%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUN071+2 : TPTP v9.0.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:37 AM UTC 2025
% Result : Theorem 27.45s 27.64s
% Output : Proof 27.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN071+2 : TPTP v9.0.0. Released v7.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:12:33 EDT 2025
% 0.12/0.33 % CPUTime :
% 27.45/27.64 % SZS status Theorem
% 27.45/27.64 % SZS output start Proof
% 27.45/27.64 tff(tptp_fun_Y23_3_type, type, (
% 27.45/27.64 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y21_1_type, type, (
% 27.45/27.64 tptp_fun_Y21_1: $i > $i)).
% 27.45/27.64 tff(tptp_fun_Y24_0_type, type, (
% 27.45/27.64 tptp_fun_Y24_0: $i)).
% 27.45/27.64 tff(tptp_fun_Y14_8_type, type, (
% 27.45/27.64 tptp_fun_Y14_8: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y22_2_type, type, (
% 27.45/27.64 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y16_10_type, type, (
% 27.45/27.64 tptp_fun_Y16_10: $i > $i)).
% 27.45/27.64 tff(r2_type, type, (
% 27.45/27.64 r2: ( $i * $i ) > $o)).
% 27.45/27.64 tff(r4_type, type, (
% 27.45/27.64 r4: ( $i * $i * $i ) > $o)).
% 27.45/27.64 tff(tptp_fun_Y6_9_type, type, (
% 27.45/27.64 tptp_fun_Y6_9: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y2_7_type, type, (
% 27.45/27.64 tptp_fun_Y2_7: ( $i * $i ) > $i)).
% 27.45/27.64 tff(r3_type, type, (
% 27.45/27.64 r3: ( $i * $i * $i ) > $o)).
% 27.45/27.64 tff(r1_type, type, (
% 27.45/27.64 r1: $i > $o)).
% 27.45/27.64 tff(tptp_fun_Y15_5_type, type, (
% 27.45/27.64 tptp_fun_Y15_5: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y8_11_type, type, (
% 27.45/27.64 tptp_fun_Y8_11: $i > $i)).
% 27.45/27.64 tff(tptp_fun_Y17_12_type, type, (
% 27.45/27.64 tptp_fun_Y17_12: $i > $i)).
% 27.45/27.64 tff(tptp_fun_Y7_6_type, type, (
% 27.45/27.64 tptp_fun_Y7_6: ( $i * $i ) > $i)).
% 27.45/27.64 tff(tptp_fun_Y4_4_type, type, (
% 27.45/27.64 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 27.45/27.64 tff(1,plain,
% 27.45/27.64 (^[X2: $i, X9: $i] : rewrite((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2))))))),
% 27.45/27.64 inference(bind,[status(th)],[])).
% 27.45/27.64 tff(2,plain,
% 27.45/27.64 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))) <=> ![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 27.45/27.64 inference(quant_intro,[status(thm)],[1])).
% 27.45/27.64 tff(3,plain,
% 27.45/27.64 (^[X2: $i, X9: $i] : rewrite(((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 27.45/27.64 inference(bind,[status(th)],[])).
% 27.45/27.64 tff(4,plain,
% 27.45/27.64 (![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))) <=> ![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 27.45/27.64 inference(quant_intro,[status(thm)],[3])).
% 27.45/27.64 tff(5,plain,
% 27.45/27.64 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 27.45/27.64 inference(rewrite,[status(thm)],[])).
% 27.45/27.64 tff(6,plain,
% 27.45/27.64 (^[X2: $i, X9: $i] : quant_intro(proof_bind(^[Y2: $i] : rewrite((?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))))), (?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))))),
% 27.45/27.64 inference(bind,[status(th)],[])).
% 27.45/27.64 tff(7,plain,
% 27.45/27.64 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 27.48/27.64 inference(quant_intro,[status(thm)],[6])).
% 27.48/27.64 tff(8,axiom,(![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2a')).
% 27.48/27.64 tff(9,plain,
% 27.48/27.64 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[8, 7])).
% 27.48/27.64 tff(10,plain,
% 27.48/27.64 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[9, 5])).
% 27.48/27.64 tff(11,plain,(
% 27.48/27.64 ![X2: $i, X9: $i] : ((r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) & (r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2))))),
% 27.48/27.64 inference(skolemize,[status(sab)],[10])).
% 27.48/27.64 tff(12,plain,
% 27.48/27.64 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_8(X9, X2)) & r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2)) & r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2)) & r4(X2, X9, tptp_fun_Y6_9(X9, X2)))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[11, 4])).
% 27.48/27.64 tff(13,plain,
% 27.48/27.64 (![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[12, 2])).
% 27.48/27.64 tff(14,plain,
% 27.48/27.64 (((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.64 inference(rewrite,[status(thm)],[])).
% 27.48/27.64 tff(15,plain,
% 27.48/27.64 ((~((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.64 inference(rewrite,[status(thm)],[])).
% 27.48/27.64 tff(16,plain,
% 27.48/27.64 (((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.64 inference(monotonicity,[status(thm)],[15])).
% 27.48/27.64 tff(17,plain,
% 27.48/27.64 (((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.64 inference(transitivity,[status(thm)],[16, 14])).
% 27.48/27.64 tff(18,plain,
% 27.48/27.64 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.64 inference(quant_inst,[status(thm)],[])).
% 27.48/27.64 tff(19,plain,
% 27.48/27.64 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[18, 17])).
% 27.48/27.64 tff(20,plain,
% 27.48/27.64 (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.64 inference(unit_resolution,[status(thm)],[19, 13])).
% 27.48/27.64 tff(21,plain,
% 27.48/27.64 (((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.64 inference(tautology,[status(thm)],[])).
% 27.48/27.64 tff(22,plain,
% 27.48/27.64 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.64 inference(unit_resolution,[status(thm)],[21, 20])).
% 27.48/27.64 tff(23,plain,
% 27.48/27.64 ((r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.64 inference(tautology,[status(thm)],[])).
% 27.48/27.64 tff(24,plain,
% 27.48/27.64 (r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.64 inference(unit_resolution,[status(thm)],[23, 22])).
% 27.48/27.64 tff(25,plain,
% 27.48/27.64 (^[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)))))))),
% 27.48/27.64 inference(bind,[status(th)],[])).
% 27.48/27.64 tff(26,plain,
% 27.48/27.64 (![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))))))),
% 27.48/27.64 inference(quant_intro,[status(thm)],[25])).
% 27.48/27.64 tff(27,plain,
% 27.48/27.64 (^[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)))))))),
% 27.48/27.64 inference(bind,[status(th)],[])).
% 27.48/27.64 tff(28,plain,
% 27.48/27.64 (![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))))))),
% 27.48/27.64 inference(quant_intro,[status(thm)],[27])).
% 27.48/27.64 tff(29,plain,
% 27.48/27.64 (![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))))),
% 27.48/27.64 inference(pull_quant,[status(thm)],[])).
% 27.48/27.64 tff(30,plain,
% 27.48/27.64 (![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)))),
% 27.48/27.64 inference(rewrite,[status(thm)],[])).
% 27.48/27.64 tff(31,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')).
% 27.48/27.64 tff(32,plain,
% 27.48/27.64 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[31, 30])).
% 27.48/27.64 tff(33,plain,(
% 27.48/27.64 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 27.48/27.64 inference(skolemize,[status(sab)],[32])).
% 27.48/27.64 tff(34,plain,
% 27.48/27.64 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 27.48/27.64 inference(modus_ponens,[status(thm)],[33, 29])).
% 27.48/27.64 tff(35,plain,
% 27.48/27.64 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[34, 28])).
% 27.48/27.65 tff(36,plain,
% 27.48/27.65 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[35, 26])).
% 27.48/27.65 tff(37,plain,
% 27.48/27.65 (((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(38,plain,
% 27.48/27.65 ((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))))),
% 27.48/27.65 inference(quant_inst,[status(thm)],[])).
% 27.48/27.65 tff(39,plain,
% 27.48/27.65 ((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[38, 37])).
% 27.48/27.65 tff(40,plain,
% 27.48/27.65 (~((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[39, 36, 24])).
% 27.48/27.65 tff(41,plain,
% 27.48/27.65 (((~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))))) | (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(42,plain,
% 27.48/27.65 (tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[41, 40])).
% 27.48/27.65 tff(43,plain,
% 27.48/27.65 (tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.65 inference(symmetry,[status(thm)],[42])).
% 27.48/27.65 tff(44,plain,
% 27.48/27.65 (^[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)))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(45,plain,
% 27.48/27.65 (![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))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[44])).
% 27.48/27.65 tff(46,plain,
% 27.48/27.65 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(47,plain,
% 27.48/27.65 (^[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))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(48,plain,
% 27.48/27.65 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[47])).
% 27.48/27.65 tff(49,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')).
% 27.48/27.65 tff(50,plain,
% 27.48/27.65 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[49, 48])).
% 27.48/27.65 tff(51,plain,
% 27.48/27.65 (![X4: $i] : ?[Y16: $i] : (r1(Y16) & r3(X4, Y16, X4))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[50, 46])).
% 27.48/27.65 tff(52,plain,(
% 27.48/27.65 ![X4: $i] : (r1(tptp_fun_Y16_10(X4)) & r3(X4, tptp_fun_Y16_10(X4), X4))),
% 27.48/27.65 inference(skolemize,[status(sab)],[51])).
% 27.48/27.65 tff(53,plain,
% 27.48/27.65 (![X4: $i] : (~((~r1(tptp_fun_Y16_10(X4))) | (~r3(X4, tptp_fun_Y16_10(X4), X4))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[52, 45])).
% 27.48/27.65 tff(54,plain,
% 27.48/27.65 ((~![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))))),
% 27.48/27.65 inference(quant_inst,[status(thm)],[])).
% 27.48/27.65 tff(55,plain,
% 27.48/27.65 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[54, 53])).
% 27.48/27.65 tff(56,plain,
% 27.48/27.65 (((~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)),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(57,plain,
% 27.48/27.65 (r3(Y24!0, tptp_fun_Y16_10(Y24!0), Y24!0)),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[56, 55])).
% 27.48/27.65 tff(58,plain,
% 27.48/27.65 ((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))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(59,plain,
% 27.48/27.65 (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))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[58, 57])).
% 27.48/27.65 tff(60,plain,
% 27.48/27.65 (^[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)))))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(61,plain,
% 27.48/27.65 (![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))))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[60])).
% 27.48/27.65 tff(62,plain,
% 27.48/27.65 (^[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)))))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(63,plain,
% 27.48/27.65 (![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))))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[62])).
% 27.48/27.65 tff(64,plain,
% 27.48/27.65 (![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))))),
% 27.48/27.65 inference(pull_quant,[status(thm)],[])).
% 27.48/27.65 tff(65,plain,
% 27.48/27.65 (![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)))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(66,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')).
% 27.48/27.65 tff(67,plain,
% 27.48/27.65 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[66, 65])).
% 27.48/27.65 tff(68,plain,(
% 27.48/27.65 ![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))))),
% 27.48/27.65 inference(skolemize,[status(sab)],[67])).
% 27.48/27.65 tff(69,plain,
% 27.48/27.65 (![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))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[68, 64])).
% 27.48/27.65 tff(70,plain,
% 27.48/27.65 (![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))))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[69, 63])).
% 27.48/27.65 tff(71,plain,
% 27.48/27.65 (![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))))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[70, 61])).
% 27.48/27.65 tff(72,plain,
% 27.48/27.65 (((~![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))))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(73,plain,
% 27.48/27.65 ((~![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))))))),
% 27.48/27.65 inference(quant_inst,[status(thm)],[])).
% 27.48/27.65 tff(74,plain,
% 27.48/27.65 ((~![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)))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[73, 72])).
% 27.48/27.65 tff(75,plain,
% 27.48/27.65 (~((~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))))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[74, 71, 59])).
% 27.48/27.65 tff(76,plain,
% 27.48/27.65 (((~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))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(77,plain,
% 27.48/27.65 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[76, 75])).
% 27.48/27.65 tff(78,plain,
% 27.48/27.65 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = Y24!0),
% 27.48/27.65 inference(symmetry,[status(thm)],[77])).
% 27.48/27.65 tff(79,plain,
% 27.48/27.65 (tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 27.48/27.65 inference(monotonicity,[status(thm)],[78])).
% 27.48/27.65 tff(80,plain,
% 27.48/27.65 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 27.48/27.65 inference(symmetry,[status(thm)],[79])).
% 27.48/27.65 tff(81,plain,
% 27.48/27.65 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.65 inference(transitivity,[status(thm)],[80, 43])).
% 27.48/27.65 tff(82,plain,
% 27.48/27.65 (tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.65 inference(monotonicity,[status(thm)],[81])).
% 27.48/27.65 tff(83,plain,
% 27.48/27.65 (tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.65 inference(symmetry,[status(thm)],[82])).
% 27.48/27.65 tff(84,plain,
% 27.48/27.65 (((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(85,plain,
% 27.48/27.65 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[84, 20])).
% 27.48/27.65 tff(86,plain,
% 27.48/27.65 (((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(87,plain,
% 27.48/27.65 ((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[86, 85])).
% 27.48/27.65 tff(88,plain,
% 27.48/27.65 (^[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))))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(89,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[88])).
% 27.48/27.65 tff(90,plain,
% 27.48/27.65 (^[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)))))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(91,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[90])).
% 27.48/27.65 tff(92,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(pull_quant,[status(thm)],[])).
% 27.48/27.65 tff(93,plain,
% 27.48/27.65 (![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))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(94,plain,
% 27.48/27.65 (^[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))))))),
% 27.48/27.65 inference(bind,[status(th)],[])).
% 27.48/27.65 tff(95,plain,
% 27.48/27.65 (![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))))),
% 27.48/27.65 inference(quant_intro,[status(thm)],[94])).
% 27.48/27.65 tff(96,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')).
% 27.48/27.65 tff(97,plain,
% 27.48/27.65 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[96, 95])).
% 27.48/27.65 tff(98,plain,
% 27.48/27.65 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[97, 93])).
% 27.48/27.65 tff(99,plain,(
% 27.48/27.65 ![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)))))),
% 27.48/27.65 inference(skolemize,[status(sab)],[98])).
% 27.48/27.65 tff(100,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[99, 92])).
% 27.48/27.65 tff(101,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[100, 91])).
% 27.48/27.65 tff(102,plain,
% 27.48/27.65 (![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)))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[101, 89])).
% 27.48/27.65 tff(103,plain,
% 27.48/27.65 (((~![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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(104,plain,
% 27.48/27.65 (((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(105,plain,
% 27.48/27.65 ((~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) <=> (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.65 inference(rewrite,[status(thm)],[])).
% 27.48/27.65 tff(106,plain,
% 27.48/27.65 (((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(monotonicity,[status(thm)],[105])).
% 27.48/27.65 tff(107,plain,
% 27.48/27.65 (((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(transitivity,[status(thm)],[106, 104])).
% 27.48/27.65 tff(108,plain,
% 27.48/27.65 (((~![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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), 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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.65 inference(monotonicity,[status(thm)],[107])).
% 27.48/27.65 tff(109,plain,
% 27.48/27.65 (((~![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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), 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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(transitivity,[status(thm)],[108, 103])).
% 27.48/27.65 tff(110,plain,
% 27.48/27.65 ((~![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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.65 inference(quant_inst,[status(thm)],[])).
% 27.48/27.65 tff(111,plain,
% 27.48/27.65 ((~![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_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.65 inference(modus_ponens,[status(thm)],[110, 109])).
% 27.48/27.65 tff(112,plain,
% 27.48/27.65 (~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[111, 102, 87])).
% 27.48/27.65 tff(113,plain,
% 27.48/27.65 (((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(114,plain,
% 27.48/27.65 (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[113, 112])).
% 27.48/27.65 tff(115,plain,
% 27.48/27.65 (((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(116,plain,
% 27.48/27.65 (r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.65 inference(unit_resolution,[status(thm)],[115, 20])).
% 27.48/27.65 tff(117,plain,
% 27.48/27.65 (((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.65 inference(tautology,[status(thm)],[])).
% 27.48/27.65 tff(118,plain,
% 27.48/27.65 ((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[117, 116])).
% 27.48/27.66 tff(119,plain,
% 27.48/27.66 (((~![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))))))) | ((~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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))))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(120,plain,
% 27.48/27.66 (((~(r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))) <=> ((~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(121,plain,
% 27.48/27.66 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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))))))) | ((~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))))),
% 27.48/27.66 inference(monotonicity,[status(thm)],[120])).
% 27.48/27.66 tff(122,plain,
% 27.48/27.66 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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))))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 27.48/27.66 inference(transitivity,[status(thm)],[121, 119])).
% 27.48/27.66 tff(123,plain,
% 27.48/27.66 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))))),
% 27.48/27.66 inference(quant_inst,[status(thm)],[])).
% 27.48/27.66 tff(124,plain,
% 27.48/27.66 ((~![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))))))) | (~((tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[123, 122])).
% 27.48/27.66 tff(125,plain,
% 27.48/27.66 (~((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[124, 71, 118])).
% 27.48/27.66 tff(126,plain,
% 27.48/27.66 (((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(127,plain,
% 27.48/27.66 (tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[126, 125])).
% 27.48/27.66 tff(128,plain,
% 27.48/27.66 (tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.66 inference(symmetry,[status(thm)],[127])).
% 27.48/27.66 tff(129,plain,
% 27.48/27.66 (^[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))))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(130,plain,
% 27.48/27.66 (![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)))))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[129])).
% 27.48/27.66 tff(131,plain,
% 27.48/27.66 (^[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))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(132,plain,
% 27.48/27.66 (![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)))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[131])).
% 27.48/27.66 tff(133,plain,
% 27.48/27.66 (![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))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(134,plain,
% 27.48/27.66 (^[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))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(135,plain,
% 27.48/27.66 (![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))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[134])).
% 27.48/27.66 tff(136,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')).
% 27.48/27.66 tff(137,plain,
% 27.48/27.66 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[136, 135])).
% 27.48/27.66 tff(138,plain,
% 27.48/27.66 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & r1(Y8))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[137, 133])).
% 27.48/27.66 tff(139,plain,(
% 27.48/27.66 ![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)))),
% 27.48/27.66 inference(skolemize,[status(sab)],[138])).
% 27.48/27.66 tff(140,plain,
% 27.48/27.66 (![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)))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[139, 132])).
% 27.48/27.66 tff(141,plain,
% 27.48/27.66 (![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)))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[140, 130])).
% 27.48/27.66 tff(142,plain,
% 27.48/27.66 (((~![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_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))) <=> ((~![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_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(143,plain,
% 27.48/27.66 ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) <=> (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(144,plain,
% 27.48/27.66 (((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))) <=> ((~![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_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))))),
% 27.48/27.66 inference(monotonicity,[status(thm)],[143])).
% 27.48/27.66 tff(145,plain,
% 27.48/27.66 (((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))) <=> ((~![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_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))))),
% 27.48/27.66 inference(transitivity,[status(thm)],[144, 142])).
% 27.48/27.66 tff(146,plain,
% 27.48/27.66 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_12(X5))) | (~r4(X5, tptp_fun_Y17_12(X5), tptp_fun_Y8_11(X5))) | (~r1(tptp_fun_Y8_11(X5)))))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))),
% 27.48/27.66 inference(quant_inst,[status(thm)],[])).
% 27.48/27.66 tff(147,plain,
% 27.48/27.66 ((~![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_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[146, 145])).
% 27.48/27.66 tff(148,plain,
% 27.48/27.66 (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[147, 141])).
% 27.48/27.66 tff(149,plain,
% 27.48/27.66 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))) | r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(150,plain,
% 27.48/27.66 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[149, 148])).
% 27.48/27.66 tff(151,plain,
% 27.48/27.66 ((r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)) | (~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(152,plain,
% 27.48/27.66 (r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[151, 150])).
% 27.48/27.66 tff(153,plain,
% 27.48/27.66 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(154,plain,
% 27.48/27.66 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[153])).
% 27.48/27.66 tff(155,plain,
% 27.48/27.66 (^[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))))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(156,plain,
% 27.48/27.66 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[155])).
% 27.48/27.66 tff(157,plain,
% 27.48/27.66 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(158,plain,
% 27.48/27.66 (^[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))))))),
% 27.48/27.66 inference(bind,[status(th)],[])).
% 27.48/27.66 tff(159,plain,
% 27.48/27.66 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 27.48/27.66 inference(quant_intro,[status(thm)],[158])).
% 27.48/27.66 tff(160,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 27.48/27.66 tff(161,plain,
% 27.48/27.66 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[160, 159])).
% 27.48/27.66 tff(162,plain,
% 27.48/27.66 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[161, 157])).
% 27.48/27.66 tff(163,plain,(
% 27.48/27.66 $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)))))),
% 27.48/27.66 inference(transitivity,[status(sab)],[162])).
% 27.48/27.66 tff(164,plain,
% 27.48/27.66 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[163, 156])).
% 27.48/27.66 tff(165,plain,
% 27.48/27.66 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[164, 154])).
% 27.48/27.66 tff(166,plain,
% 27.48/27.66 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(167,plain,
% 27.48/27.66 (((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) <=> ((~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.66 tff(168,plain,
% 27.48/27.66 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))))),
% 27.48/27.66 inference(monotonicity,[status(thm)],[167])).
% 27.48/27.66 tff(169,plain,
% 27.48/27.66 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.66 inference(transitivity,[status(thm)],[168, 166])).
% 27.48/27.66 tff(170,plain,
% 27.48/27.66 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))),
% 27.48/27.66 inference(quant_inst,[status(thm)],[])).
% 27.48/27.66 tff(171,plain,
% 27.48/27.66 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))),
% 27.48/27.66 inference(modus_ponens,[status(thm)],[170, 169])).
% 27.48/27.66 tff(172,plain,
% 27.48/27.66 (~((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[171, 165, 152])).
% 27.48/27.66 tff(173,plain,
% 27.48/27.66 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(174,plain,
% 27.48/27.66 (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[173, 172])).
% 27.48/27.66 tff(175,plain,
% 27.48/27.66 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))) | r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(176,plain,
% 27.48/27.66 (r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[175, 148])).
% 27.48/27.66 tff(177,plain,
% 27.48/27.66 ((r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))),
% 27.48/27.66 inference(tautology,[status(thm)],[])).
% 27.48/27.66 tff(178,plain,
% 27.48/27.66 (r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.66 inference(unit_resolution,[status(thm)],[177, 176])).
% 27.48/27.66 tff(179,plain,
% 27.48/27.66 (((~![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(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) | (~(r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(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_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) | (~(r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))),
% 27.48/27.66 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(180,plain,
% 27.48/27.67 ((~![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(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) | (~(r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(181,plain,
% 27.48/27.67 ((~![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(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))) | (~(r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[180, 179])).
% 27.48/27.67 tff(182,plain,
% 27.48/27.67 (~((~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[181, 102, 178])).
% 27.48/27.67 tff(183,plain,
% 27.48/27.67 (((~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))) | (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(184,plain,
% 27.48/27.67 (tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[183, 182])).
% 27.48/27.67 tff(185,plain,
% 27.48/27.67 (tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.67 inference(symmetry,[status(thm)],[184])).
% 27.48/27.67 tff(186,plain,
% 27.48/27.67 (((~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))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(187,plain,
% 27.48/27.67 (r1(tptp_fun_Y16_10(Y24!0))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[186, 55])).
% 27.48/27.67 tff(188,plain,
% 27.48/27.67 ((r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_10(Y24!0)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(189,plain,
% 27.48/27.67 (r1(tptp_fun_Y16_10(Y24!0)) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[188, 187])).
% 27.48/27.67 tff(190,plain,
% 27.48/27.67 (((~![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))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(191,plain,
% 27.48/27.67 ((~![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))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(192,plain,
% 27.48/27.67 ((~![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)))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[191, 190])).
% 27.48/27.67 tff(193,plain,
% 27.48/27.67 (~((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[192, 165, 189])).
% 27.48/27.67 tff(194,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y16_10(Y24!0))) | (~(tptp_fun_Y16_10(Y24!0) = Y24!0))) | (tptp_fun_Y16_10(Y24!0) = Y24!0)),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(195,plain,
% 27.48/27.67 (tptp_fun_Y16_10(Y24!0) = Y24!0),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[194, 193])).
% 27.48/27.67 tff(196,plain,
% 27.48/27.67 (Y24!0 = tptp_fun_Y16_10(Y24!0)),
% 27.48/27.67 inference(symmetry,[status(thm)],[195])).
% 27.48/27.67 tff(197,plain,
% 27.48/27.67 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)),
% 27.48/27.67 inference(monotonicity,[status(thm)],[196])).
% 27.48/27.67 tff(198,plain,
% 27.48/27.67 (((~![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)))) | (~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))))))) <=> ((~![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)))) | (~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)))))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(199,plain,
% 27.48/27.67 ((~((~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)))) | (~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))))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(200,plain,
% 27.48/27.67 (((~![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))))))) <=> ((~![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)))) | (~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)))))))),
% 27.48/27.67 inference(monotonicity,[status(thm)],[199])).
% 27.48/27.67 tff(201,plain,
% 27.48/27.67 (((~![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))))))) <=> ((~![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)))) | (~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)))))))),
% 27.48/27.67 inference(transitivity,[status(thm)],[200, 198])).
% 27.48/27.67 tff(202,plain,
% 27.48/27.67 ((~![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))))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(203,plain,
% 27.48/27.67 ((~![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)))) | (~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))))))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[202, 201])).
% 27.48/27.67 tff(204,plain,
% 27.48/27.67 (~((~r1(tptp_fun_Y17_12(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)))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[203, 141])).
% 27.48/27.67 tff(205,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y17_12(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))))) | r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(206,plain,
% 27.48/27.67 (r1(tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[205, 204])).
% 27.48/27.67 tff(207,plain,
% 27.48/27.67 ((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))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(208,plain,
% 27.48/27.67 (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)),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[207, 206])).
% 27.48/27.67 tff(209,plain,
% 27.48/27.67 (((~![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))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(210,plain,
% 27.48/27.67 ((~![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))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(211,plain,
% 27.48/27.67 ((~![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)))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[210, 209])).
% 27.48/27.67 tff(212,plain,
% 27.48/27.67 (~((~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)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[211, 165, 208])).
% 27.48/27.67 tff(213,plain,
% 27.48/27.67 (((~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)),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(214,plain,
% 27.48/27.67 (tptp_fun_Y8_11(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[213, 212])).
% 27.48/27.67 tff(215,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y17_12(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))))) | 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)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(216,plain,
% 27.48/27.67 (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)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[215, 204])).
% 27.48/27.67 tff(217,plain,
% 27.48/27.67 ((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))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(218,plain,
% 27.48/27.67 (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)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[217, 216])).
% 27.48/27.67 tff(219,plain,
% 27.48/27.67 (((~![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))))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(220,plain,
% 27.48/27.67 ((~![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))))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(221,plain,
% 27.48/27.67 ((~![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)))))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[220, 219])).
% 27.48/27.67 tff(222,plain,
% 27.48/27.67 (~((~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)))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[221, 102, 218])).
% 27.48/27.67 tff(223,plain,
% 27.48/27.67 (((~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)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(224,plain,
% 27.48/27.67 (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))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[223, 222])).
% 27.48/27.67 tff(225,plain,
% 27.48/27.67 (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))),
% 27.48/27.67 inference(symmetry,[status(thm)],[224])).
% 27.48/27.67 tff(226,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y17_12(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))))) | r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(227,plain,
% 27.48/27.67 (r1(tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[226, 204])).
% 27.48/27.67 tff(228,plain,
% 27.48/27.67 ((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))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(229,plain,
% 27.48/27.67 (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)),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[228, 227])).
% 27.48/27.67 tff(230,plain,
% 27.48/27.67 (((~![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))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(231,plain,
% 27.48/27.67 ((~![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))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(232,plain,
% 27.48/27.67 ((~![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)))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[231, 230])).
% 27.48/27.67 tff(233,plain,
% 27.48/27.67 (~((~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)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[232, 165, 229])).
% 27.48/27.67 tff(234,plain,
% 27.48/27.67 (((~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)),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(235,plain,
% 27.48/27.67 (tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0)) = Y24!0),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[234, 233])).
% 27.48/27.67 tff(236,plain,
% 27.48/27.67 (Y24!0 = tptp_fun_Y17_12(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0))),
% 27.48/27.67 inference(symmetry,[status(thm)],[235])).
% 27.48/27.67 tff(237,plain,
% 27.48/27.67 (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))),
% 27.48/27.67 inference(monotonicity,[status(thm)],[236, 77])).
% 27.48/27.67 tff(238,plain,
% 27.48/27.67 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_8(X9, X2))) | (~r4(X2, tptp_fun_Y14_8(X9, X2), tptp_fun_Y2_7(X9, X2))) | (~r3(tptp_fun_Y6_9(X9, X2), X2, tptp_fun_Y2_7(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_9(X9, X2)))))) | (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(239,plain,
% 27.48/27.67 (~((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[238, 13])).
% 27.48/27.67 tff(240,plain,
% 27.48/27.67 (((~r2(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_8(Y24!0, Y24!0), tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_9(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_7(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) | r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(241,plain,
% 27.48/27.67 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[240, 239])).
% 27.48/27.67 tff(242,plain,
% 27.48/27.67 ((r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(243,plain,
% 27.48/27.67 (r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[242, 241])).
% 27.48/27.67 tff(244,plain,
% 27.48/27.67 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(245,plain,
% 27.48/27.67 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(246,plain,
% 27.48/27.67 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[245, 244])).
% 27.48/27.67 tff(247,plain,
% 27.48/27.67 (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[246, 102, 243])).
% 27.48/27.67 tff(248,plain,
% 27.48/27.67 (((~r4(Y24!0, Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) | (~(tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(249,plain,
% 27.48/27.67 (tptp_fun_Y6_9(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[248, 247])).
% 27.48/27.67 tff(250,plain,
% 27.48/27.67 (tptp_fun_Y6_9(Y24!0, Y24!0) = Y24!0),
% 27.48/27.67 inference(transitivity,[status(thm)],[249, 237, 225, 214])).
% 27.48/27.67 tff(251,plain,
% 27.48/27.67 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 27.48/27.67 inference(monotonicity,[status(thm)],[250])).
% 27.48/27.67 tff(252,plain,
% 27.48/27.67 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)) = Y24!0),
% 27.48/27.67 inference(transitivity,[status(thm)],[251, 197, 78])).
% 27.48/27.67 tff(253,plain,
% 27.48/27.67 (tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))) = tptp_fun_Y21_1(Y24!0)),
% 27.48/27.67 inference(monotonicity,[status(thm)],[252])).
% 27.48/27.67 tff(254,plain,
% 27.48/27.67 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))),
% 27.48/27.67 inference(symmetry,[status(thm)],[253])).
% 27.48/27.67 tff(255,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r4(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))), tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y8_11(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))) | r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(256,plain,
% 27.48/27.67 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[255, 148])).
% 27.48/27.67 tff(257,plain,
% 27.48/27.67 ((r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)) | (~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))))),
% 27.48/27.67 inference(tautology,[status(thm)],[])).
% 27.48/27.67 tff(258,plain,
% 27.48/27.67 (r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[257, 256])).
% 27.48/27.67 tff(259,plain,
% 27.48/27.67 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(260,plain,
% 27.48/27.67 (((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) <=> ((~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.67 inference(rewrite,[status(thm)],[])).
% 27.48/27.67 tff(261,plain,
% 27.48/27.67 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))))),
% 27.48/27.67 inference(monotonicity,[status(thm)],[260])).
% 27.48/27.67 tff(262,plain,
% 27.48/27.67 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))))),
% 27.48/27.67 inference(transitivity,[status(thm)],[261, 259])).
% 27.48/27.67 tff(263,plain,
% 27.48/27.67 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))),
% 27.48/27.67 inference(quant_inst,[status(thm)],[])).
% 27.48/27.67 tff(264,plain,
% 27.48/27.67 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~(r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))))),
% 27.48/27.67 inference(modus_ponens,[status(thm)],[263, 262])).
% 27.48/27.67 tff(265,plain,
% 27.48/27.67 (~((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)))),
% 27.48/27.67 inference(unit_resolution,[status(thm)],[264, 165, 258])).
% 27.48/27.67 tff(266,plain,
% 27.48/27.67 (((~r1(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))))) | (~(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0))) | (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0)),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(267,plain,
% 27.48/27.68 (tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))) = Y24!0),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[266, 265])).
% 27.48/27.68 tff(268,plain,
% 27.48/27.68 (Y24!0 = tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.68 inference(symmetry,[status(thm)],[267])).
% 27.48/27.68 tff(269,plain,
% 27.48/27.68 (tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0) = tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.68 inference(transitivity,[status(thm)],[78, 268])).
% 27.48/27.68 tff(270,plain,
% 27.48/27.68 (tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y17_12(tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_9(Y24!0, Y24!0))))),
% 27.48/27.68 inference(monotonicity,[status(thm)],[269, 254])).
% 27.48/27.68 tff(271,plain,
% 27.48/27.68 (((~r3(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y21_1(Y24!0), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)), tptp_fun_Y2_7(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r2(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y14_8(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(272,plain,
% 27.48/27.68 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[271, 20])).
% 27.48/27.68 tff(273,plain,
% 27.48/27.68 ((r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(274,plain,
% 27.48/27.68 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[273, 272])).
% 27.48/27.68 tff(275,plain,
% 27.48/27.68 (((~![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)))))) | ((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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)))))) | (~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(276,plain,
% 27.48/27.68 (((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(277,plain,
% 27.48/27.68 ((~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) <=> (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(278,plain,
% 27.48/27.68 ((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> (~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(279,plain,
% 27.48/27.68 (((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(monotonicity,[status(thm)],[278, 277])).
% 27.48/27.68 tff(280,plain,
% 27.48/27.68 (((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) <=> ((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(transitivity,[status(thm)],[279, 276])).
% 27.48/27.68 tff(281,plain,
% 27.48/27.68 (((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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)))))) | ((~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))))),
% 27.48/27.68 inference(monotonicity,[status(thm)],[280])).
% 27.48/27.68 tff(282,plain,
% 27.48/27.68 (((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), 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)))))) | (~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(transitivity,[status(thm)],[281, 275])).
% 27.48/27.68 tff(283,plain,
% 27.48/27.68 ((~![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_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.68 inference(quant_inst,[status(thm)],[])).
% 27.48/27.68 tff(284,plain,
% 27.48/27.68 ((~![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)))))) | (~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[283, 282])).
% 27.48/27.68 tff(285,plain,
% 27.48/27.68 (~((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[284, 102, 274])).
% 27.48/27.68 tff(286,plain,
% 27.48/27.68 (((~(tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))))) | (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(287,plain,
% 27.48/27.68 (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = tptp_fun_Y23_3(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[286, 285])).
% 27.48/27.68 tff(288,plain,
% 27.48/27.68 (tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)) = Y24!0),
% 27.48/27.68 inference(transitivity,[status(thm)],[287, 270, 185, 174])).
% 27.48/27.68 tff(289,plain,
% 27.48/27.68 (^[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))))))),
% 27.48/27.68 inference(bind,[status(th)],[])).
% 27.48/27.68 tff(290,plain,
% 27.48/27.68 (![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)))))),
% 27.48/27.68 inference(quant_intro,[status(thm)],[289])).
% 27.48/27.68 tff(291,plain,
% 27.48/27.68 (^[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))))),
% 27.48/27.68 inference(bind,[status(th)],[])).
% 27.48/27.68 tff(292,plain,
% 27.48/27.68 (![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)))),
% 27.48/27.68 inference(quant_intro,[status(thm)],[291])).
% 27.48/27.68 tff(293,plain,
% 27.48/27.68 (![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)))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(294,plain,
% 27.48/27.68 (^[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)))))),
% 27.48/27.68 inference(bind,[status(th)],[])).
% 27.48/27.68 tff(295,plain,
% 27.48/27.68 (![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)))),
% 27.48/27.68 inference(quant_intro,[status(thm)],[294])).
% 27.48/27.68 tff(296,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')).
% 27.48/27.68 tff(297,plain,
% 27.48/27.68 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[296, 295])).
% 27.48/27.68 tff(298,plain,
% 27.48/27.68 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[297, 293])).
% 27.48/27.68 tff(299,plain,(
% 27.48/27.68 ![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))))),
% 27.48/27.68 inference(skolemize,[status(sab)],[298])).
% 27.48/27.68 tff(300,plain,
% 27.48/27.68 (![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)))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[299, 292])).
% 27.48/27.68 tff(301,plain,
% 27.48/27.68 (![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)))))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[300, 290])).
% 27.48/27.68 tff(302,plain,
% 27.48/27.68 ((~![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)))))),
% 27.48/27.68 inference(quant_inst,[status(thm)],[])).
% 27.48/27.68 tff(303,plain,
% 27.48/27.68 (~((~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))))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[302, 301])).
% 27.48/27.68 tff(304,plain,
% 27.48/27.68 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(305,plain,
% 27.48/27.68 (r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[304, 303])).
% 27.48/27.68 tff(306,plain,
% 27.48/27.68 ((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)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(307,plain,
% 27.48/27.68 (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))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[306, 305])).
% 27.48/27.68 tff(308,plain,
% 27.48/27.68 (((~![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))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(309,plain,
% 27.48/27.68 ((~![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))))))),
% 27.48/27.68 inference(quant_inst,[status(thm)],[])).
% 27.48/27.68 tff(310,plain,
% 27.48/27.68 ((~![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)))))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[309, 308])).
% 27.48/27.68 tff(311,plain,
% 27.48/27.68 (~((~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))))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[310, 36, 307])).
% 27.48/27.68 tff(312,plain,
% 27.48/27.68 (((~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))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(313,plain,
% 27.48/27.68 (tptp_fun_Y15_5(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[312, 311])).
% 27.48/27.68 tff(314,plain,
% 27.48/27.68 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_5(Y24!0, Y24!0)),
% 27.48/27.68 inference(symmetry,[status(thm)],[313])).
% 27.48/27.68 tff(315,plain,
% 27.48/27.68 (tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0))) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)),
% 27.48/27.68 inference(monotonicity,[status(thm)],[314, 288])).
% 27.48/27.68 tff(316,plain,
% 27.48/27.68 (tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y21_1(Y24!0), tptp_fun_Y6_9(tptp_fun_Y22_2(tptp_fun_Y16_10(Y24!0), Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.68 inference(symmetry,[status(thm)],[315])).
% 27.48/27.68 tff(317,plain,
% 27.48/27.68 (((~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))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(318,plain,
% 27.48/27.68 (r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[317, 303])).
% 27.48/27.68 tff(319,plain,
% 27.48/27.68 ((r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(320,plain,
% 27.48/27.68 (r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[319, 318])).
% 27.48/27.68 tff(321,plain,
% 27.48/27.68 (((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, 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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(322,plain,
% 27.48/27.68 ((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))))),
% 27.48/27.68 inference(quant_inst,[status(thm)],[])).
% 27.48/27.68 tff(323,plain,
% 27.48/27.68 ((~![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_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[322, 321])).
% 27.48/27.68 tff(324,plain,
% 27.48/27.68 (~((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[323, 71, 320])).
% 27.48/27.68 tff(325,plain,
% 27.48/27.68 (((~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(326,plain,
% 27.48/27.68 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_5(Y24!0, Y24!0), Y24!0)),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[325, 324])).
% 27.48/27.68 tff(327,plain,
% 27.48/27.68 (((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))) | r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(328,plain,
% 27.48/27.68 (r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[327, 303])).
% 27.48/27.68 tff(329,plain,
% 27.48/27.68 ((r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(330,plain,
% 27.48/27.68 (r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[329, 328])).
% 27.48/27.68 tff(331,plain,
% 27.48/27.68 (((~![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(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, 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(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))))),
% 27.48/27.68 inference(rewrite,[status(thm)],[])).
% 27.48/27.68 tff(332,plain,
% 27.48/27.68 ((~![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(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))))),
% 27.48/27.68 inference(quant_inst,[status(thm)],[])).
% 27.48/27.68 tff(333,plain,
% 27.48/27.68 ((~![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(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(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))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))))))),
% 27.48/27.68 inference(modus_ponens,[status(thm)],[332, 331])).
% 27.48/27.68 tff(334,plain,
% 27.48/27.68 (~((~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[333, 36, 330])).
% 27.48/27.68 tff(335,plain,
% 27.48/27.68 (((~r2(tptp_fun_Y7_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(336,plain,
% 27.48/27.68 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[335, 334])).
% 27.48/27.68 tff(337,plain,
% 27.48/27.68 (tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)) = tptp_fun_Y4_4(Y24!0, Y24!0)),
% 27.48/27.68 inference(symmetry,[status(thm)],[336])).
% 27.48/27.68 tff(338,plain,
% 27.48/27.68 (((~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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 27.48/27.68 inference(tautology,[status(thm)],[])).
% 27.48/27.68 tff(339,plain,
% 27.48/27.68 (r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))),
% 27.48/27.68 inference(unit_resolution,[status(thm)],[338, 303])).
% 27.48/27.68 tff(340,plain,
% 27.48/27.68 ((r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)))),
% 27.48/27.69 inference(tautology,[status(thm)],[])).
% 27.48/27.69 tff(341,plain,
% 27.48/27.69 (r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[340, 339])).
% 27.48/27.69 tff(342,plain,
% 27.48/27.69 (((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(343,plain,
% 27.48/27.69 ((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 27.48/27.69 inference(quant_inst,[status(thm)],[])).
% 27.48/27.69 tff(344,plain,
% 27.48/27.69 ((~![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, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0)) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[343, 342])).
% 27.48/27.69 tff(345,plain,
% 27.48/27.69 (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[344, 71, 341])).
% 27.48/27.69 tff(346,plain,
% 27.48/27.69 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_6(Y24!0, Y24!0))) | (~(tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 27.48/27.69 inference(tautology,[status(thm)],[])).
% 27.48/27.69 tff(347,plain,
% 27.48/27.69 (tptp_fun_Y7_6(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[346, 345])).
% 27.48/27.69 tff(348,plain,
% 27.48/27.69 (tptp_fun_Y7_6(Y24!0, Y24!0) = Y24!0),
% 27.48/27.69 inference(transitivity,[status(thm)],[347, 197, 78])).
% 27.48/27.69 tff(349,plain,
% 27.48/27.69 (tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 27.48/27.69 inference(monotonicity,[status(thm)],[348])).
% 27.48/27.69 tff(350,plain,
% 27.48/27.69 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_6(Y24!0, Y24!0))),
% 27.48/27.69 inference(symmetry,[status(thm)],[349])).
% 27.48/27.69 tff(351,plain,
% 27.48/27.69 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.69 inference(transitivity,[status(thm)],[350, 337, 326, 316, 128, 114, 83])).
% 27.48/27.69 tff(352,plain,
% 27.48/27.69 (r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) <=> r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))),
% 27.48/27.69 inference(monotonicity,[status(thm)],[314, 314, 314])).
% 27.48/27.69 tff(353,plain,
% 27.48/27.69 (r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0)) <=> r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.69 inference(symmetry,[status(thm)],[352])).
% 27.48/27.69 tff(354,plain,
% 27.48/27.69 ((~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))) <=> (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.69 inference(monotonicity,[status(thm)],[353])).
% 27.48/27.69 tff(355,plain,
% 27.48/27.69 (r1(tptp_fun_Y16_10(Y24!0)) <=> r1(Y24!0)),
% 27.48/27.69 inference(monotonicity,[status(thm)],[195])).
% 27.48/27.69 tff(356,plain,
% 27.48/27.69 (r1(Y24!0)),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[187, 355])).
% 27.48/27.69 tff(357,plain,
% 27.48/27.69 (^[Y1: $i, Y5: $i, Y2: $i, Y4: $i] : trans(monotonicity(rewrite(((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) <=> ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)))), ((((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> (((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y1)))))), rewrite((((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))), ((((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(358,plain,
% 27.48/27.69 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))),
% 27.48/27.69 inference(quant_intro,[status(thm)],[357])).
% 27.48/27.69 tff(359,plain,
% 27.48/27.69 (^[Y1: $i, Y5: $i, Y2: $i, Y4: $i] : refl((((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(360,plain,
% 27.48/27.69 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(quant_intro,[status(thm)],[359])).
% 27.48/27.69 tff(361,plain,
% 27.48/27.69 (![Y1: $i] : ![Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(pull_quant,[status(thm)],[])).
% 27.48/27.69 tff(362,plain,
% 27.48/27.69 (^[Y1: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y2: $i] : pull_quant(((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) <=> ![Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))))), (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) <=> ![Y2: $i] : ![Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))))), pull_quant(![Y2: $i] : ![Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) <=> ![Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2))))), (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) <=> ![Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))))), ((![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> (![Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))))), pull_quant((![Y2: $i, Y4: $i] : ((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))), ((![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(363,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i] : ![Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(quant_intro,[status(thm)],[362])).
% 27.48/27.69 tff(364,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(transitivity,[status(thm)],[363, 361])).
% 27.48/27.69 tff(365,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(transitivity,[status(thm)],[364, 360])).
% 27.48/27.69 tff(366,plain,
% 27.48/27.69 (^[Y1: $i] : rewrite((![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(367,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(quant_intro,[status(thm)],[366])).
% 27.48/27.69 tff(368,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(transitivity,[status(thm)],[367, 365])).
% 27.48/27.69 tff(369,plain,
% 27.48/27.69 (^[Y1: $i] : rewrite((![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2)))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y1)))) <=> (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1)))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(370,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2)))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y1)))) <=> ![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(quant_intro,[status(thm)],[369])).
% 27.48/27.69 tff(371,plain,
% 27.48/27.69 ((~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(372,plain,
% 27.48/27.69 ((~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y3))))) <=> (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(373,axiom,(~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y3: $i] : ((Y1 = Y3) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','onetimesoneeqone')).
% 27.48/27.69 tff(374,plain,
% 27.48/27.69 (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[373, 372])).
% 27.48/27.69 tff(375,plain,
% 27.48/27.69 (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[374, 371])).
% 27.48/27.69 tff(376,plain,
% 27.48/27.69 (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[375, 371])).
% 27.48/27.69 tff(377,plain,
% 27.48/27.69 (~?[Y1: $i] : (?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[376, 371])).
% 27.48/27.69 tff(378,plain,
% 27.48/27.69 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : nnf_neg(refl($oeq((~r4(Y2, Y2, Y1)), (~r4(Y2, Y2, Y1)))), nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r2(Y4, Y2))), (~(r1(Y4) & r2(Y4, Y2)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))), ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2))))), $oeq((~(r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2)))), ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2))))))), $oeq((~?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2)))), ![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2)))))), nnf_neg(proof_bind(^[Y5: $i] : refl($oeq((~(r1(Y5) & r2(Y5, Y1))), (~(r1(Y5) & r2(Y5, Y1)))))), $oeq((~?[Y5: $i] : (r1(Y5) & r2(Y5, Y1))), ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y1))))), $oeq((~(?[Y2: $i] : (r4(Y2, Y2, Y1) & ?[Y4: $i] : (r1(Y4) & r2(Y4, Y2))) & ?[Y5: $i] : (r1(Y5) & r2(Y5, Y1)))), (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2)))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y1))))))),
% 27.48/27.69 inference(bind,[status(th)],[])).
% 27.48/27.69 tff(379,plain,(
% 27.48/27.69 ![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : (~(r1(Y4) & r2(Y4, Y2)))) | ![Y5: $i] : (~(r1(Y5) & r2(Y5, Y1))))),
% 27.48/27.69 inference(nnf-neg,[status(sab)],[377, 378])).
% 27.48/27.69 tff(380,plain,
% 27.48/27.69 (![Y1: $i] : (![Y2: $i] : ((~r4(Y2, Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[379, 370])).
% 27.48/27.69 tff(381,plain,
% 27.48/27.69 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : (((~r4(Y2, Y2, Y1)) | ((~r1(Y4)) | (~r2(Y4, Y2)))) | ((~r1(Y5)) | (~r2(Y5, Y1))))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[380, 368])).
% 27.48/27.69 tff(382,plain,
% 27.48/27.69 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[381, 358])).
% 27.48/27.69 tff(383,plain,
% 27.48/27.69 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | ((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(384,plain,
% 27.48/27.69 (((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0)))) <=> ((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(385,plain,
% 27.48/27.69 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | ((~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0)))))),
% 27.48/27.69 inference(monotonicity,[status(thm)],[384])).
% 27.48/27.69 tff(386,plain,
% 27.48/27.69 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 27.48/27.69 inference(transitivity,[status(thm)],[385, 383])).
% 27.48/27.69 tff(387,plain,
% 27.48/27.69 ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))))),
% 27.48/27.69 inference(quant_inst,[status(thm)],[])).
% 27.48/27.69 tff(388,plain,
% 27.48/27.69 ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)) | (~r4(Y2, Y2, Y1)) | (~r1(Y5)) | (~r2(Y5, Y1)))) | (~r2(Y24!0, tptp_fun_Y15_5(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[387, 386])).
% 27.48/27.69 tff(389,plain,
% 27.48/27.69 ((~r1(Y24!0)) | (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0)))),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[388, 382, 305])).
% 27.48/27.69 tff(390,plain,
% 27.48/27.69 (~r4(tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0), tptp_fun_Y15_5(Y24!0, Y24!0))),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[389, 356])).
% 27.48/27.69 tff(391,plain,
% 27.48/27.69 (~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[390, 354])).
% 27.48/27.69 tff(392,plain,
% 27.48/27.69 (((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))) | r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))),
% 27.48/27.69 inference(tautology,[status(thm)],[])).
% 27.48/27.69 tff(393,plain,
% 27.48/27.69 ((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.69 inference(unit_resolution,[status(thm)],[392, 391])).
% 27.48/27.69 tff(394,plain,
% 27.48/27.69 (((~![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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.69 inference(rewrite,[status(thm)],[])).
% 27.48/27.69 tff(395,plain,
% 27.48/27.69 ((~![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_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))))),
% 27.48/27.69 inference(quant_inst,[status(thm)],[])).
% 27.48/27.69 tff(396,plain,
% 27.48/27.69 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.69 inference(modus_ponens,[status(thm)],[395, 394])).
% 27.48/27.69 tff(397,plain,
% 27.48/27.69 ((~((~r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))) | (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))))),
% 27.48/27.70 inference(unit_resolution,[status(thm)],[396, 102])).
% 27.48/27.70 tff(398,plain,
% 27.48/27.70 (~(r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.70 inference(unit_resolution,[status(thm)],[397, 393])).
% 27.48/27.70 tff(399,plain,
% 27.48/27.70 ((r4(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)) | (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))) | (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0))))),
% 27.48/27.70 inference(tautology,[status(thm)],[])).
% 27.48/27.70 tff(400,plain,
% 27.48/27.70 (~(tptp_fun_Y21_1(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y21_1(Y24!0), tptp_fun_Y21_1(Y24!0)))),
% 27.48/27.70 inference(unit_resolution,[status(thm)],[399, 398])).
% 27.48/27.70 tff(401,plain,
% 27.48/27.70 ($false),
% 27.48/27.70 inference(unit_resolution,[status(thm)],[400, 351])).
% 27.48/27.70 % SZS output end Proof
% 27.48/27.71 % E exiting
%------------------------------------------------------------------------------