TSTP Solution File: NUN066+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 0.18s 0.50s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : NUN066+2 : TPTP v8.1.0. Released v7.3.0.
% 0.13/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n024.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 16:19:48 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.
% 0.18/0.50 % SZS status Theorem
% 0.18/0.50 % SZS output start Proof
% 0.18/0.50 tff(r1_type, type, (
% 0.18/0.50 r1: $i > $o)).
% 0.18/0.50 tff(tptp_fun_Y4_4_type, type, (
% 0.18/0.50 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.18/0.50 tff(tptp_fun_Y24_0_type, type, (
% 0.18/0.50 tptp_fun_Y24_0: $i)).
% 0.18/0.50 tff(tptp_fun_Y5_23_type, type, (
% 0.18/0.50 tptp_fun_Y5_23: $i > $i)).
% 0.18/0.50 tff(tptp_fun_Y4_22_type, type, (
% 0.18/0.50 tptp_fun_Y4_22: $i > $i)).
% 0.18/0.50 tff(r2_type, type, (
% 0.18/0.50 r2: ( $i * $i ) > $o)).
% 0.18/0.50 tff(tptp_fun_Y2_20_type, type, (
% 0.18/0.50 tptp_fun_Y2_20: $i > $i)).
% 0.18/0.50 tff(tptp_fun_Y3_21_type, type, (
% 0.18/0.50 tptp_fun_Y3_21: $i > $i)).
% 0.18/0.50 tff(tptp_fun_Y21_1_type, type, (
% 0.18/0.50 tptp_fun_Y21_1: $i > $i)).
% 0.18/0.50 tff(tptp_fun_Y7_7_type, type, (
% 0.18/0.50 tptp_fun_Y7_7: ( $i * $i ) > $i)).
% 0.18/0.50 tff(r3_type, type, (
% 0.18/0.50 r3: ( $i * $i * $i ) > $o)).
% 0.18/0.50 tff(tptp_fun_Y5_5_type, type, (
% 0.18/0.50 tptp_fun_Y5_5: ( $i * $i ) > $i)).
% 0.18/0.50 tff(tptp_fun_Y15_6_type, type, (
% 0.18/0.50 tptp_fun_Y15_6: ( $i * $i ) > $i)).
% 0.18/0.50 tff(tptp_fun_Y22_2_type, type, (
% 0.18/0.50 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.18/0.50 tff(tptp_fun_Y16_13_type, type, (
% 0.18/0.50 tptp_fun_Y16_13: $i > $i)).
% 0.18/0.50 tff(tptp_fun_Y9_12_type, type, (
% 0.18/0.50 tptp_fun_Y9_12: $i > $i)).
% 0.18/0.50 tff(1,assumption,(~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))), introduced(assumption)).
% 0.18/0.50 tff(2,plain,
% 0.18/0.50 (((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(3,plain,
% 0.18/0.50 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.18/0.50 tff(4,plain,
% 0.18/0.50 (r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0)) <=> r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[3])).
% 0.18/0.50 tff(5,plain,
% 0.18/0.50 (r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0))) <=> r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(symmetry,[status(thm)],[4])).
% 0.18/0.50 tff(6,plain,
% 0.18/0.50 (((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))) | r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(7,plain,
% 0.18/0.50 (r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[6, 1])).
% 0.18/0.50 tff(8,plain,
% 0.18/0.50 (r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[7, 5])).
% 0.18/0.50 tff(9,plain,
% 0.18/0.50 ((tptp_fun_Y4_4(Y24!0, Y24!0) = Y24!0) <=> (Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(commutativity,[status(thm)],[])).
% 0.18/0.50 tff(10,plain,
% 0.18/0.50 (^[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))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(11,plain,
% 0.18/0.50 (![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)))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.50 tff(12,plain,
% 0.18/0.50 (^[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)))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(13,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.50 tff(14,plain,
% 0.18/0.50 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7))) <=> ![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(15,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/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.18/0.50 tff(16,plain,
% 0.18/0.50 (![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.18/0.50 tff(17,plain,(
% 0.18/0.50 ![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))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[16])).
% 0.18/0.50 tff(18,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.18/0.50 tff(19,plain,
% 0.18/0.50 (![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)))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 ((~![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(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(21,plain,
% 0.18/0.50 (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 (((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))) | r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(23,plain,
% 0.18/0.50 (r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 ((r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 (r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.18/0.50 tff(26,plain,
% 0.18/0.50 (^[X11: $i, X12: $i] : refl(((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[26])).
% 0.18/0.50 tff(28,plain,
% 0.18/0.50 (^[X11: $i, X12: $i] : rewrite((((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11)))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(29,plain,
% 0.18/0.50 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[28])).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11)))) <=> ![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.18/0.50 inference(pull_quant,[status(thm)],[])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.50 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(32,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.18/0.50 tff(33,plain,
% 0.18/0.50 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.18/0.50 tff(34,plain,(
% 0.18/0.50 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[33])).
% 0.18/0.50 tff(35,plain,
% 0.18/0.50 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.18/0.50 tff(36,plain,
% 0.18/0.50 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.18/0.50 tff(37,plain,
% 0.18/0.50 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.18/0.50 tff(38,plain,
% 0.18/0.50 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(39,plain,
% 0.18/0.50 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(40,plain,
% 0.18/0.50 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.50 tff(41,plain,
% 0.18/0.50 (~((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[40, 37, 25])).
% 0.18/0.50 tff(42,plain,
% 0.18/0.50 (((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(43,plain,
% 0.18/0.50 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.50 tff(44,plain,
% 0.18/0.50 (tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)) = tptp_fun_Y4_4(Y24!0, Y24!0)),
% 0.18/0.50 inference(symmetry,[status(thm)],[43])).
% 0.18/0.50 tff(45,plain,
% 0.18/0.50 (((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))) | r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(46,plain,
% 0.18/0.50 (r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[45, 21])).
% 0.18/0.50 tff(47,plain,
% 0.18/0.50 ((r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))),
% 0.18/0.50 inference(tautology,[status(thm)],[])).
% 0.18/0.50 tff(48,plain,
% 0.18/0.50 (r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 0.18/0.50 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.18/0.50 tff(49,plain,
% 0.18/0.50 (^[X13: $i, X14: $i, X15: $i] : refl(((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.18/0.50 inference(bind,[status(th)],[])).
% 0.18/0.50 tff(50,plain,
% 0.18/0.50 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.18/0.50 inference(quant_intro,[status(thm)],[49])).
% 0.18/0.50 tff(51,plain,
% 0.18/0.50 (^[X13: $i, X14: $i, X15: $i] : rewrite((((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13)))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.51 tff(53,plain,
% 0.18/0.51 (![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13)))) <=> ![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.18/0.51 inference(pull_quant,[status(thm)],[])).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22))) <=> ![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(55,axiom,(![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.18/0.51 tff(57,plain,(
% 0.18/0.51 ![X13: $i, X14: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[56])).
% 0.18/0.51 tff(58,plain,
% 0.18/0.51 (![X13: $i, X14: $i, X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = tptp_fun_Y22_2(X14, X13)))) | (r3(X13, X14, X15) & (X15 = tptp_fun_Y22_2(X14, X13))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[57, 53])).
% 0.18/0.51 tff(59,plain,
% 0.18/0.51 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[58, 52])).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 (![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[59, 50])).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(62,plain,
% 0.18/0.51 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (~((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[63, 60, 48])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 (((~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))) | (~(tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)))) | (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y7_7(Y24!0, Y24!0)),
% 0.18/0.51 inference(symmetry,[status(thm)],[66])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 (^[X4: $i] : rewrite((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)) <=> (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 (![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)) <=> ![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[68])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (^[X4: $i] : rewrite(((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4)) <=> (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4)))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (![X4: $i] : ((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4)) <=> ![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[70])).
% 0.18/0.51 tff(72,plain,
% 0.18/0.51 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4)) <=> ![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(73,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.18/0.51 tff(74,plain,
% 0.18/0.51 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.18/0.51 tff(75,plain,(
% 0.18/0.51 ![X4: $i] : ((r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) & (tptp_fun_Y9_12(X4) = X4))),
% 0.18/0.51 inference(skolemize,[status(sab)],[74])).
% 0.18/0.51 tff(76,plain,
% 0.18/0.51 (![X4: $i] : (r1(tptp_fun_Y16_13(X4)) & r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4)) & (tptp_fun_Y9_12(X4) = X4))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.18/0.51 tff(77,plain,
% 0.18/0.51 (![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.18/0.51 tff(78,plain,
% 0.18/0.51 ((~![X4: $i] : (~((~r1(tptp_fun_Y16_13(X4))) | (~r3(X4, tptp_fun_Y16_13(X4), tptp_fun_Y9_12(X4))) | (~(tptp_fun_Y9_12(X4) = X4))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(79,plain,
% 0.18/0.51 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.18/0.51 tff(80,plain,
% 0.18/0.51 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | r1(tptp_fun_Y16_13(Y24!0))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(81,plain,
% 0.18/0.51 (r1(tptp_fun_Y16_13(Y24!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.18/0.51 tff(82,plain,
% 0.18/0.51 ((r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_13(Y24!0)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(83,plain,
% 0.18/0.51 (r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.18/0.51 tff(84,plain,
% 0.18/0.51 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(85,plain,
% 0.18/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[84])).
% 0.18/0.51 tff(86,plain,
% 0.18/0.51 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(87,plain,
% 0.18/0.51 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[86])).
% 0.18/0.51 tff(88,plain,
% 0.18/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(89,plain,
% 0.18/0.51 (^[Y24: $i] : quant_intro(proof_bind(^[X19: $i] : rewrite((((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))))), (![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(90,plain,
% 0.18/0.51 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[89])).
% 0.18/0.51 tff(91,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.18/0.51 tff(92,plain,
% 0.18/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.18/0.51 tff(93,plain,
% 0.18/0.51 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.18/0.51 tff(94,plain,(
% 0.18/0.51 $oeq(![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))), ![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))))),
% 0.18/0.51 inference(transitivity,[status(sab)],[93])).
% 0.18/0.51 tff(95,plain,
% 0.18/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.18/0.51 tff(96,plain,
% 0.18/0.51 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.18/0.51 tff(97,plain,
% 0.18/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(98,plain,
% 0.18/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(99,plain,
% 0.18/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.18/0.51 tff(100,plain,
% 0.18/0.51 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[99, 96, 83])).
% 0.18/0.51 tff(101,plain,
% 0.18/0.51 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0))) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(102,plain,
% 0.18/0.51 (tptp_fun_Y16_13(Y24!0) = Y24!0),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.18/0.51 tff(103,plain,
% 0.18/0.51 (Y24!0 = tptp_fun_Y16_13(Y24!0)),
% 0.18/0.51 inference(symmetry,[status(thm)],[102])).
% 0.18/0.51 tff(104,plain,
% 0.18/0.51 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[103])).
% 0.18/0.51 tff(105,plain,
% 0.18/0.51 (tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.51 inference(symmetry,[status(thm)],[104])).
% 0.18/0.51 tff(106,plain,
% 0.18/0.51 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | (tptp_fun_Y9_12(Y24!0) = Y24!0)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(107,plain,
% 0.18/0.51 (tptp_fun_Y9_12(Y24!0) = Y24!0),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[106, 79])).
% 0.18/0.51 tff(108,plain,
% 0.18/0.51 (Y24!0 = tptp_fun_Y9_12(Y24!0)),
% 0.18/0.51 inference(symmetry,[status(thm)],[107])).
% 0.18/0.51 tff(109,plain,
% 0.18/0.51 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0) <=> r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[108])).
% 0.18/0.51 tff(110,plain,
% 0.18/0.51 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0)) <=> r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.51 inference(symmetry,[status(thm)],[109])).
% 0.18/0.51 tff(111,plain,
% 0.18/0.51 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))) | (~(tptp_fun_Y9_12(Y24!0) = Y24!0))) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(112,plain,
% 0.18/0.51 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[111, 79])).
% 0.18/0.51 tff(113,plain,
% 0.18/0.51 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[112, 110])).
% 0.18/0.51 tff(114,plain,
% 0.18/0.51 (((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(115,plain,
% 0.18/0.51 ((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.18/0.51 tff(116,plain,
% 0.18/0.51 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(117,plain,
% 0.18/0.51 (((~(r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))))) <=> ((~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(118,plain,
% 0.18/0.51 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))))))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[117])).
% 0.18/0.51 tff(119,plain,
% 0.18/0.51 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[118, 116])).
% 0.18/0.51 tff(120,plain,
% 0.18/0.51 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(121,plain,
% 0.18/0.51 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.18/0.51 tff(122,plain,
% 0.18/0.51 ((~((Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)) | r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0))) | (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[121, 60])).
% 0.18/0.51 tff(123,plain,
% 0.18/0.51 (~((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[122, 115])).
% 0.18/0.51 tff(124,plain,
% 0.18/0.51 (((~r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)) | (~(Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)))) | (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(125,plain,
% 0.18/0.51 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.18/0.51 tff(126,plain,
% 0.18/0.51 (Y24!0 = tptp_fun_Y7_7(Y24!0, Y24!0)),
% 0.18/0.51 inference(transitivity,[status(thm)],[125, 105, 67])).
% 0.18/0.51 tff(127,plain,
% 0.18/0.51 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.18/0.51 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.51 tff(128,plain,
% 0.18/0.51 (((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))) | r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(129,plain,
% 0.18/0.51 (r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[128, 1])).
% 0.18/0.51 tff(130,plain,
% 0.18/0.51 ((r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(131,plain,
% 0.18/0.51 (r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.18/0.51 tff(132,plain,
% 0.18/0.51 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(133,plain,
% 0.18/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(134,plain,
% 0.18/0.51 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))) | (~(r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.18/0.51 tff(135,plain,
% 0.18/0.51 (~((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[134, 96, 131])).
% 0.18/0.51 tff(136,plain,
% 0.18/0.51 (((~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))) | (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(137,plain,
% 0.18/0.51 (tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.18/0.51 tff(138,plain,
% 0.18/0.51 (tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))) = tptp_fun_Y21_1(Y24!0)),
% 0.18/0.51 inference(monotonicity,[status(thm)],[137])).
% 0.18/0.51 tff(139,plain,
% 0.18/0.51 (((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))) | r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(140,plain,
% 0.18/0.51 (r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[139, 1])).
% 0.18/0.51 tff(141,plain,
% 0.18/0.51 ((r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(142,plain,
% 0.18/0.51 (r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.18/0.51 tff(143,plain,
% 0.18/0.51 (((~![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_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(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_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(144,plain,
% 0.18/0.51 ((~![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_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(145,plain,
% 0.18/0.52 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.18/0.52 tff(146,plain,
% 0.18/0.52 (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[145, 37, 142])).
% 0.18/0.52 tff(147,plain,
% 0.18/0.52 (((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(148,plain,
% 0.18/0.52 (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.18/0.52 tff(149,plain,
% 0.18/0.52 (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y4_4(Y24!0, Y24!0)),
% 0.18/0.52 inference(transitivity,[status(thm)],[148, 138, 127, 44])).
% 0.18/0.52 tff(150,plain,
% 0.18/0.52 ((tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0) <=> (tptp_fun_Y4_4(Y24!0, Y24!0) = Y24!0)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[149])).
% 0.18/0.52 tff(151,plain,
% 0.18/0.52 ((tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0) <=> (Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[150, 9])).
% 0.18/0.52 tff(152,plain,
% 0.18/0.52 ((Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0)) <=> (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.52 inference(symmetry,[status(thm)],[151])).
% 0.18/0.52 tff(153,plain,
% 0.18/0.52 ((~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))) <=> (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[152])).
% 0.18/0.52 tff(154,plain,
% 0.18/0.52 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(155,plain,
% 0.18/0.52 (![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))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[154])).
% 0.18/0.52 tff(156,plain,
% 0.18/0.52 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(157,plain,
% 0.18/0.52 (![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))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[156])).
% 0.18/0.52 tff(158,plain,
% 0.18/0.52 (![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))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[157, 155])).
% 0.18/0.52 tff(159,plain,
% 0.18/0.52 (![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))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(160,plain,
% 0.18/0.52 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(161,plain,
% 0.18/0.52 (![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))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[160])).
% 0.18/0.52 tff(162,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.18/0.52 tff(163,plain,
% 0.18/0.52 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.18/0.52 tff(164,plain,
% 0.18/0.52 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.18/0.52 tff(165,plain,(
% 0.18/0.52 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.18/0.52 inference(skolemize,[status(sab)],[164])).
% 0.18/0.52 tff(166,plain,
% 0.18/0.52 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[165, 158])).
% 0.18/0.52 tff(167,plain,
% 0.18/0.52 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0)))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(168,plain,
% 0.18/0.52 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(169,plain,
% 0.18/0.52 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.18/0.52 tff(170,plain,
% 0.18/0.52 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[169, 166, 23])).
% 0.18/0.52 tff(171,plain,
% 0.18/0.52 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(172,plain,
% 0.18/0.52 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(173,plain,
% 0.18/0.52 ((~$true) <=> $false),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(174,plain,
% 0.18/0.52 ((r1(Y24!0) | $true) <=> $true),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(175,plain,
% 0.18/0.52 ((Y24!0 = Y24!0) <=> $true),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(176,plain,
% 0.18/0.52 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[175])).
% 0.18/0.52 tff(177,plain,
% 0.18/0.52 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.18/0.52 inference(transitivity,[status(thm)],[176, 174])).
% 0.18/0.52 tff(178,plain,
% 0.18/0.52 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[177])).
% 0.18/0.52 tff(179,plain,
% 0.18/0.52 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.18/0.52 inference(transitivity,[status(thm)],[178, 173])).
% 0.18/0.52 tff(180,plain,
% 0.18/0.52 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(181,plain,
% 0.18/0.52 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(182,plain,
% 0.18/0.52 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[175])).
% 0.18/0.52 tff(183,plain,
% 0.18/0.52 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.18/0.52 inference(transitivity,[status(thm)],[182, 173])).
% 0.18/0.52 tff(184,plain,
% 0.18/0.52 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[183])).
% 0.18/0.52 tff(185,plain,
% 0.18/0.52 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[184, 181])).
% 0.18/0.52 tff(186,plain,
% 0.18/0.52 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[185])).
% 0.18/0.52 tff(187,plain,
% 0.18/0.52 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.52 inference(transitivity,[status(thm)],[186, 180])).
% 0.18/0.52 tff(188,plain,
% 0.18/0.52 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[187, 179])).
% 0.18/0.52 tff(189,plain,
% 0.18/0.52 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.52 inference(transitivity,[status(thm)],[188, 172])).
% 0.18/0.52 tff(190,plain,
% 0.18/0.52 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[189])).
% 0.18/0.52 tff(191,plain,
% 0.18/0.52 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[190, 171])).
% 0.18/0.52 tff(192,plain,
% 0.18/0.52 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(193,plain,
% 0.18/0.52 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.18/0.52 tff(194,plain,
% 0.18/0.52 (r1(Y24!0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[193, 96])).
% 0.18/0.52 tff(195,plain,
% 0.18/0.52 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))) | ((~r1(Y24!0)) | (~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~r1(Y24!0)) | (~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(196,plain,
% 0.18/0.52 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))) | ((~r1(Y24!0)) | (~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(197,plain,
% 0.18/0.52 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~r1(Y24!0)) | (~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.18/0.52 tff(198,plain,
% 0.18/0.52 (~(Y24!0 = tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[197, 194, 170])).
% 0.18/0.52 tff(199,plain,
% 0.18/0.52 (~(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[198, 153])).
% 0.18/0.52 tff(200,plain,
% 0.18/0.52 (r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0)) <=> r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[126])).
% 0.18/0.52 tff(201,plain,
% 0.18/0.52 (r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) <=> r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.52 inference(symmetry,[status(thm)],[200])).
% 0.18/0.52 tff(202,plain,
% 0.18/0.52 (r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[23, 201])).
% 0.18/0.52 tff(203,plain,
% 0.18/0.52 (^[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))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(204,plain,
% 0.18/0.52 (![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))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[203])).
% 0.18/0.52 tff(205,plain,
% 0.18/0.52 (^[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))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(206,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[205])).
% 0.18/0.52 tff(207,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(pull_quant,[status(thm)],[])).
% 0.18/0.52 tff(208,plain,
% 0.18/0.52 (^[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)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(209,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[208])).
% 0.18/0.52 tff(210,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[209, 207])).
% 0.18/0.52 tff(211,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[210, 206])).
% 0.18/0.52 tff(212,plain,
% 0.18/0.52 (^[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))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(213,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[212])).
% 0.18/0.52 tff(214,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[213, 211])).
% 0.18/0.52 tff(215,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(216,plain,
% 0.18/0.52 (^[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)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(217,plain,
% 0.18/0.52 (![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)))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[216])).
% 0.18/0.52 tff(218,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 0.18/0.52 tff(219,plain,
% 0.18/0.52 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.18/0.52 tff(220,plain,
% 0.18/0.52 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.18/0.52 tff(221,plain,(
% 0.18/0.52 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.18/0.52 inference(skolemize,[status(sab)],[220])).
% 0.18/0.52 tff(222,plain,
% 0.18/0.52 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.18/0.52 tff(223,plain,
% 0.18/0.52 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[222, 204])).
% 0.18/0.52 tff(224,plain,
% 0.18/0.52 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(225,plain,
% 0.18/0.52 (($false | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)) <=> ((~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(226,plain,
% 0.18/0.52 ((tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0)) <=> $true),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(227,plain,
% 0.18/0.52 ((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) <=> (~$true)),
% 0.18/0.52 inference(monotonicity,[status(thm)],[226])).
% 0.18/0.52 tff(228,plain,
% 0.18/0.52 ((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) <=> $false),
% 0.18/0.52 inference(transitivity,[status(thm)],[227, 173])).
% 0.18/0.52 tff(229,plain,
% 0.18/0.52 (((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)) <=> ($false | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[228])).
% 0.18/0.52 tff(230,plain,
% 0.18/0.52 (((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)) <=> ((~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[229, 225])).
% 0.18/0.52 tff(231,plain,
% 0.18/0.52 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[230])).
% 0.18/0.52 tff(232,plain,
% 0.18/0.52 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(transitivity,[status(thm)],[231, 224])).
% 0.18/0.52 tff(233,plain,
% 0.18/0.52 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(234,plain,
% 0.18/0.52 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.18/0.52 tff(235,plain,
% 0.18/0.52 ((~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y4_4(Y24!0, Y24!0))) | (tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)) = Y24!0)),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[234, 223, 202])).
% 0.18/0.52 tff(236,plain,
% 0.18/0.52 ($false),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[235, 199, 8])).
% 0.18/0.52 tff(237,plain,((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.52 tff(238,plain,
% 0.18/0.52 (^[Y1: $i] : rewrite(((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(239,plain,
% 0.18/0.52 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[238])).
% 0.18/0.52 tff(240,plain,
% 0.18/0.52 (^[Y1: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~(Y1 = tptp_fun_Y2_20(Y1)))) <=> (Y1 = tptp_fun_Y2_20(Y1))), rewrite(((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))) <=> (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))), (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ((Y1 = tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))))), rewrite(((Y1 = tptp_fun_Y2_20(Y1)) & (r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))), (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) <=> ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), ((((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1)))))) <=> (((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1)))))))), rewrite((((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1)))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), ((((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1)))))) <=> ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(241,plain,
% 0.18/0.53 (![Y1: $i] : (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1)))))) <=> ![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[240])).
% 0.18/0.53 tff(242,plain,
% 0.18/0.53 ((~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(243,plain,
% 0.18/0.53 ((~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))) <=> (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(244,axiom,(~?[Y1: $i] : (![Y2: $i] : (![Y3: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))) | (~r2(Y3, Y2))) | (~(Y1 = Y2))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','nonzerononetwoexist')).
% 0.18/0.53 tff(245,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[244, 243])).
% 0.18/0.53 tff(246,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[245, 242])).
% 0.18/0.53 tff(247,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[246, 242])).
% 0.18/0.53 tff(248,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[247, 242])).
% 0.18/0.53 tff(249,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[248, 242])).
% 0.18/0.53 tff(250,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.18/0.53 tff(251,plain,
% 0.18/0.53 (~?[Y1: $i] : (![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[250, 242])).
% 0.18/0.53 tff(252,plain,
% 0.18/0.53 (^[Y1: $i] : nnf_neg(trans(sk($oeq((~![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), (~((~(Y1 = tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))))), nnf_neg(refl($oeq((~(~(Y1 = tptp_fun_Y2_20(Y1)))), (~(~(Y1 = tptp_fun_Y2_20(Y1)))))), trans(sk($oeq((~![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), (~((~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1)))))))), nnf_neg(refl($oeq((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))), (~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))))), sk($oeq((~![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1))))), (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))), $oeq((~((~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, tptp_fun_Y3_21(Y1)))))), ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), $oeq((~![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))), ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))), $oeq((~((~(Y1 = tptp_fun_Y2_20(Y1))) | ![Y3: $i] : ((~r2(Y3, tptp_fun_Y2_20(Y1))) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), ((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))))), $oeq((~![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3)))))), ((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))))), sk($oeq((~![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))), (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))))), $oeq((~(![Y2: $i] : ((~(Y1 = Y2)) | ![Y3: $i] : ((~r2(Y3, Y2)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y3))))) & ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))), (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(253,plain,(
% 0.18/0.53 ![Y1: $i] : (((~(~(Y1 = tptp_fun_Y2_20(Y1)))) & ((~(~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)))) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))))),
% 0.18/0.53 inference(nnf-neg,[status(sab)],[251, 252])).
% 0.18/0.53 tff(254,plain,
% 0.18/0.53 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | ((Y1 = tptp_fun_Y2_20(Y1)) & r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1)) & (~((~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1)))))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[253, 241])).
% 0.18/0.53 tff(255,plain,
% 0.18/0.53 (![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[254, 239])).
% 0.18/0.53 tff(256,plain,
% 0.18/0.53 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(257,plain,
% 0.18/0.53 (((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0))))))) <=> ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(258,plain,
% 0.18/0.53 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[257])).
% 0.18/0.53 tff(259,plain,
% 0.18/0.53 (((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))))))) <=> ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.18/0.53 inference(transitivity,[status(thm)],[258, 256])).
% 0.18/0.53 tff(260,plain,
% 0.18/0.53 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(261,plain,
% 0.18/0.53 ((~![Y1: $i] : ((~((~r1(tptp_fun_Y5_23(Y1))) | (~(Y1 = tptp_fun_Y5_23(Y1))))) | (~((~(Y1 = tptp_fun_Y2_20(Y1))) | (~r2(tptp_fun_Y3_21(Y1), tptp_fun_Y2_20(Y1))) | (~r1(tptp_fun_Y4_22(Y1))) | (~r2(tptp_fun_Y4_22(Y1), tptp_fun_Y3_21(Y1))))))) | (~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.18/0.53 tff(262,plain,
% 0.18/0.53 ((~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))) | (~((~r2(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y3_21(tptp_fun_Y4_4(Y24!0, Y24!0)), tptp_fun_Y2_20(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r1(tptp_fun_Y4_22(tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[261, 255])).
% 0.18/0.53 tff(263,plain,
% 0.18/0.53 (~((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[262, 237])).
% 0.18/0.53 tff(264,plain,
% 0.18/0.53 (((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(265,plain,
% 0.18/0.53 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.18/0.53 tff(266,plain,
% 0.18/0.53 (r1(tptp_fun_Y4_4(Y24!0, Y24!0)) <=> r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[265])).
% 0.18/0.53 tff(267,plain,
% 0.18/0.53 (r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0))) <=> r1(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.53 inference(symmetry,[status(thm)],[266])).
% 0.18/0.53 tff(268,plain,
% 0.18/0.53 (((~r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0))))) | r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(269,plain,
% 0.18/0.53 (r1(tptp_fun_Y5_23(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[268, 263])).
% 0.18/0.53 tff(270,plain,
% 0.18/0.53 (r1(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[269, 267])).
% 0.18/0.53 tff(271,plain,
% 0.18/0.53 (((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))) | (~(tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(272,plain,
% 0.18/0.53 (r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[271, 21])).
% 0.18/0.53 tff(273,plain,
% 0.18/0.53 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0)))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0)))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(274,plain,
% 0.18/0.53 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0)))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(275,plain,
% 0.18/0.53 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.18/0.53 tff(276,plain,
% 0.18/0.53 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[275, 166, 272])).
% 0.18/0.53 tff(277,plain,
% 0.18/0.53 ((r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(278,plain,
% 0.18/0.53 (r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[277, 272])).
% 0.18/0.53 tff(279,plain,
% 0.18/0.53 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(280,plain,
% 0.18/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(281,plain,
% 0.18/0.53 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0)) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[280, 279])).
% 0.18/0.53 tff(282,plain,
% 0.18/0.53 (~((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[281, 37, 278])).
% 0.18/0.53 tff(283,plain,
% 0.18/0.53 (((~r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))) | (~(tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)))) | (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(284,plain,
% 0.18/0.53 (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.18/0.53 tff(285,plain,
% 0.18/0.54 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0)),
% 0.18/0.54 inference(symmetry,[status(thm)],[284])).
% 0.18/0.54 tff(286,plain,
% 0.18/0.54 (tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 0.18/0.54 inference(symmetry,[status(thm)],[127])).
% 0.18/0.54 tff(287,plain,
% 0.18/0.54 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0)),
% 0.18/0.54 inference(transitivity,[status(thm)],[43, 286, 285])).
% 0.18/0.54 tff(288,plain,
% 0.18/0.54 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))) | ((~r1(tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0))))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))) | (~r1(tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(289,plain,
% 0.18/0.54 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))) | ((~r1(tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(290,plain,
% 0.18/0.54 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = tptp_fun_Y15_6(Y24!0, Y24!0))))) | (~r1(tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0)))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.18/0.54 tff(291,plain,
% 0.18/0.54 (~r1(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[290, 287, 276])).
% 0.18/0.54 tff(292,plain,
% 0.18/0.54 ($false),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[291, 270])).
% 0.18/0.54 % SZS output end Proof
%------------------------------------------------------------------------------