tff(192,plain,
% 0.18/0.44 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.44 inference(monotonicity,[status(thm)],[191])).
% 0.18/0.44 tff(193,plain,
% 0.18/0.44 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.44 inference(symmetry,[status(thm)],[192])).
% 0.18/0.44 tff(194,plain,
% 0.18/0.44 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0))) | r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(195,plain,
% 0.18/0.44 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[194, 180])).
% 0.18/0.44 tff(196,plain,
% 0.18/0.44 ((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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(197,plain,
% 0.18/0.44 (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))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.18/0.44 tff(198,plain,
% 0.18/0.44 (((~![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))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(199,plain,
% 0.18/0.44 ((~![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))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(200,plain,
% 0.18/0.44 ((~![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)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.18/0.44 tff(201,plain,
% 0.18/0.44 (~((~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))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[200, 72, 197])).
% 0.18/0.44 tff(202,plain,
% 0.18/0.44 (((~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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(203,plain,
% 0.18/0.44 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.18/0.44 tff(204,plain,
% 0.18/0.44 (Y24!0 = tptp_fun_Y2_7(Y24!0, Y24!0)),
% 0.18/0.44 inference(transitivity,[status(thm)],[203, 193, 168, 79])).
% 0.18/0.44 tff(205,plain,
% 0.18/0.44 (((~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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(206,plain,
% 0.18/0.44 (r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[205, 56])).
% 0.18/0.44 tff(207,plain,
% 0.18/0.44 ((r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(208,plain,
% 0.18/0.44 (r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[207, 206])).
% 0.18/0.44 tff(209,plain,
% 0.18/0.44 (((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(210,plain,
% 0.18/0.44 ((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(211,plain,
% 0.18/0.44 ((~![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_Y14_8(Y24!0, Y24!0)) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.18/0.44 tff(212,plain,
% 0.18/0.44 (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[211, 31, 208])).
% 0.18/0.44 tff(213,plain,
% 0.18/0.44 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~(tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(214,plain,
% 0.18/0.44 (tptp_fun_Y14_8(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.18/0.44 tff(215,plain,
% 0.18/0.44 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y14_8(Y24!0, Y24!0)),
% 0.18/0.44 inference(symmetry,[status(thm)],[214])).
% 0.18/0.44 tff(216,plain,
% 0.18/0.44 (r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0) <=> r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[215, 204])).
% 0.18/0.44 tff(217,plain,
% 0.18/0.44 (r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0)) <=> r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)),
% 0.18/0.44 inference(symmetry,[status(thm)],[216])).
% 0.18/0.44 tff(218,plain,
% 0.18/0.44 (((~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))),
% 0.18/0.44 inference(tautology,[status(thm)],[])).
% 0.18/0.44 tff(219,plain,
% 0.18/0.45 (r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[218, 56])).
% 0.18/0.45 tff(220,plain,
% 0.18/0.45 (r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[219, 217])).
% 0.18/0.45 tff(221,plain,
% 0.18/0.45 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(222,plain,
% 0.18/0.45 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(223,plain,
% 0.18/0.45 ((~$true) <=> $false),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(224,plain,
% 0.18/0.45 ((r1(Y24!0) | $true) <=> $true),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(225,plain,
% 0.18/0.45 ((Y24!0 = Y24!0) <=> $true),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(226,plain,
% 0.18/0.45 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[225])).
% 0.18/0.45 tff(227,plain,
% 0.18/0.45 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.18/0.45 inference(transitivity,[status(thm)],[226, 224])).
% 0.18/0.45 tff(228,plain,
% 0.18/0.45 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[227])).
% 0.18/0.45 tff(229,plain,
% 0.18/0.45 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.18/0.45 inference(transitivity,[status(thm)],[228, 223])).
% 0.18/0.45 tff(230,plain,
% 0.18/0.45 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(231,plain,
% 0.18/0.45 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(232,plain,
% 0.18/0.45 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[225])).
% 0.18/0.45 tff(233,plain,
% 0.18/0.45 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.18/0.45 inference(transitivity,[status(thm)],[232, 223])).
% 0.18/0.45 tff(234,plain,
% 0.18/0.45 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[233])).
% 0.18/0.45 tff(235,plain,
% 0.18/0.45 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.18/0.45 inference(transitivity,[status(thm)],[234, 231])).
% 0.18/0.45 tff(236,plain,
% 0.18/0.45 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[235])).
% 0.18/0.45 tff(237,plain,
% 0.18/0.45 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.45 inference(transitivity,[status(thm)],[236, 230])).
% 0.18/0.45 tff(238,plain,
% 0.18/0.45 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.18/0.45 inference(monotonicity,[status(thm)],[237, 229])).
% 0.18/0.45 tff(239,plain,
% 0.18/0.45 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.45 inference(transitivity,[status(thm)],[238, 222])).
% 0.18/0.45 tff(240,plain,
% 0.18/0.45 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[239])).
% 0.18/0.45 tff(241,plain,
% 0.18/0.45 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.45 inference(transitivity,[status(thm)],[240, 221])).
% 0.18/0.45 tff(242,plain,
% 0.18/0.45 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(243,plain,
% 0.18/0.45 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[242, 241])).
% 0.18/0.45 tff(244,plain,
% 0.18/0.45 (r1(Y24!0)),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[243, 111])).
% 0.18/0.45 tff(245,plain,
% 0.18/0.45 (^[Y1: $i] : rewrite(((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(246,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[245])).
% 0.18/0.45 tff(247,plain,
% 0.18/0.45 (^[Y1: $i] : refl(((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(248,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[247])).
% 0.18/0.45 tff(249,plain,
% 0.18/0.45 (^[Y1: $i] : rewrite(((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(250,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[249])).
% 0.18/0.45 tff(251,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(transitivity,[status(thm)],[250, 248])).
% 0.18/0.45 tff(252,plain,
% 0.18/0.45 (^[Y1: $i] : rewrite(((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))) <=> ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(253,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[252])).
% 0.18/0.45 tff(254,plain,
% 0.18/0.45 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | (~r1(Y1))) <=> ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(255,plain,
% 0.18/0.45 (![Y1: $i] : (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | (~r1(Y1))) <=> ![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(quant_intro,[status(thm)],[254])).
% 0.18/0.45 tff(256,plain,
% 0.18/0.45 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(257,plain,
% 0.18/0.45 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(258,axiom,(~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerotimesoneeqzero')).
% 0.18/0.45 tff(259,plain,
% 0.18/0.45 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[258, 257])).
% 0.18/0.45 tff(260,plain,
% 0.18/0.45 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[259, 256])).
% 0.18/0.45 tff(261,plain,
% 0.18/0.45 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.18/0.45 tff(262,plain,
% 0.18/0.45 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[261, 256])).
% 0.18/0.45 tff(263,plain,
% 0.18/0.45 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : nnf_neg(nnf_neg(proof_bind(^[Y3: $i] : refl($oeq((~(r1(Y3) & r2(Y3, Y2))), (~(r1(Y3) & r2(Y3, Y2)))))), $oeq((~?[Y3: $i] : (r1(Y3) & r2(Y3, Y2))), ![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))))), nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r4(Y4, Y2, Y1))), (~(r1(Y4) & r4(Y4, Y2, Y1)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))), ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))), $oeq((~(?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1)))), (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))))), $oeq((~?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1)))), ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))))), refl($oeq((~r1(Y1)), (~r1(Y1)))), $oeq((~(?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & r1(Y1))), (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | (~r1(Y1)))))),
% 0.18/0.45 inference(bind,[status(th)],[])).
% 0.18/0.45 tff(264,plain,(
% 0.18/0.45 ![Y1: $i] : (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | (~r1(Y1)))),
% 0.18/0.45 inference(nnf-neg,[status(sab)],[262, 263])).
% 0.18/0.45 tff(265,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[264, 255])).
% 0.18/0.45 tff(266,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[265, 253])).
% 0.18/0.45 tff(267,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[266, 251])).
% 0.18/0.45 tff(268,plain,
% 0.18/0.45 (![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[267, 246])).
% 0.18/0.45 tff(269,plain,
% 0.18/0.45 (((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))) | ((~r1(Y24!0)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0))))) <=> ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))) | (~r1(Y24!0)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0))))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(270,plain,
% 0.18/0.45 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))) | ((~r1(Y24!0)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0))))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(271,plain,
% 0.18/0.45 ((~![Y1: $i] : ((~r1(Y1)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y1))))) | (~r1(Y24!0)) | ![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.18/0.45 tff(272,plain,
% 0.18/0.45 (![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[271, 268, 244])).
% 0.18/0.45 tff(273,plain,
% 0.18/0.45 (((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))) <=> ((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(274,plain,
% 0.18/0.45 (((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0))) <=> ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))),
% 0.18/0.45 inference(rewrite,[status(thm)],[])).
% 0.18/0.45 tff(275,plain,
% 0.18/0.45 (((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))) <=> ((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0))))),
% 0.18/0.45 inference(monotonicity,[status(thm)],[274])).
% 0.18/0.45 tff(276,plain,
% 0.18/0.45 (((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))) <=> ((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))),
% 0.18/0.45 inference(transitivity,[status(thm)],[275, 273])).
% 0.18/0.45 tff(277,plain,
% 0.18/0.45 ((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r1(Y24!0)) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0)))),
% 0.18/0.45 inference(quant_inst,[status(thm)],[])).
% 0.18/0.45 tff(278,plain,
% 0.18/0.45 ((~![Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r1(Y4)) | (~r4(Y4, Y2, Y24!0)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0))),
% 0.18/0.45 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.18/0.45 tff(279,plain,
% 0.18/0.45 ((~r2(Y24!0, tptp_fun_Y21_1(Y24!0))) | (~r4(Y24!0, tptp_fun_Y21_1(Y24!0), Y24!0))),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[278, 244, 272])).
% 0.18/0.45 tff(280,plain,
% 0.18/0.45 ($false),
% 0.18/0.45 inference(unit_resolution,[status(thm)],[279, 220, 41])).
% 0.18/0.45 % SZS output end Proof
% 0.18/0.46 % E exiting
%------------------------------------------------------------------------------