%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN081+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN081+2 : TPTP v9.0.0. Released v7.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.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 02:17:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(r2_type, type, (
% 0.20/0.50 r2: ( $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_Y21_1_type, type, (
% 0.20/0.50 tptp_fun_Y21_1: $i > $i)).
% 0.20/0.50 tff(tptp_fun_Y24_0_type, type, (
% 0.20/0.50 tptp_fun_Y24_0: $i)).
% 0.20/0.50 tff(r1_type, type, (
% 0.20/0.50 r1: $i > $o)).
% 0.20/0.50 tff(tptp_fun_Y4_4_type, type, (
% 0.20/0.50 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_Y15_5_type, type, (
% 0.20/0.50 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 0.20/0.50 tff(r3_type, type, (
% 0.20/0.50 r3: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_Y7_6_type, type, (
% 0.20/0.50 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_Y23_3_type, type, (
% 0.20/0.50 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_Y22_2_type, type, (
% 0.20/0.50 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_Y16_10_type, type, (
% 0.20/0.50 tptp_fun_Y16_10: $i > $i)).
% 0.20/0.50 tff(tptp_fun_Y8_11_type, type, (
% 0.20/0.50 tptp_fun_Y8_11: $i > $i)).
% 0.20/0.50 tff(r4_type, type, (
% 0.20/0.50 r4: ( $i * $i * $i ) > $o)).
% 0.20/0.50 tff(tptp_fun_Y17_12_type, type, (
% 0.20/0.50 tptp_fun_Y17_12: $i > $i)).
% 0.20/0.50 tff(1,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(2,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(4,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (^[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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.50 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')).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.50 tff(11,plain,(
% 0.20/0.50 ![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))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[10])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 ((~![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(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[14, 13])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r3(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[16, 15])).
% 0.20/0.50 tff(18,plain,
% 0.20/0.50 ((r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(19,plain,
% 0.20/0.50 (r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.50 tff(20,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(21,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.50 tff(22,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(23,plain,
% 0.20/0.50 (![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))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.50 tff(24,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(pull_quant,[status(thm)],[])).
% 0.20/0.50 tff(25,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 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')).
% 0.20/0.50 tff(27,plain,
% 0.20/0.50 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.50 tff(28,plain,(
% 0.20/0.50 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[27])).
% 0.20/0.50 tff(29,plain,
% 0.20/0.50 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.20/0.50 tff(30,plain,
% 0.20/0.50 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[29, 23])).
% 0.20/0.50 tff(31,plain,
% 0.20/0.50 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[30, 21])).
% 0.20/0.50 tff(32,plain,
% 0.20/0.50 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(33,plain,
% 0.20/0.50 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 (~((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[34, 31, 19])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 (((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~(tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(37,plain,
% 0.20/0.51 (tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[36, 35])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[37])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[42])).
% 0.20/0.51 tff(44,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')).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.51 tff(47,plain,(
% 0.20/0.51 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 0.20/0.51 inference(skolemize,[status(sab)],[46])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.51 tff(51,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(52,plain,
% 0.20/0.51 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.51 tff(53,plain,
% 0.20/0.51 ((r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(54,plain,
% 0.20/0.51 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.51 tff(55,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(56,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.51 tff(57,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(58,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[57])).
% 0.20/0.51 tff(59,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(pull_quant,[status(thm)],[])).
% 0.20/0.51 tff(60,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(61,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')).
% 0.20/0.51 tff(62,plain,
% 0.20/0.51 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.20/0.51 tff(63,plain,(
% 0.20/0.51 ![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))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[62])).
% 0.20/0.51 tff(64,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.20/0.51 tff(65,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[64, 58])).
% 0.20/0.51 tff(66,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[65, 56])).
% 0.20/0.51 tff(67,plain,
% 0.20/0.51 (((~![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_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(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_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(68,plain,
% 0.20/0.51 ((~![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_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(69,plain,
% 0.20/0.51 ((~![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_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.51 tff(70,plain,
% 0.20/0.51 (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[69, 66, 54])).
% 0.20/0.51 tff(71,plain,
% 0.20/0.51 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(72,plain,
% 0.20/0.51 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.51 tff(73,plain,
% 0.20/0.51 (tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 0.20/0.51 inference(symmetry,[status(thm)],[72])).
% 0.20/0.51 tff(74,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(75,plain,
% 0.20/0.51 (r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[74, 50])).
% 0.20/0.51 tff(76,plain,
% 0.20/0.51 ((r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(77,plain,
% 0.20/0.51 (r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.51 tff(78,plain,
% 0.20/0.51 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(79,plain,
% 0.20/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.51 tff(80,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(81,plain,
% 0.20/0.51 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.51 tff(82,plain,
% 0.20/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(83,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(84,plain,
% 0.20/0.51 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[83])).
% 0.20/0.51 tff(85,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.20/0.51 tff(86,plain,
% 0.20/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.51 tff(87,plain,
% 0.20/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.20/0.51 tff(88,plain,(
% 0.20/0.51 $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)))))),
% 0.20/0.51 inference(transitivity,[status(sab)],[87])).
% 0.20/0.51 tff(89,plain,
% 0.20/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.20/0.51 tff(90,plain,
% 0.20/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.20/0.51 tff(91,plain,
% 0.20/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(92,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(93,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.51 tff(94,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[93, 90, 77])).
% 0.20/0.51 tff(95,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0))) | (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(96,plain,
% 0.20/0.51 (tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[95, 94])).
% 0.20/0.51 tff(97,plain,
% 0.20/0.51 (Y24!0 = tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(symmetry,[status(thm)],[96])).
% 0.20/0.51 tff(98,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(99,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.51 tff(100,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(101,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.51 tff(102,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(103,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(104,plain,
% 0.20/0.51 (![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))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.51 tff(105,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')).
% 0.20/0.51 tff(106,plain,
% 0.20/0.51 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.51 tff(107,plain,
% 0.20/0.51 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[106, 102])).
% 0.20/0.51 tff(108,plain,(
% 0.20/0.51 ![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)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[107])).
% 0.20/0.51 tff(109,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[108, 101])).
% 0.20/0.51 tff(110,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[109, 99])).
% 0.20/0.51 tff(111,plain,
% 0.20/0.51 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))) | r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[113, 112])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 ((r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[119, 90, 116])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[123, 112])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 ((r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[125, 124])).
% 0.20/0.51 tff(127,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(128,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[127])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(pull_quant,[status(thm)],[])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 (^[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))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(134,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.51 tff(135,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')).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.51 tff(137,plain,
% 0.20/0.51 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.20/0.51 tff(138,plain,(
% 0.20/0.51 ![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)))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[137])).
% 0.20/0.51 tff(139,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.20/0.51 tff(140,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[139, 130])).
% 0.20/0.51 tff(141,plain,
% 0.20/0.51 (![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)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[140, 128])).
% 0.20/0.51 tff(142,plain,
% 0.20/0.51 (((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(143,plain,
% 0.20/0.51 ((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(144,plain,
% 0.20/0.51 ((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.51 tff(145,plain,
% 0.20/0.51 (~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[144, 141, 126])).
% 0.20/0.51 tff(146,plain,
% 0.20/0.51 (((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(147,plain,
% 0.20/0.51 (tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[146, 145])).
% 0.20/0.51 tff(148,plain,
% 0.20/0.51 (tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(symmetry,[status(thm)],[147])).
% 0.20/0.51 tff(149,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(Y24!0))))) | r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(150,plain,
% 0.20/0.51 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[149, 112])).
% 0.20/0.51 tff(151,plain,
% 0.20/0.51 ((r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(152,plain,
% 0.20/0.51 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[155, 90, 152])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 (tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[157, 156])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 (Y24!0 = tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.51 inference(symmetry,[status(thm)],[158])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[160, 110])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 (r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 ((r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 (r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 (~((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[168, 90, 165])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[172, 161])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 ((r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 (r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (((~![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(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))) | (~(r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(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(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))) | (~(r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 ((~![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(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))) | (~(r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 ((~![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(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))) | (~(r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (~((~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[178, 141, 175])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 (((~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.52 inference(symmetry,[status(thm)],[181])).
% 0.20/0.52 tff(183,plain,
% 0.20/0.52 ((~![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))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[183, 48])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (((~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)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 ((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))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (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))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (((~![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))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 ((~![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))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 ((~![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)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 (~((~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))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[191, 66, 188])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (((~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))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r4(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[195, 161])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 ((r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 (r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[201, 90, 198])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (((~r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))) | (~(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 (Y24!0 = tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.52 inference(symmetry,[status(thm)],[204])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[205, 194])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(transitivity,[status(thm)],[206, 182, 171, 159])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(transitivity,[status(thm)],[208, 148, 122, 97])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y16_10(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[209])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 ((~![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(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[211, 13])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 ((r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 (((~![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_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(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_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 ((~![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_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 ((~![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_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[219, 66, 216])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 (tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 0.20/0.52 inference(transitivity,[status(thm)],[222, 210, 73])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 (tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[223])).
% 0.20/0.52 tff(225,plain,
% 0.20/0.52 (((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 (r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[225, 212])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 ((r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 (r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[227, 226])).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(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(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (~((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[231, 31, 228])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (((~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 (((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[235, 212])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 ((r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.20/0.52 tff(239,plain,
% 0.20/0.52 (((~![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_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(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_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 ((~![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_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 ((~![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_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[241, 66, 238])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 (tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 (tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(symmetry,[status(thm)],[244])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 (((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y7_6(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[246, 212])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 ((r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(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(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (~((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[252, 31, 249])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (((~r2(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 (tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[254, 253])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 (tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(symmetry,[status(thm)],[255])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 0.20/0.53 inference(transitivity,[status(thm)],[208, 148, 122])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 (tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(Y24!0)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[257])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[258])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(transitivity,[status(thm)],[259, 256])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y15_5(tptp_fun_Y23_3(tptp_fun_Y23_3(Y24!0, Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[260])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (((~![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)))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![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)))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(263,plain,
% 0.20/0.53 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 (((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![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)))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[263])).
% 0.20/0.53 tff(265,plain,
% 0.20/0.53 (((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![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)))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[264, 262])).
% 0.20/0.53 tff(266,plain,
% 0.20/0.53 ((~![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(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(267,plain,
% 0.20/0.53 ((~![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)))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.20/0.53 tff(268,plain,
% 0.20/0.53 (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[267, 13])).
% 0.20/0.53 tff(269,plain,
% 0.20/0.53 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(270,plain,
% 0.20/0.53 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[269, 268])).
% 0.20/0.53 tff(271,plain,
% 0.20/0.53 ((r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(272,plain,
% 0.20/0.53 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.20/0.53 tff(273,plain,
% 0.20/0.53 (((~![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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(274,plain,
% 0.20/0.53 ((~![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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(275,plain,
% 0.20/0.53 ((~![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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.20/0.53 tff(276,plain,
% 0.20/0.53 (~((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[275, 66, 272])).
% 0.20/0.53 tff(277,plain,
% 0.20/0.53 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(278,plain,
% 0.20/0.53 (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[277, 276])).
% 0.20/0.53 tff(279,plain,
% 0.20/0.53 (tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))),
% 0.20/0.53 inference(transitivity,[status(thm)],[278, 261, 245, 234, 224])).
% 0.20/0.53 tff(280,plain,
% 0.20/0.53 (tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[279])).
% 0.20/0.53 tff(281,plain,
% 0.20/0.53 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(282,plain,
% 0.20/0.53 (r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[281, 268])).
% 0.20/0.53 tff(283,plain,
% 0.20/0.53 ((r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(284,plain,
% 0.20/0.53 (r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.20/0.53 tff(285,plain,
% 0.20/0.53 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(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(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(286,plain,
% 0.20/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(287,plain,
% 0.20/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.53 tff(288,plain,
% 0.20/0.53 (~((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[287, 31, 284])).
% 0.20/0.53 tff(289,plain,
% 0.20/0.53 (((~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(290,plain,
% 0.20/0.53 (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[289, 288])).
% 0.20/0.53 tff(291,plain,
% 0.20/0.53 (tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[290, 280, 38])).
% 0.20/0.53 tff(292,plain,
% 0.20/0.53 (r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) <=> r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[291])).
% 0.20/0.53 tff(293,plain,
% 0.20/0.53 (r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y15_5(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[292])).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 (r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[17, 293])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 (((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y7_6(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 (r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[295, 268])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 (^[Y1: $i, Y2: $i, Y3: $i] : refl(((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[297])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 (^[Y1: $i, Y2: $i, Y3: $i] : rewrite(((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[299])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[300, 298])).
% 0.20/0.54 tff(302,plain,
% 0.20/0.54 (^[Y1: $i, Y2: $i, Y3: $i] : rewrite(((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6)))))) <=> ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(303,plain,
% 0.20/0.54 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[302])).
% 0.20/0.54 tff(304,plain,
% 0.20/0.54 ((~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))) <=> (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(305,plain,
% 0.20/0.54 ((~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y4: $i] : ((Y3 = Y4) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))))) <=> (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(306,axiom,(~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y4: $i] : ((Y3 = Y4) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xplusyeqthree')).
% 0.20/0.54 tff(307,plain,
% 0.20/0.54 (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.54 tff(308,plain,
% 0.20/0.54 (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[307, 304])).
% 0.20/0.54 tff(309,plain,
% 0.20/0.54 (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[308, 304])).
% 0.20/0.54 tff(310,plain,
% 0.20/0.54 (~?[Y1: $i, Y2: $i, Y3: $i] : (r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[309, 304])).
% 0.20/0.54 tff(311,plain,
% 0.20/0.54 (^[Y1: $i, Y2: $i, Y3: $i] : nnf_neg(refl($oeq((~r3(Y1, Y2, Y3)), (~r3(Y1, Y2, Y3)))), nnf_neg(proof_bind(^[Y5: $i] : nnf_neg(refl($oeq((~r2(Y5, Y3)), (~r2(Y5, Y3)))), nnf_neg(proof_bind(^[Y6: $i] : nnf_neg(refl($oeq((~r2(Y6, Y5)), (~r2(Y6, Y5)))), nnf_neg(proof_bind(^[Y7: $i] : refl($oeq((~(r1(Y7) & r2(Y7, Y6))), (~(r1(Y7) & r2(Y7, Y6)))))), $oeq((~?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))), ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6))))), $oeq((~(r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))), ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6))))))), $oeq((~?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))), ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6)))))), $oeq((~(r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))), ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6)))))))), $oeq((~?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6))))), ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6))))))), $oeq((~(r3(Y1, Y2, Y3) & ?[Y5: $i] : (r2(Y5, Y3) & ?[Y6: $i] : (r2(Y6, Y5) & ?[Y7: $i] : (r1(Y7) & r2(Y7, Y6)))))), ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(312,plain,(
% 0.20/0.54 ![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : (~(r1(Y7) & r2(Y7, Y6))))))),
% 0.20/0.54 inference(nnf-neg,[status(sab)],[310, 311])).
% 0.20/0.54 tff(313,plain,
% 0.20/0.54 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[312, 303])).
% 0.20/0.54 tff(314,plain,
% 0.20/0.54 (![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[313, 301])).
% 0.20/0.54 tff(315,plain,
% 0.20/0.54 (((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))) | ((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(316,plain,
% 0.20/0.54 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))) | ((~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(317,plain,
% 0.20/0.54 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~r3(Y1, Y2, Y3)) | ![Y5: $i] : ((~r2(Y5, Y3)) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))))) | (~r3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y15_5(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.54 tff(318,plain,
% 0.20/0.54 (![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[317, 314, 296])).
% 0.20/0.54 tff(319,plain,
% 0.20/0.54 (((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) <=> ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(320,plain,
% 0.20/0.54 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(321,plain,
% 0.20/0.54 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, Y5)) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6)))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.20/0.54 tff(322,plain,
% 0.20/0.54 ((~r2(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | ![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[321, 318])).
% 0.20/0.54 tff(323,plain,
% 0.20/0.54 (![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[322, 294])).
% 0.20/0.54 tff(324,plain,
% 0.20/0.54 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(325,plain,
% 0.20/0.54 (($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(326,plain,
% 0.20/0.54 ((~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(327,plain,
% 0.20/0.54 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 ((~$true) <=> $false),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(329,plain,
% 0.20/0.54 ((tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) <=> $true),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (~$true)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[329])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $false),
% 0.20/0.54 inference(transitivity,[status(thm)],[330, 328])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | $false)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 (((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[332, 327])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> (~(~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 ((~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[334, 326])).
% 0.20/0.54 tff(336,plain,
% 0.20/0.54 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true) <=> $true),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(337,plain,
% 0.20/0.54 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | $true)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[329])).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 ((r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) <=> $true),
% 0.20/0.54 inference(transitivity,[status(thm)],[337, 336])).
% 0.20/0.54 tff(339,plain,
% 0.20/0.54 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> (~$true)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[338])).
% 0.20/0.54 tff(340,plain,
% 0.20/0.54 ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) <=> $false),
% 0.20/0.54 inference(transitivity,[status(thm)],[339, 328])).
% 0.20/0.54 tff(341,plain,
% 0.20/0.54 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> ($false | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[340, 335])).
% 0.20/0.54 tff(342,plain,
% 0.20/0.54 (((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))))) <=> r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[341, 325])).
% 0.20/0.54 tff(343,plain,
% 0.20/0.54 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[342])).
% 0.20/0.54 tff(344,plain,
% 0.20/0.54 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[343, 324])).
% 0.20/0.54 tff(345,plain,
% 0.20/0.54 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0))))) | (~((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(346,plain,
% 0.20/0.54 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.20/0.54 tff(347,plain,
% 0.20/0.54 (r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[346, 31])).
% 0.20/0.54 tff(348,plain,
% 0.20/0.54 (((~![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0)))))) <=> ((~![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(349,plain,
% 0.20/0.54 ((~![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))) | ((~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(350,plain,
% 0.20/0.54 ((~![Y6: $i] : ((~r2(Y6, tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, Y6))))) | (~r2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(tptp_fun_Y21_1(Y24!0)))) | ![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.20/0.54 tff(351,plain,
% 0.20/0.54 (![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[350, 347, 323])).
% 0.20/0.54 tff(352,plain,
% 0.20/0.54 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 0.20/0.54 inference(symmetry,[status(thm)],[194])).
% 0.20/0.54 tff(353,plain,
% 0.20/0.54 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) <=> r1(Y24!0)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[352])).
% 0.20/0.54 tff(354,plain,
% 0.20/0.54 (r1(Y24!0) <=> r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.54 inference(symmetry,[status(thm)],[353])).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (((~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))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(356,plain,
% 0.20/0.54 (r1(tptp_fun_Y16_10(Y24!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[355, 184])).
% 0.20/0.54 tff(357,plain,
% 0.20/0.54 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(358,plain,
% 0.20/0.54 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[357, 356])).
% 0.20/0.54 tff(359,plain,
% 0.20/0.54 (((~![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))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(360,plain,
% 0.20/0.54 ((~![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))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(361,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.20/0.54 tff(362,plain,
% 0.20/0.54 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[361, 90, 358])).
% 0.20/0.54 tff(363,plain,
% 0.20/0.54 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(364,plain,
% 0.20/0.54 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[363, 362])).
% 0.20/0.54 tff(365,plain,
% 0.20/0.54 (r1(tptp_fun_Y16_10(Y24!0)) <=> r1(Y24!0)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[364])).
% 0.20/0.54 tff(366,plain,
% 0.20/0.54 (r1(Y24!0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[356, 365])).
% 0.20/0.54 tff(367,plain,
% 0.20/0.54 (r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[366, 354])).
% 0.20/0.54 tff(368,plain,
% 0.20/0.54 (((~![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)))))) | (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(369,plain,
% 0.20/0.54 ((~((~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))))) <=> (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(370,plain,
% 0.20/0.54 (((~![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)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[369])).
% 0.20/0.54 tff(371,plain,
% 0.20/0.54 (((~![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)))))) <=> ((~![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)))))) | (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[370, 368])).
% 0.20/0.54 tff(372,plain,
% 0.20/0.54 ((~![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)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(373,plain,
% 0.20/0.54 ((~![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)))))) | (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.20/0.54 tff(374,plain,
% 0.20/0.54 (~((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[373, 13])).
% 0.20/0.54 tff(375,plain,
% 0.20/0.54 (((~r3(Y24!0, tptp_fun_Y15_5(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(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(376,plain,
% 0.20/0.54 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[375, 374])).
% 0.20/0.54 tff(377,plain,
% 0.20/0.54 ((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)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(378,plain,
% 0.20/0.54 (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))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[377, 376])).
% 0.20/0.54 tff(379,plain,
% 0.20/0.54 (((~![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))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(380,plain,
% 0.20/0.54 ((~![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))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(381,plain,
% 0.20/0.54 ((~![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)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.20/0.54 tff(382,plain,
% 0.20/0.54 (~((~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))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[381, 31, 378])).
% 0.20/0.54 tff(383,plain,
% 0.20/0.54 (((~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))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(384,plain,
% 0.20/0.54 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[383, 382])).
% 0.20/0.54 tff(385,plain,
% 0.20/0.54 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 0.20/0.54 inference(symmetry,[status(thm)],[384])).
% 0.20/0.54 tff(386,plain,
% 0.20/0.54 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) <=> r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[352, 385])).
% 0.20/0.54 tff(387,plain,
% 0.20/0.54 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.54 inference(symmetry,[status(thm)],[386])).
% 0.20/0.54 tff(388,plain,
% 0.20/0.54 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[376, 387])).
% 0.20/0.54 tff(389,plain,
% 0.20/0.54 (((~![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(390,plain,
% 0.20/0.54 ((~![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))) | ((~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(391,plain,
% 0.20/0.54 ((~![Y7: $i] : ((~r1(Y7)) | (~r2(Y7, tptp_fun_Y21_1(Y24!0))))) | (~r1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.20/0.54 tff(392,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[391, 388, 367, 351])).
% 0.20/0.54 % SZS output end Proof
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------