TSTP Solution File: NUN086+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN086+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 13:27:58 EDT 2022
% Result : Theorem 0.18s 0.39s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUN086+2 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.33 % Computer : n002.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Sep 2 16:44:01 EDT 2022
% 0.18/0.33 % CPUTime :
% 0.18/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.18/0.33 Usage: tptp [options] [-file:]file
% 0.18/0.33 -h, -? prints this message.
% 0.18/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.18/0.33 -m, -model generate model.
% 0.18/0.33 -p, -proof generate proof.
% 0.18/0.33 -c, -core generate unsat core of named formulas.
% 0.18/0.33 -st, -statistics display statistics.
% 0.18/0.33 -t:timeout set timeout (in second).
% 0.18/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.18/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.18/0.33 -<param>:<value> configuration parameter and value.
% 0.18/0.33 -o:<output-file> file to place output in.
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 tff(tptp_fun_Y24_0_type, type, (
% 0.18/0.39 tptp_fun_Y24_0: $i)).
% 0.18/0.39 tff(tptp_fun_Y2_8_type, type, (
% 0.18/0.39 tptp_fun_Y2_8: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y22_2_type, type, (
% 0.18/0.39 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y16_13_type, type, (
% 0.18/0.39 tptp_fun_Y16_13: $i > $i)).
% 0.18/0.39 tff(r3_type, type, (
% 0.18/0.39 r3: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Y9_12_type, type, (
% 0.18/0.39 tptp_fun_Y9_12: $i > $i)).
% 0.18/0.39 tff(r1_type, type, (
% 0.18/0.39 r1: $i > $o)).
% 0.18/0.39 tff(tptp_fun_Y6_11_type, type, (
% 0.18/0.39 tptp_fun_Y6_11: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y18_16_type, type, (
% 0.18/0.39 tptp_fun_Y18_16: $i > $i)).
% 0.18/0.39 tff(tptp_fun_Y8_14_type, type, (
% 0.18/0.39 tptp_fun_Y8_14: $i > $i)).
% 0.18/0.39 tff(r4_type, type, (
% 0.18/0.39 r4: ( $i * $i * $i ) > $o)).
% 0.18/0.39 tff(tptp_fun_Y17_15_type, type, (
% 0.18/0.39 tptp_fun_Y17_15: $i > $i)).
% 0.18/0.39 tff(tptp_fun_Y23_3_type, type, (
% 0.18/0.39 tptp_fun_Y23_3: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y3_9_type, type, (
% 0.18/0.39 tptp_fun_Y3_9: ( $i * $i ) > $i)).
% 0.18/0.39 tff(tptp_fun_Y14_10_type, type, (
% 0.18/0.39 tptp_fun_Y14_10: ( $i * $i ) > $i)).
% 0.18/0.39 tff(r2_type, type, (
% 0.18/0.39 r2: ( $i * $i ) > $o)).
% 0.18/0.39 tff(1,plain,
% 0.18/0.39 (^[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)))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(2,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.39 tff(3,plain,
% 0.18/0.39 (^[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)))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(4,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.39 tff(5,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(6,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')).
% 0.18/0.39 tff(7,plain,
% 0.18/0.39 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.18/0.39 tff(8,plain,(
% 0.18/0.39 ![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))),
% 0.18/0.39 inference(skolemize,[status(sab)],[7])).
% 0.18/0.39 tff(9,plain,
% 0.18/0.39 (![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))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.18/0.39 tff(10,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.18/0.39 tff(11,plain,
% 0.18/0.39 ((~![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))))),
% 0.18/0.39 inference(quant_inst,[status(thm)],[])).
% 0.18/0.39 tff(12,plain,
% 0.18/0.39 (~((~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)))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.18/0.39 tff(13,plain,
% 0.18/0.39 (((~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)),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(14,plain,
% 0.18/0.39 (tptp_fun_Y9_12(Y24!0) = Y24!0),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.18/0.39 tff(15,plain,
% 0.18/0.39 (Y24!0 = tptp_fun_Y9_12(Y24!0)),
% 0.18/0.39 inference(symmetry,[status(thm)],[14])).
% 0.18/0.39 tff(16,plain,
% 0.18/0.39 (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))),
% 0.18/0.39 inference(monotonicity,[status(thm)],[15])).
% 0.18/0.39 tff(17,plain,
% 0.18/0.39 (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)),
% 0.18/0.39 inference(symmetry,[status(thm)],[16])).
% 0.18/0.39 tff(18,plain,
% 0.18/0.39 (((~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))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(19,plain,
% 0.18/0.39 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[18, 12])).
% 0.18/0.39 tff(20,plain,
% 0.18/0.39 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[19, 17])).
% 0.18/0.39 tff(21,plain,
% 0.18/0.39 (((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))),
% 0.18/0.39 inference(tautology,[status(thm)],[])).
% 0.18/0.39 tff(22,plain,
% 0.18/0.39 ((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)),
% 0.18/0.39 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.18/0.39 tff(23,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(24,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[23])).
% 0.18/0.39 tff(25,plain,
% 0.18/0.39 (^[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)))))))),
% 0.18/0.39 inference(bind,[status(th)],[])).
% 0.18/0.39 tff(26,plain,
% 0.18/0.39 (![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))))))),
% 0.18/0.39 inference(quant_intro,[status(thm)],[25])).
% 0.18/0.39 tff(27,plain,
% 0.18/0.39 (![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))))),
% 0.18/0.39 inference(pull_quant,[status(thm)],[])).
% 0.18/0.39 tff(28,plain,
% 0.18/0.39 (![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)))),
% 0.18/0.39 inference(rewrite,[status(thm)],[])).
% 0.18/0.39 tff(29,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')).
% 0.18/0.39 tff(30,plain,
% 0.18/0.39 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.18/0.39 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.18/0.39 tff(31,plain,(
% 0.18/0.39 ![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))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[30])).
% 0.18/0.40 tff(32,plain,
% 0.18/0.40 (![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))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[31, 27])).
% 0.18/0.40 tff(33,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[32, 26])).
% 0.18/0.40 tff(34,plain,
% 0.18/0.40 (![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))))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[33, 24])).
% 0.18/0.40 tff(35,plain,
% 0.18/0.40 (((~![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))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(36,plain,
% 0.18/0.40 (((~(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))))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(37,plain,
% 0.18/0.40 (((~![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)))))))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[36])).
% 0.18/0.40 tff(38,plain,
% 0.18/0.40 (((~![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))))))),
% 0.18/0.40 inference(transitivity,[status(thm)],[37, 35])).
% 0.18/0.40 tff(39,plain,
% 0.18/0.40 ((~![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))))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(40,plain,
% 0.18/0.40 ((~![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)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.18/0.40 tff(41,plain,
% 0.18/0.40 ((~((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)))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[40, 34])).
% 0.18/0.40 tff(42,plain,
% 0.18/0.40 (~((~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))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[41, 22])).
% 0.18/0.40 tff(43,plain,
% 0.18/0.40 (((~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))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(44,plain,
% 0.18/0.40 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.18/0.40 tff(45,plain,
% 0.18/0.40 (tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0) = Y24!0),
% 0.18/0.40 inference(symmetry,[status(thm)],[44])).
% 0.18/0.40 tff(46,plain,
% 0.18/0.40 (((~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))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(47,plain,
% 0.18/0.40 (r1(tptp_fun_Y16_13(Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[46, 12])).
% 0.18/0.40 tff(48,plain,
% 0.18/0.40 ((r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_13(Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(49,plain,
% 0.18/0.40 (r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.18/0.40 tff(50,plain,
% 0.18/0.40 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(51,plain,
% 0.18/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.18/0.40 tff(52,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(53,plain,
% 0.18/0.40 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.18/0.40 tff(54,plain,
% 0.18/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(55,plain,
% 0.18/0.40 (^[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))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(56,plain,
% 0.18/0.40 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[55])).
% 0.18/0.40 tff(57,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.18/0.40 tff(58,plain,
% 0.18/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.18/0.40 tff(59,plain,
% 0.18/0.40 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.18/0.40 tff(60,plain,(
% 0.18/0.40 $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)))))),
% 0.18/0.40 inference(transitivity,[status(sab)],[59])).
% 0.18/0.40 tff(61,plain,
% 0.18/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.18/0.40 tff(62,plain,
% 0.18/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.18/0.40 tff(63,plain,
% 0.18/0.40 (((~![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))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(64,plain,
% 0.18/0.40 ((~![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))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(65,plain,
% 0.18/0.40 ((~![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)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.18/0.40 tff(66,plain,
% 0.18/0.40 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 0.18/0.40 tff(67,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0))) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(68,plain,
% 0.18/0.40 (tptp_fun_Y16_13(Y24!0) = Y24!0),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.18/0.40 tff(69,plain,
% 0.18/0.40 (Y24!0 = tptp_fun_Y16_13(Y24!0)),
% 0.18/0.40 inference(symmetry,[status(thm)],[68])).
% 0.18/0.40 tff(70,plain,
% 0.18/0.40 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.18/0.40 inference(monotonicity,[status(thm)],[69])).
% 0.18/0.40 tff(71,plain,
% 0.18/0.40 (^[X5: $i] : rewrite((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))) <=> (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(72,plain,
% 0.18/0.40 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))) <=> ![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.40 tff(73,plain,
% 0.18/0.40 (^[X5: $i] : rewrite(((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))) <=> (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(74,plain,
% 0.18/0.40 (![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))) <=> ![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.40 tff(75,plain,
% 0.18/0.40 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18))) <=> ![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(76,axiom,(![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_5a')).
% 0.18/0.40 tff(77,plain,
% 0.18/0.40 (![X5: $i] : ?[Y8: $i] : (?[Y17: $i] : (r1(Y17) & r4(X5, Y17, Y8)) & ?[Y18: $i] : (r1(Y18) & (Y8 = Y18)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.18/0.40 tff(78,plain,(
% 0.18/0.40 ![X5: $i] : ((r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) & (r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5))))),
% 0.18/0.40 inference(skolemize,[status(sab)],[77])).
% 0.18/0.40 tff(79,plain,
% 0.18/0.40 (![X5: $i] : (r1(tptp_fun_Y17_15(X5)) & r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5)) & r1(tptp_fun_Y18_16(X5)) & (tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.18/0.40 tff(80,plain,
% 0.18/0.40 (![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[79, 72])).
% 0.18/0.40 tff(81,plain,
% 0.18/0.40 ((~![X5: $i] : (~((~r1(tptp_fun_Y17_15(X5))) | (~r4(X5, tptp_fun_Y17_15(X5), tptp_fun_Y8_14(X5))) | (~r1(tptp_fun_Y18_16(X5))) | (~(tptp_fun_Y8_14(X5) = tptp_fun_Y18_16(X5)))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(82,plain,
% 0.18/0.40 (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0))))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.18/0.40 tff(83,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r1(tptp_fun_Y18_16(Y24!0))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(84,plain,
% 0.18/0.40 (r1(tptp_fun_Y18_16(Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.18/0.40 tff(85,plain,
% 0.18/0.40 ((r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y18_16(Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(86,plain,
% 0.18/0.40 (r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.18/0.40 tff(87,plain,
% 0.18/0.40 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))),
% 0.18/0.40 inference(rewrite,[status(thm)],[])).
% 0.18/0.40 tff(88,plain,
% 0.18/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0))))),
% 0.18/0.40 inference(quant_inst,[status(thm)],[])).
% 0.18/0.40 tff(89,plain,
% 0.18/0.40 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = Y24!0)))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.18/0.40 tff(90,plain,
% 0.18/0.40 (~((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0)))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[89, 62, 86])).
% 0.18/0.40 tff(91,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = Y24!0))) | (tptp_fun_Y18_16(Y24!0) = Y24!0)),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(92,plain,
% 0.18/0.40 (tptp_fun_Y18_16(Y24!0) = Y24!0),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.18/0.40 tff(93,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | (tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(94,plain,
% 0.18/0.40 (tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[93, 82])).
% 0.18/0.40 tff(95,plain,
% 0.18/0.40 (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y8_14(Y24!0)),
% 0.18/0.40 inference(symmetry,[status(thm)],[94])).
% 0.18/0.40 tff(96,plain,
% 0.18/0.40 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) <=> r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.18/0.40 inference(monotonicity,[status(thm)],[95])).
% 0.18/0.40 tff(97,plain,
% 0.18/0.40 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0)) <=> r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))),
% 0.18/0.40 inference(symmetry,[status(thm)],[96])).
% 0.18/0.40 tff(98,plain,
% 0.18/0.40 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(99,plain,
% 0.18/0.40 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[98, 82])).
% 0.18/0.40 tff(100,plain,
% 0.18/0.40 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))),
% 0.18/0.40 inference(modus_ponens,[status(thm)],[99, 97])).
% 0.18/0.40 tff(101,plain,
% 0.18/0.40 ((r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)))),
% 0.18/0.40 inference(tautology,[status(thm)],[])).
% 0.18/0.40 tff(102,plain,
% 0.18/0.40 (r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))),
% 0.18/0.40 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.18/0.40 tff(103,plain,
% 0.18/0.40 (^[X16: $i, X17: $i, X18: $i] : refl(((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))))),
% 0.18/0.40 inference(bind,[status(th)],[])).
% 0.18/0.40 tff(104,plain,
% 0.18/0.40 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.40 inference(quant_intro,[status(thm)],[103])).
% 0.18/0.40 tff(105,plain,
% 0.18/0.40 (^[X16: $i, X17: $i, X18: $i] : trans(monotonicity(rewrite((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) <=> (~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16)))))), rewrite(((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))) <=> (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))), (((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))))), rewrite(((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))), (((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(106,plain,
% 0.18/0.41 (![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.18/0.41 tff(107,plain,
% 0.18/0.41 (![X16: $i, X17: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16))))) <=> ![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(pull_quant,[status(thm)],[])).
% 0.18/0.41 tff(108,plain,
% 0.18/0.41 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23)))) <=> ![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(109,plain,
% 0.18/0.41 (^[X16: $i, X17: $i] : quant_intro(proof_bind(^[Y23: $i] : quant_intro(proof_bind(^[X18: $i] : rewrite((((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23)))))), (![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))))), (?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(110,plain,
% 0.18/0.41 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23))) <=> ![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[109])).
% 0.18/0.41 tff(111,axiom,(![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : (((~r4(X16, X17, X18)) & (~(X18 = Y23))) | (r4(X16, X17, X18) & (X18 = Y23)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_4')).
% 0.18/0.41 tff(112,plain,
% 0.18/0.41 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.18/0.41 tff(113,plain,
% 0.18/0.41 (![X16: $i, X17: $i] : ?[Y23: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = Y23)) | ((~r4(X16, X17, X18)) & (~(X18 = Y23))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[112, 108])).
% 0.18/0.41 tff(114,plain,(
% 0.18/0.41 ![X16: $i, X17: $i] : ![X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[113])).
% 0.18/0.41 tff(115,plain,
% 0.18/0.41 (![X16: $i, X17: $i, X18: $i] : ((r4(X16, X17, X18) & (X18 = tptp_fun_Y23_3(X17, X16))) | ((~r4(X16, X17, X18)) & (~(X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[114, 107])).
% 0.18/0.41 tff(116,plain,
% 0.18/0.41 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[115, 106])).
% 0.18/0.41 tff(117,plain,
% 0.18/0.41 (![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[116, 104])).
% 0.18/0.41 tff(118,plain,
% 0.18/0.41 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(119,plain,
% 0.18/0.41 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(120,plain,
% 0.18/0.41 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.18/0.41 tff(121,plain,
% 0.18/0.41 ((~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))) | (~(r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0)) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[120, 117])).
% 0.18/0.41 tff(122,plain,
% 0.18/0.41 (~((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[121, 102])).
% 0.18/0.41 tff(123,plain,
% 0.18/0.41 (((~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)))) | (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(124,plain,
% 0.18/0.41 (tptp_fun_Y18_16(Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[123, 122])).
% 0.18/0.41 tff(125,plain,
% 0.18/0.41 (tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0) = tptp_fun_Y18_16(Y24!0)),
% 0.18/0.41 inference(symmetry,[status(thm)],[124])).
% 0.18/0.41 tff(126,plain,
% 0.18/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~r4(Y24!0, tptp_fun_Y17_15(Y24!0), tptp_fun_Y8_14(Y24!0))) | (~r1(tptp_fun_Y18_16(Y24!0))) | (~(tptp_fun_Y8_14(Y24!0) = tptp_fun_Y18_16(Y24!0)))) | r1(tptp_fun_Y17_15(Y24!0))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(127,plain,
% 0.18/0.41 (r1(tptp_fun_Y17_15(Y24!0))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[126, 82])).
% 0.18/0.41 tff(128,plain,
% 0.18/0.41 ((r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y17_15(Y24!0)))),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(129,plain,
% 0.18/0.41 (r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[128, 127])).
% 0.18/0.41 tff(130,plain,
% 0.18/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(131,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(132,plain,
% 0.18/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))) | (~(r1(tptp_fun_Y17_15(Y24!0)) | (tptp_fun_Y17_15(Y24!0) = Y24!0)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.18/0.41 tff(133,plain,
% 0.18/0.41 (~((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0)))),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[132, 62, 129])).
% 0.18/0.41 tff(134,plain,
% 0.18/0.41 (((~r1(tptp_fun_Y17_15(Y24!0))) | (~(tptp_fun_Y17_15(Y24!0) = Y24!0))) | (tptp_fun_Y17_15(Y24!0) = Y24!0)),
% 0.18/0.41 inference(tautology,[status(thm)],[])).
% 0.18/0.41 tff(135,plain,
% 0.18/0.41 (tptp_fun_Y17_15(Y24!0) = Y24!0),
% 0.18/0.41 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.18/0.41 tff(136,plain,
% 0.18/0.41 (Y24!0 = tptp_fun_Y17_15(Y24!0)),
% 0.18/0.41 inference(symmetry,[status(thm)],[135])).
% 0.18/0.41 tff(137,plain,
% 0.18/0.41 (tptp_fun_Y23_3(Y24!0, Y24!0) = tptp_fun_Y23_3(tptp_fun_Y17_15(Y24!0), Y24!0)),
% 0.18/0.41 inference(monotonicity,[status(thm)],[136])).
% 0.18/0.41 tff(138,plain,
% 0.18/0.41 (^[X2: $i, X9: $i] : rewrite((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))) <=> (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2))))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(139,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))) <=> ![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[138])).
% 0.18/0.41 tff(140,plain,
% 0.18/0.41 (^[X2: $i, X9: $i] : trans(monotonicity(rewrite(((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)))), ((((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> ((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))), rewrite(((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))), ((((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 0.18/0.41 inference(bind,[status(th)],[])).
% 0.18/0.41 tff(141,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : (((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))) <=> ![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))),
% 0.18/0.41 inference(quant_intro,[status(thm)],[140])).
% 0.18/0.41 tff(142,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6))) <=> ![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.18/0.41 inference(rewrite,[status(thm)],[])).
% 0.18/0.41 tff(143,axiom,(![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2a')).
% 0.18/0.41 tff(144,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : ?[Y2: $i] : (?[Y3: $i] : (?[Y14: $i] : (r2(X9, Y14) & r4(X2, Y14, Y3)) & (Y3 = Y2)) & ?[Y6: $i] : (r3(Y6, X2, Y2) & r4(X2, X9, Y6)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.18/0.41 tff(145,plain,(
% 0.18/0.41 ![X2: $i, X9: $i] : (((r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) & (r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2))))),
% 0.18/0.41 inference(skolemize,[status(sab)],[144])).
% 0.18/0.41 tff(146,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : (r2(X9, tptp_fun_Y14_10(X9, X2)) & r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2)) & (tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2)) & r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2)) & r4(X2, X9, tptp_fun_Y6_11(X9, X2)))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[145, 141])).
% 0.18/0.41 tff(147,plain,
% 0.18/0.41 (![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))),
% 0.18/0.41 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.18/0.41 tff(148,plain,
% 0.18/0.41 ((~![X2: $i, X9: $i] : (~((~r2(X9, tptp_fun_Y14_10(X9, X2))) | (~r4(X2, tptp_fun_Y14_10(X9, X2), tptp_fun_Y3_9(X9, X2))) | (~(tptp_fun_Y3_9(X9, X2) = tptp_fun_Y2_8(X9, X2))) | (~r3(tptp_fun_Y6_11(X9, X2), X2, tptp_fun_Y2_8(X9, X2))) | (~r4(X2, X9, tptp_fun_Y6_11(X9, X2)))))) | (~((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))))),
% 0.18/0.41 inference(quant_inst,[status(thm)],[])).
% 0.18/0.41 tff(149,plain,
% 0.18/0.41 (~((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.18/0.42 tff(150,plain,
% 0.18/0.42 (((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(151,plain,
% 0.18/0.42 (r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.18/0.42 tff(152,plain,
% 0.18/0.42 ((r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(153,plain,
% 0.18/0.42 (r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.18/0.42 tff(154,plain,
% 0.18/0.42 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(155,plain,
% 0.18/0.42 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(156,plain,
% 0.18/0.42 ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) <=> (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(157,plain,
% 0.18/0.42 ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(158,plain,
% 0.18/0.42 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[157, 156])).
% 0.18/0.42 tff(159,plain,
% 0.18/0.42 (((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) <=> ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[158, 155])).
% 0.18/0.42 tff(160,plain,
% 0.18/0.42 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))))),
% 0.18/0.42 inference(monotonicity,[status(thm)],[159])).
% 0.18/0.42 tff(161,plain,
% 0.18/0.42 (((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))) <=> ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))))),
% 0.18/0.42 inference(transitivity,[status(thm)],[160, 154])).
% 0.18/0.42 tff(162,plain,
% 0.18/0.42 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | ((~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(163,plain,
% 0.18/0.42 ((~![X16: $i, X17: $i, X18: $i] : ((~((~r4(X16, X17, X18)) | (~(X18 = tptp_fun_Y23_3(X17, X16))))) | (~(r4(X16, X17, X18) | (X18 = tptp_fun_Y23_3(X17, X16)))))) | (~(r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.18/0.42 tff(164,plain,
% 0.18/0.42 (~((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[163, 117, 153])).
% 0.18/0.42 tff(165,plain,
% 0.18/0.42 (((~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))) | (~(tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)))) | (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(166,plain,
% 0.18/0.42 (tptp_fun_Y6_11(Y24!0, Y24!0) = tptp_fun_Y23_3(Y24!0, Y24!0)),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.18/0.42 tff(167,plain,
% 0.18/0.42 (tptp_fun_Y6_11(Y24!0, Y24!0) = Y24!0),
% 0.18/0.42 inference(transitivity,[status(thm)],[166, 137, 125, 92])).
% 0.18/0.42 tff(168,plain,
% 0.18/0.42 (tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.18/0.42 inference(monotonicity,[status(thm)],[167])).
% 0.18/0.42 tff(169,plain,
% 0.18/0.42 (((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(170,plain,
% 0.18/0.42 (r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[169, 149])).
% 0.18/0.42 tff(171,plain,
% 0.18/0.42 ((r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(172,plain,
% 0.18/0.42 (r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.18/0.42 tff(173,plain,
% 0.18/0.42 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(174,plain,
% 0.18/0.42 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(175,plain,
% 0.18/0.42 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0)) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))) | (~((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.42 tff(176,plain,
% 0.18/0.42 (~((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[175, 34, 172])).
% 0.18/0.42 tff(177,plain,
% 0.18/0.42 (((~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))))) | (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(178,plain,
% 0.18/0.42 (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.18/0.42 tff(179,plain,
% 0.18/0.42 (tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0),
% 0.18/0.42 inference(transitivity,[status(thm)],[178, 168, 70, 45])).
% 0.18/0.42 tff(180,plain,
% 0.18/0.42 (((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | (tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(181,plain,
% 0.18/0.43 (tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[180, 149])).
% 0.18/0.43 tff(182,plain,
% 0.18/0.43 (tptp_fun_Y2_8(Y24!0, Y24!0) = tptp_fun_Y3_9(Y24!0, Y24!0)),
% 0.18/0.43 inference(symmetry,[status(thm)],[181])).
% 0.18/0.43 tff(183,plain,
% 0.18/0.43 (r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0)) <=> r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[182])).
% 0.18/0.43 tff(184,plain,
% 0.18/0.43 (r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0)) <=> r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))),
% 0.18/0.43 inference(symmetry,[status(thm)],[183])).
% 0.18/0.43 tff(185,plain,
% 0.18/0.43 (((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(186,plain,
% 0.18/0.43 (r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[185, 149])).
% 0.18/0.43 tff(187,plain,
% 0.18/0.43 (r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[186, 184])).
% 0.18/0.43 tff(188,plain,
% 0.18/0.43 (((~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y3_9(Y24!0, Y24!0))) | (~(tptp_fun_Y3_9(Y24!0, Y24!0) = tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r3(tptp_fun_Y6_11(Y24!0, Y24!0), Y24!0, tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r4(Y24!0, Y24!0, tptp_fun_Y6_11(Y24!0, Y24!0)))) | r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))),
% 0.18/0.43 inference(tautology,[status(thm)],[])).
% 0.18/0.43 tff(189,plain,
% 0.18/0.43 (r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[188, 149])).
% 0.18/0.43 tff(190,plain,
% 0.18/0.43 (((~![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))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(191,plain,
% 0.18/0.43 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(192,plain,
% 0.18/0.43 ((~$true) <=> $false),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(193,plain,
% 0.18/0.43 ((r1(Y24!0) | $true) <=> $true),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(194,plain,
% 0.18/0.43 ((Y24!0 = Y24!0) <=> $true),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(195,plain,
% 0.18/0.43 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[194])).
% 0.18/0.43 tff(196,plain,
% 0.18/0.43 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.18/0.43 inference(transitivity,[status(thm)],[195, 193])).
% 0.18/0.43 tff(197,plain,
% 0.18/0.43 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[196])).
% 0.18/0.43 tff(198,plain,
% 0.18/0.43 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.18/0.43 inference(transitivity,[status(thm)],[197, 192])).
% 0.18/0.43 tff(199,plain,
% 0.18/0.43 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(200,plain,
% 0.18/0.43 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(201,plain,
% 0.18/0.43 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[194])).
% 0.18/0.43 tff(202,plain,
% 0.18/0.43 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.18/0.43 inference(transitivity,[status(thm)],[201, 192])).
% 0.18/0.43 tff(203,plain,
% 0.18/0.43 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[202])).
% 0.18/0.43 tff(204,plain,
% 0.18/0.43 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.18/0.43 inference(transitivity,[status(thm)],[203, 200])).
% 0.18/0.43 tff(205,plain,
% 0.18/0.43 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[204])).
% 0.18/0.43 tff(206,plain,
% 0.18/0.43 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.43 inference(transitivity,[status(thm)],[205, 199])).
% 0.18/0.43 tff(207,plain,
% 0.18/0.43 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.18/0.43 inference(monotonicity,[status(thm)],[206, 198])).
% 0.18/0.43 tff(208,plain,
% 0.18/0.43 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.18/0.43 inference(transitivity,[status(thm)],[207, 191])).
% 0.18/0.43 tff(209,plain,
% 0.18/0.43 (((~![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))),
% 0.18/0.43 inference(monotonicity,[status(thm)],[208])).
% 0.18/0.43 tff(210,plain,
% 0.18/0.43 (((~![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))),
% 0.18/0.43 inference(transitivity,[status(thm)],[209, 190])).
% 0.18/0.43 tff(211,plain,
% 0.18/0.43 ((~![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))))),
% 0.18/0.43 inference(quant_inst,[status(thm)],[])).
% 0.18/0.43 tff(212,plain,
% 0.18/0.43 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.18/0.43 tff(213,plain,
% 0.18/0.43 (r1(Y24!0)),
% 0.18/0.43 inference(unit_resolution,[status(thm)],[212, 62])).
% 0.18/0.43 tff(214,plain,
% 0.18/0.43 (^[Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : trans(monotonicity(rewrite((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) <=> ((~r1(Y3)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)))), (((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> (((~r1(Y3)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4))) | ((~r1(Y5)) | (~(Y1 = Y5)))))), rewrite((((~r1(Y3)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))), (((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(215,plain,
% 0.18/0.43 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[214])).
% 0.18/0.43 tff(216,plain,
% 0.18/0.43 (^[Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : refl(((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(217,plain,
% 0.18/0.43 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[216])).
% 0.18/0.43 tff(218,plain,
% 0.18/0.43 (![Y1: $i] : ![Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(pull_quant,[status(thm)],[])).
% 0.18/0.43 tff(219,plain,
% 0.18/0.43 (^[Y1: $i] : pull_quant((![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(220,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i] : ![Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[219])).
% 0.18/0.43 tff(221,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[220, 218])).
% 0.18/0.43 tff(222,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[221, 217])).
% 0.18/0.43 tff(223,plain,
% 0.18/0.43 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> (![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(224,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i] : (![Y2: $i, Y4: $i, Y3: $i] : (((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[223])).
% 0.18/0.43 tff(225,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))) <=> ![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(transitivity,[status(thm)],[224, 222])).
% 0.18/0.43 tff(226,plain,
% 0.18/0.43 (^[Y1: $i] : rewrite((![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | ![Y5: $i] : (~(r1(Y5) & (Y1 = Y5)))) <=> (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5)))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(227,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | ![Y5: $i] : (~(r1(Y5) & (Y1 = Y5)))) <=> ![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(quant_intro,[status(thm)],[226])).
% 0.18/0.43 tff(228,plain,
% 0.18/0.43 ((~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))) <=> (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5))))),
% 0.18/0.43 inference(rewrite,[status(thm)],[])).
% 0.18/0.43 tff(229,axiom,(~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','zerotimesoneeqzero')).
% 0.18/0.43 tff(230,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.18/0.43 tff(231,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[230, 228])).
% 0.18/0.43 tff(232,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[231, 228])).
% 0.18/0.43 tff(233,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.18/0.43 tff(234,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[233, 228])).
% 0.18/0.43 tff(235,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[234, 228])).
% 0.18/0.43 tff(236,plain,
% 0.18/0.43 (~?[Y1: $i] : (?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[235, 228])).
% 0.18/0.43 tff(237,plain,
% 0.18/0.43 (^[Y1: $i] : nnf_neg(nnf_neg(proof_bind(^[Y2: $i] : nnf_neg(nnf_neg(proof_bind(^[Y3: $i] : refl($oeq((~(r1(Y3) & r2(Y3, Y2))), (~(r1(Y3) & r2(Y3, Y2)))))), $oeq((~?[Y3: $i] : (r1(Y3) & r2(Y3, Y2))), ![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))))), nnf_neg(proof_bind(^[Y4: $i] : refl($oeq((~(r1(Y4) & r4(Y4, Y2, Y1))), (~(r1(Y4) & r4(Y4, Y2, Y1)))))), $oeq((~?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))), ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))), $oeq((~(?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1)))), (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1))))))), $oeq((~?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1)))), ![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))))), nnf_neg(proof_bind(^[Y5: $i] : refl($oeq((~(r1(Y5) & (Y1 = Y5))), (~(r1(Y5) & (Y1 = Y5)))))), $oeq((~?[Y5: $i] : (r1(Y5) & (Y1 = Y5))), ![Y5: $i] : (~(r1(Y5) & (Y1 = Y5))))), $oeq((~(?[Y2: $i] : (?[Y3: $i] : (r1(Y3) & r2(Y3, Y2)) & ?[Y4: $i] : (r1(Y4) & r4(Y4, Y2, Y1))) & ?[Y5: $i] : (r1(Y5) & (Y1 = Y5)))), (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | ![Y5: $i] : (~(r1(Y5) & (Y1 = Y5))))))),
% 0.18/0.43 inference(bind,[status(th)],[])).
% 0.18/0.43 tff(238,plain,(
% 0.18/0.43 ![Y1: $i] : (![Y2: $i] : (![Y3: $i] : (~(r1(Y3) & r2(Y3, Y2))) | ![Y4: $i] : (~(r1(Y4) & r4(Y4, Y2, Y1)))) | ![Y5: $i] : (~(r1(Y5) & (Y1 = Y5))))),
% 0.18/0.43 inference(nnf-neg,[status(sab)],[236, 237])).
% 0.18/0.43 tff(239,plain,
% 0.18/0.43 (![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | ![Y4: $i] : ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ![Y5: $i] : ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[238, 227])).
% 0.18/0.43 tff(240,plain,
% 0.18/0.43 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((((~r1(Y3)) | (~r2(Y3, Y2))) | ((~r1(Y4)) | (~r4(Y4, Y2, Y1)))) | ((~r1(Y5)) | (~(Y1 = Y5))))),
% 0.18/0.43 inference(modus_ponens,[status(thm)],[239, 225])).
% 0.18/0.43 tff(241,plain,
% 0.18/0.43 (![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[240, 215])).
% 0.18/0.44 tff(242,plain,
% 0.18/0.44 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(243,plain,
% 0.18/0.44 (((~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0))) <=> ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))),
% 0.18/0.44 inference(rewrite,[status(thm)],[])).
% 0.18/0.44 tff(244,plain,
% 0.18/0.44 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | ((~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0))))),
% 0.18/0.44 inference(monotonicity,[status(thm)],[243])).
% 0.18/0.44 tff(245,plain,
% 0.18/0.44 (((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | ((~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))) <=> ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))),
% 0.18/0.44 inference(transitivity,[status(thm)],[244, 242])).
% 0.18/0.44 tff(246,plain,
% 0.18/0.44 ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | ((~r1(Y24!0)) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~r1(Y24!0)) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)))),
% 0.18/0.44 inference(quant_inst,[status(thm)],[])).
% 0.18/0.44 tff(247,plain,
% 0.18/0.44 ((~![Y1: $i, Y5: $i, Y2: $i, Y4: $i, Y3: $i] : ((~r1(Y3)) | (~r1(Y5)) | (~r2(Y3, Y2)) | (~r4(Y4, Y2, Y1)) | (~r1(Y4)) | (~(Y1 = Y5)))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0))) | (~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0))),
% 0.18/0.44 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.18/0.44 tff(248,plain,
% 0.18/0.44 ((~r4(Y24!0, tptp_fun_Y14_10(Y24!0, Y24!0), tptp_fun_Y2_8(Y24!0, Y24!0))) | (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0))),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[247, 241, 213, 189])).
% 0.18/0.44 tff(249,plain,
% 0.18/0.44 (~(tptp_fun_Y2_8(Y24!0, Y24!0) = Y24!0)),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[248, 187])).
% 0.18/0.44 tff(250,plain,
% 0.18/0.44 ($false),
% 0.18/0.44 inference(unit_resolution,[status(thm)],[249, 179])).
% 0.18/0.44 % SZS output end Proof
%------------------------------------------------------------------------------