TSTP Solution File: NUN068+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:27:52 EDT 2022
% Result : Theorem 19.79s 12.94s
% Output : Proof 19.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN068+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 16:30:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 19.79/12.94 % SZS status Theorem
% 19.79/12.94 % SZS output start Proof
% 19.79/12.94 tff(r2_type, type, (
% 19.79/12.94 r2: ( $i * $i ) > $o)).
% 19.79/12.94 tff(tptp_fun_Y21_1_type, type, (
% 19.79/12.94 tptp_fun_Y21_1: $i > $i)).
% 19.79/12.94 tff(tptp_fun_Y1_19_type, type, (
% 19.79/12.94 tptp_fun_Y1_19: $i > $i)).
% 19.79/12.94 tff(tptp_fun_Y24_0_type, type, (
% 19.79/12.94 tptp_fun_Y24_0: $i)).
% 19.79/12.94 tff(tptp_fun_Y3_21_type, type, (
% 19.79/12.94 tptp_fun_Y3_21: $i > $i)).
% 19.79/12.94 tff(tptp_fun_Y2_20_type, type, (
% 19.79/12.94 tptp_fun_Y2_20: $i > $i)).
% 19.79/12.94 tff(r1_type, type, (
% 19.79/12.94 r1: $i > $o)).
% 19.79/12.94 tff(tptp_fun_Y4_22_type, type, (
% 19.79/12.94 tptp_fun_Y4_22: $i > $i)).
% 19.79/12.94 tff(tptp_fun_Y15_6_type, type, (
% 19.79/12.94 tptp_fun_Y15_6: ( $i * $i ) > $i)).
% 19.79/12.94 tff(tptp_fun_Y4_4_type, type, (
% 19.79/12.94 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 19.79/12.94 tff(tptp_fun_Y5_5_type, type, (
% 19.79/12.94 tptp_fun_Y5_5: ( $i * $i ) > $i)).
% 19.79/12.94 tff(r3_type, type, (
% 19.79/12.94 r3: ( $i * $i * $i ) > $o)).
% 19.79/12.94 tff(tptp_fun_Y7_7_type, type, (
% 19.79/12.94 tptp_fun_Y7_7: ( $i * $i ) > $i)).
% 19.79/12.94 tff(tptp_fun_Y14_10_type, type, (
% 19.79/12.94 tptp_fun_Y14_10: ( $i * $i ) > $i)).
% 19.79/12.94 tff(r4_type, type, (
% 19.79/12.94 r4: ( $i * $i * $i ) > $o)).
% 19.79/12.94 tff(tptp_fun_Y6_11_type, type, (
% 19.79/12.94 tptp_fun_Y6_11: ( $i * $i ) > $i)).
% 19.79/12.94 tff(tptp_fun_Y2_8_type, type, (
% 19.79/12.94 tptp_fun_Y2_8: ( $i * $i ) > $i)).
% 19.79/12.94 tff(tptp_fun_Y3_9_type, type, (
% 19.79/12.94 tptp_fun_Y3_9: ( $i * $i ) > $i)).
% 19.79/12.94 tff(1,assumption,(~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))), introduced(assumption)).
% 19.79/12.94 tff(2,plain,
% 19.79/12.94 (((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.94 inference(tautology,[status(thm)],[])).
% 19.79/12.94 tff(3,plain,
% 19.79/12.94 (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.94 inference(unit_resolution,[status(thm)],[2, 1])).
% 19.79/12.94 tff(4,plain,
% 19.79/12.94 (r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.94 inference(monotonicity,[status(thm)],[3])).
% 19.79/12.94 tff(5,plain,
% 19.79/12.94 (r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.94 inference(symmetry,[status(thm)],[4])).
% 19.79/12.94 tff(6,plain,
% 19.79/12.94 (((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) | r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.94 inference(tautology,[status(thm)],[])).
% 19.79/12.94 tff(7,plain,
% 19.79/12.94 (r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.94 inference(unit_resolution,[status(thm)],[6, 1])).
% 19.79/12.94 tff(8,plain,
% 19.79/12.94 (r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.94 inference(modus_ponens,[status(thm)],[7, 5])).
% 19.79/12.94 tff(9,plain,
% 19.79/12.94 (^[X1: $i, X8: $i] : rewrite((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))) <=> (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1))))))),
% 19.79/12.94 inference(bind,[status(th)],[])).
% 19.79/12.94 tff(10,plain,
% 19.79/12.94 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))) <=> ![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 19.79/12.94 inference(quant_intro,[status(thm)],[9])).
% 19.79/12.94 tff(11,plain,
% 19.79/12.94 (^[X1: $i, X8: $i] : trans(monotonicity(rewrite(((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)))), ((((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> ((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))), rewrite(((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))), ((((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 19.79/12.94 inference(bind,[status(th)],[])).
% 19.79/12.94 tff(12,plain,
% 19.79/12.94 (![X1: $i, X8: $i] : (((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))) <=> ![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))),
% 19.79/12.94 inference(quant_intro,[status(thm)],[11])).
% 19.79/12.94 tff(13,plain,
% 19.79/12.94 (![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] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 19.79/12.94 inference(rewrite,[status(thm)],[])).
% 19.79/12.94 tff(14,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')).
% 19.79/12.94 tff(15,plain,
% 19.79/12.94 (![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)))),
% 19.79/12.94 inference(modus_ponens,[status(thm)],[14, 13])).
% 19.79/12.94 tff(16,plain,(
% 19.79/12.94 ![X1: $i, X8: $i] : (((r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) & (r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1))))),
% 19.79/12.94 inference(skolemize,[status(sab)],[15])).
% 19.79/12.94 tff(17,plain,
% 19.79/12.94 (![X1: $i, X8: $i] : (r2(X8, tptp_fun_Y15_6(X8, X1)) & r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1)) & (tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1)) & r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1)) & r3(X1, X8, tptp_fun_Y7_7(X8, X1)))),
% 19.79/12.94 inference(modus_ponens,[status(thm)],[16, 12])).
% 19.79/12.94 tff(18,plain,
% 19.79/12.94 (![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))),
% 19.79/12.94 inference(modus_ponens,[status(thm)],[17, 10])).
% 19.79/12.94 tff(19,plain,
% 19.79/12.94 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.94 inference(rewrite,[status(thm)],[])).
% 19.79/12.94 tff(20,plain,
% 19.79/12.94 ((~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) <=> (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.94 inference(rewrite,[status(thm)],[])).
% 19.79/12.94 tff(21,plain,
% 19.79/12.94 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.94 inference(monotonicity,[status(thm)],[20])).
% 19.79/12.94 tff(22,plain,
% 19.79/12.94 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.95 inference(transitivity,[status(thm)],[21, 19])).
% 19.79/12.95 tff(23,plain,
% 19.79/12.95 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(24,plain,
% 19.79/12.95 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[23, 22])).
% 19.79/12.95 tff(25,plain,
% 19.79/12.95 (~((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[24, 18])).
% 19.79/12.95 tff(26,plain,
% 19.79/12.95 (((~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y5_5(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))) | r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.95 inference(tautology,[status(thm)],[])).
% 19.79/12.95 tff(27,plain,
% 19.79/12.95 (r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[26, 25])).
% 19.79/12.95 tff(28,plain,
% 19.79/12.95 ((r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 19.79/12.95 inference(tautology,[status(thm)],[])).
% 19.79/12.95 tff(29,plain,
% 19.79/12.95 (r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[28, 27])).
% 19.79/12.95 tff(30,plain,
% 19.79/12.95 (^[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)))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(31,plain,
% 19.79/12.95 (![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))))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[30])).
% 19.79/12.95 tff(32,plain,
% 19.79/12.95 (^[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)))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(33,plain,
% 19.79/12.95 (![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))))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[32])).
% 19.79/12.95 tff(34,plain,
% 19.79/12.95 (![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))))),
% 19.79/12.95 inference(pull_quant,[status(thm)],[])).
% 19.79/12.95 tff(35,plain,
% 19.79/12.95 (![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)))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(36,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')).
% 19.79/12.95 tff(37,plain,
% 19.79/12.95 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[36, 35])).
% 19.79/12.95 tff(38,plain,(
% 19.79/12.95 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 19.79/12.95 inference(skolemize,[status(sab)],[37])).
% 19.79/12.95 tff(39,plain,
% 19.79/12.95 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[38, 34])).
% 19.79/12.95 tff(40,plain,
% 19.79/12.95 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[39, 33])).
% 19.79/12.95 tff(41,plain,
% 19.79/12.95 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[40, 31])).
% 19.79/12.95 tff(42,plain,
% 19.79/12.95 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(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_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(43,plain,
% 19.79/12.95 (((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) <=> ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(44,plain,
% 19.79/12.95 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))))),
% 19.79/12.95 inference(monotonicity,[status(thm)],[43])).
% 19.79/12.95 tff(45,plain,
% 19.79/12.95 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 19.79/12.95 inference(transitivity,[status(thm)],[44, 42])).
% 19.79/12.95 tff(46,plain,
% 19.79/12.95 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(47,plain,
% 19.79/12.95 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[46, 45])).
% 19.79/12.95 tff(48,plain,
% 19.79/12.95 (~((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[47, 41, 29])).
% 19.79/12.95 tff(49,plain,
% 19.79/12.95 (((~(tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))) | (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(tautology,[status(thm)],[])).
% 19.79/12.95 tff(50,plain,
% 19.79/12.95 (tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[49, 48])).
% 19.79/12.95 tff(51,plain,
% 19.79/12.95 (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 19.79/12.95 inference(symmetry,[status(thm)],[50])).
% 19.79/12.95 tff(52,plain,
% 19.79/12.95 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(53,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[52])).
% 19.79/12.95 tff(54,plain,
% 19.79/12.95 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(55,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[54])).
% 19.79/12.95 tff(56,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(transitivity,[status(thm)],[55, 53])).
% 19.79/12.95 tff(57,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(58,plain,
% 19.79/12.95 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(59,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[58])).
% 19.79/12.95 tff(60,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 19.79/12.95 tff(61,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[60, 59])).
% 19.79/12.95 tff(62,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[61, 57])).
% 19.79/12.95 tff(63,plain,(
% 19.79/12.95 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(skolemize,[status(sab)],[62])).
% 19.79/12.95 tff(64,plain,
% 19.79/12.95 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[63, 56])).
% 19.79/12.95 tff(65,plain,
% 19.79/12.95 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(66,plain,
% 19.79/12.95 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(67,plain,
% 19.79/12.95 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[66, 65])).
% 19.79/12.95 tff(68,plain,
% 19.79/12.95 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[67, 64, 27])).
% 19.79/12.95 tff(69,plain,
% 19.79/12.95 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | ((~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(70,plain,
% 19.79/12.95 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | ((~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(71,plain,
% 19.79/12.95 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[70, 69])).
% 19.79/12.95 tff(72,plain,
% 19.79/12.95 (~r1(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[71, 68, 51])).
% 19.79/12.95 tff(73,plain,
% 19.79/12.95 ($false),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[72, 8])).
% 19.79/12.95 tff(74,plain,((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))), inference(lemma,lemma(discharge,[]))).
% 19.79/12.95 tff(75,plain,
% 19.79/12.95 (^[Y1: $i] : rewrite(((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) <=> ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(76,plain,
% 19.79/12.95 (![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[75])).
% 19.79/12.95 tff(77,plain,
% 19.79/12.95 (^[Y1: $i] : trans(monotonicity(rewrite(((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) <=> ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))), ((((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1)))))) <=> (((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1)))))))), rewrite((((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1)))))) <=> ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))), ((((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1)))))) <=> ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(78,plain,
% 19.79/12.95 (![Y1: $i] : (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1)))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[77])).
% 19.79/12.95 tff(79,plain,
% 19.79/12.95 ((~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4)))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(80,plain,
% 19.79/12.95 ((~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4)))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(81,axiom,(~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','nonzerosnononesexist')).
% 19.79/12.95 tff(82,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[81, 80])).
% 19.79/12.95 tff(83,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[82, 79])).
% 19.79/12.95 tff(84,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[83, 79])).
% 19.79/12.95 tff(85,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[84, 79])).
% 19.79/12.95 tff(86,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[85, 79])).
% 19.79/12.95 tff(87,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[86, 79])).
% 19.79/12.95 tff(88,plain,
% 19.79/12.95 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[87, 79])).
% 19.79/12.95 tff(89,plain,
% 19.79/12.95 (^[Y1: $i] : nnf_neg(trans(sk($oeq((~![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))))), (~((~(Y1 = tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, tptp_fun_Y2_20(Y1)))))))), nnf_neg(refl($oeq((~(~(Y1 = tptp_fun_Y2_20(Y1)))), (~(~(Y1 = tptp_fun_Y2_20(Y1)))))), sk($oeq((~![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, tptp_fun_Y2_20(Y1))))), (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))), $oeq((~((~(Y1 = tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, tptp_fun_Y2_20(Y1)))))), ((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))), $oeq((~![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))))), ((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))), sk($oeq((~![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4)))), (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))))), $oeq((~(![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) & ![Y4: $i] : ((~r1(Y4)) | (~(Y1 = Y4))))), (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(90,plain,(
% 19.79/12.95 ![Y1: $i] : (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))) | (~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))))),
% 19.79/12.95 inference(nnf-neg,[status(sab)],[88, 89])).
% 19.79/12.95 tff(91,plain,
% 19.79/12.95 (![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[90, 78])).
% 19.79/12.95 tff(92,plain,
% 19.79/12.95 (![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[91, 76])).
% 19.79/12.95 tff(93,plain,
% 19.79/12.95 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(94,plain,
% 19.79/12.95 (((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))) <=> ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(95,plain,
% 19.79/12.95 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))))),
% 19.79/12.95 inference(monotonicity,[status(thm)],[94])).
% 19.79/12.95 tff(96,plain,
% 19.79/12.95 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))),
% 19.79/12.95 inference(transitivity,[status(thm)],[95, 93])).
% 19.79/12.95 tff(97,plain,
% 19.79/12.95 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(98,plain,
% 19.79/12.95 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y4_22(Y1))) | (~(Y1 = tptp_fun_Y4_22(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y3_21(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[97, 96])).
% 19.79/12.95 tff(99,plain,
% 19.79/12.95 ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y4_22(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))) | (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[98, 92])).
% 19.79/12.95 tff(100,plain,
% 19.79/12.95 (~((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[99, 74])).
% 19.79/12.95 tff(101,plain,
% 19.79/12.95 (((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) | (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.95 inference(tautology,[status(thm)],[])).
% 19.79/12.95 tff(102,plain,
% 19.79/12.95 (tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[101, 100])).
% 19.79/12.95 tff(103,plain,
% 19.79/12.95 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.95 inference(monotonicity,[status(thm)],[102])).
% 19.79/12.95 tff(104,plain,
% 19.79/12.95 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(symmetry,[status(thm)],[103])).
% 19.79/12.95 tff(105,plain,
% 19.79/12.95 (((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) | r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.95 inference(tautology,[status(thm)],[])).
% 19.79/12.95 tff(106,plain,
% 19.79/12.95 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.95 inference(unit_resolution,[status(thm)],[105, 100])).
% 19.79/12.95 tff(107,plain,
% 19.79/12.95 (r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[106, 104])).
% 19.79/12.95 tff(108,plain,
% 19.79/12.95 (^[X2: $i, X9: $i] : rewrite((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))) <=> (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2))))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(109,plain,
% 19.79/12.95 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))) <=> ![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[108])).
% 19.79/12.95 tff(110,plain,
% 19.79/12.95 (^[X2: $i, X9: $i] : trans(monotonicity(rewrite(((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)))), ((((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> ((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))), rewrite(((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))), ((((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 19.79/12.95 inference(bind,[status(th)],[])).
% 19.79/12.95 tff(111,plain,
% 19.79/12.95 (![X2: $i, X9: $i] : (((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> ![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))),
% 19.79/12.95 inference(quant_intro,[status(thm)],[110])).
% 19.79/12.95 tff(112,plain,
% 19.79/12.95 (![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] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 19.79/12.95 inference(rewrite,[status(thm)],[])).
% 19.79/12.95 tff(113,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')).
% 19.79/12.95 tff(114,plain,
% 19.79/12.95 (![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)))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[113, 112])).
% 19.79/12.95 tff(115,plain,(
% 19.79/12.95 ![X2: $i, X9: $i] : (((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))))),
% 19.79/12.95 inference(skolemize,[status(sab)],[114])).
% 19.79/12.95 tff(116,plain,
% 19.79/12.95 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[115, 111])).
% 19.79/12.95 tff(117,plain,
% 19.79/12.95 (![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 19.79/12.95 inference(modus_ponens,[status(thm)],[116, 109])).
% 19.79/12.95 tff(118,plain,
% 19.79/12.95 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))) | (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y1_19(Y24!0), tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.95 inference(quant_inst,[status(thm)],[])).
% 19.79/12.95 tff(119,plain,
% 19.79/12.95 (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y1_19(Y24!0), tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[118, 117])).
% 19.79/12.96 tff(120,plain,
% 19.79/12.96 (((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_9(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y2_8(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r4(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y1_19(Y24!0), tptp_fun_Y6_11(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))) | r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.96 inference(tautology,[status(thm)],[])).
% 19.79/12.96 tff(121,plain,
% 19.79/12.96 (r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[120, 119])).
% 19.79/12.96 tff(122,plain,
% 19.79/12.96 ((r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) | (~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 19.79/12.96 inference(tautology,[status(thm)],[])).
% 19.79/12.96 tff(123,plain,
% 19.79/12.96 (r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[122, 121])).
% 19.79/12.96 tff(124,plain,
% 19.79/12.96 (((~![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_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(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_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(125,plain,
% 19.79/12.96 ((~![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_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))),
% 19.79/12.96 inference(quant_inst,[status(thm)],[])).
% 19.79/12.96 tff(126,plain,
% 19.79/12.96 ((~![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_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[125, 124])).
% 19.79/12.96 tff(127,plain,
% 19.79/12.96 (~((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[126, 41, 123])).
% 19.79/12.96 tff(128,plain,
% 19.79/12.96 (((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))),
% 19.79/12.96 inference(tautology,[status(thm)],[])).
% 19.79/12.96 tff(129,plain,
% 19.79/12.96 (tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[128, 127])).
% 19.79/12.96 tff(130,plain,
% 19.79/12.96 (tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 19.79/12.96 inference(symmetry,[status(thm)],[129])).
% 19.79/12.96 tff(131,plain,
% 19.79/12.96 ((tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) <=> (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.96 inference(monotonicity,[status(thm)],[130])).
% 19.79/12.96 tff(132,plain,
% 19.79/12.96 ((tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) <=> (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))),
% 19.79/12.96 inference(symmetry,[status(thm)],[131])).
% 19.79/12.96 tff(133,plain,
% 19.79/12.96 ((~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) <=> (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.96 inference(monotonicity,[status(thm)],[132])).
% 19.79/12.96 tff(134,plain,
% 19.79/12.96 (((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y2_20(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) | r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.96 inference(tautology,[status(thm)],[])).
% 19.79/12.96 tff(135,plain,
% 19.79/12.96 (r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[134, 100])).
% 19.79/12.96 tff(136,plain,
% 19.79/12.96 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(137,plain,
% 19.79/12.96 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 19.79/12.96 inference(quant_inst,[status(thm)],[])).
% 19.79/12.96 tff(138,plain,
% 19.79/12.96 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y1_19(Y24!0), tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[137, 136])).
% 19.79/12.96 tff(139,plain,
% 19.79/12.96 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[138, 64, 121])).
% 19.79/12.96 tff(140,plain,
% 19.79/12.96 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | ((~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(141,plain,
% 19.79/12.96 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | ((~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 19.79/12.96 inference(quant_inst,[status(thm)],[])).
% 19.79/12.96 tff(142,plain,
% 19.79/12.96 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~r1(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))) | (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[141, 140])).
% 19.79/12.96 tff(143,plain,
% 19.79/12.96 (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y14_10(tptp_fun_Y1_19(Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.96 inference(unit_resolution,[status(thm)],[142, 139, 135])).
% 19.79/12.96 tff(144,plain,
% 19.79/12.96 (~(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[143, 133])).
% 19.79/12.96 tff(145,plain,
% 19.79/12.96 (r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 19.79/12.96 inference(monotonicity,[status(thm)],[51])).
% 19.79/12.96 tff(146,plain,
% 19.79/12.96 (r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y15_6(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) <=> r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.96 inference(symmetry,[status(thm)],[145])).
% 19.79/12.96 tff(147,plain,
% 19.79/12.96 (r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[27, 146])).
% 19.79/12.96 tff(148,plain,
% 19.79/12.96 (^[X3: $i, X10: $i, Y12: $i, Y13: $i] : trans(monotonicity(rewrite(((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))), (((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))))), rewrite(((X3 = X10) | ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))), (((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))))),
% 19.79/12.96 inference(bind,[status(th)],[])).
% 19.79/12.96 tff(149,plain,
% 19.79/12.96 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))),
% 19.79/12.96 inference(quant_intro,[status(thm)],[148])).
% 19.79/12.96 tff(150,plain,
% 19.79/12.96 (^[X3: $i, X10: $i, Y12: $i, Y13: $i] : refl(((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))))),
% 19.79/12.96 inference(bind,[status(th)],[])).
% 19.79/12.96 tff(151,plain,
% 19.79/12.96 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(quant_intro,[status(thm)],[150])).
% 19.79/12.96 tff(152,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(pull_quant,[status(thm)],[])).
% 19.79/12.96 tff(153,plain,
% 19.79/12.96 (^[X3: $i, X10: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y12: $i] : pull_quant(((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i] : ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), pull_quant(![Y12: $i] : ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))))), pull_quant(((X3 = X10) | ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))))),
% 19.79/12.96 inference(bind,[status(th)],[])).
% 19.79/12.96 tff(154,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(quant_intro,[status(thm)],[153])).
% 19.79/12.96 tff(155,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(transitivity,[status(thm)],[154, 152])).
% 19.79/12.96 tff(156,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(transitivity,[status(thm)],[155, 151])).
% 19.79/12.96 tff(157,plain,
% 19.79/12.96 (^[X3: $i, X10: $i] : rewrite(((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))))),
% 19.79/12.96 inference(bind,[status(th)],[])).
% 19.79/12.96 tff(158,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(quant_intro,[status(thm)],[157])).
% 19.79/12.96 tff(159,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(transitivity,[status(thm)],[158, 156])).
% 19.79/12.96 tff(160,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(161,plain,
% 19.79/12.96 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y13: $i] : rewrite(((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> (![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))))), rewrite((![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) <=> ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))))), (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) | (X3 = X10)))), rewrite((![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))))),
% 19.79/12.96 inference(bind,[status(th)],[])).
% 19.79/12.96 tff(162,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(quant_intro,[status(thm)],[161])).
% 19.79/12.96 tff(163,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 19.79/12.96 tff(164,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[163, 162])).
% 19.79/12.96 tff(165,plain,
% 19.79/12.96 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[164, 160])).
% 19.79/12.96 tff(166,plain,(
% 19.79/12.96 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(skolemize,[status(sab)],[165])).
% 19.79/12.96 tff(167,plain,
% 19.79/12.96 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[166, 159])).
% 19.79/12.96 tff(168,plain,
% 19.79/12.96 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))),
% 19.79/12.96 inference(modus_ponens,[status(thm)],[167, 149])).
% 19.79/12.96 tff(169,plain,
% 19.79/12.96 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(170,plain,
% 19.79/12.96 (($false | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(171,plain,
% 19.79/12.96 ((~$true) <=> $false),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(172,plain,
% 19.79/12.96 ((tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> $true),
% 19.79/12.96 inference(rewrite,[status(thm)],[])).
% 19.79/12.96 tff(173,plain,
% 19.79/12.96 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> (~$true)),
% 19.79/12.96 inference(monotonicity,[status(thm)],[172])).
% 19.79/12.96 tff(174,plain,
% 19.79/12.96 ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> $false),
% 19.79/12.96 inference(transitivity,[status(thm)],[173, 171])).
% 19.79/12.96 tff(175,plain,
% 19.79/12.96 (((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> ($false | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.96 inference(monotonicity,[status(thm)],[174])).
% 19.79/12.96 tff(176,plain,
% 19.79/12.96 (((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) <=> ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))),
% 19.79/12.96 inference(transitivity,[status(thm)],[175, 170])).
% 19.79/12.96 tff(177,plain,
% 19.79/12.96 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))))),
% 19.79/12.97 inference(monotonicity,[status(thm)],[176])).
% 19.79/12.97 tff(178,plain,
% 19.79/12.97 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))))),
% 19.79/12.97 inference(transitivity,[status(thm)],[177, 169])).
% 19.79/12.97 tff(179,plain,
% 19.79/12.97 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) = tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))),
% 19.79/12.97 inference(quant_inst,[status(thm)],[])).
% 19.79/12.97 tff(180,plain,
% 19.79/12.97 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))))) | (tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.97 inference(modus_ponens,[status(thm)],[179, 178])).
% 19.79/12.97 tff(181,plain,
% 19.79/12.97 ((tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))) = tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))), tptp_fun_Y21_1(tptp_fun_Y21_1(tptp_fun_Y1_19(Y24!0)))))),
% 19.79/12.97 inference(unit_resolution,[status(thm)],[180, 168, 147])).
% 19.79/12.97 tff(182,plain,
% 19.79/12.97 ($false),
% 19.79/12.97 inference(unit_resolution,[status(thm)],[181, 144, 107])).
% 19.79/12.97 % SZS output end Proof
%------------------------------------------------------------------------------