TSTP Solution File: NUN080+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 13:27:56 EDT 2022
% Result : Theorem 0.50s 0.56s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN080+2 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 16:28:10 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.
% 0.50/0.56 % SZS status Theorem
% 0.50/0.56 % SZS output start Proof
% 0.50/0.56 tff(r2_type, type, (
% 0.50/0.56 r2: ( $i * $i ) > $o)).
% 0.50/0.56 tff(tptp_fun_Y4_4_type, type, (
% 0.50/0.56 tptp_fun_Y4_4: ( $i * $i ) > $i)).
% 0.50/0.56 tff(tptp_fun_Y24_0_type, type, (
% 0.50/0.56 tptp_fun_Y24_0: $i)).
% 0.50/0.56 tff(r1_type, type, (
% 0.50/0.56 r1: $i > $o)).
% 0.50/0.56 tff(r3_type, type, (
% 0.50/0.56 r3: ( $i * $i * $i ) > $o)).
% 0.50/0.56 tff(tptp_fun_Y5_5_type, type, (
% 0.50/0.56 tptp_fun_Y5_5: ( $i * $i ) > $i)).
% 0.50/0.56 tff(tptp_fun_Y15_6_type, type, (
% 0.50/0.56 tptp_fun_Y15_6: ( $i * $i ) > $i)).
% 0.50/0.56 tff(tptp_fun_Y7_7_type, type, (
% 0.50/0.56 tptp_fun_Y7_7: ( $i * $i ) > $i)).
% 0.50/0.56 tff(tptp_fun_Y21_1_type, type, (
% 0.50/0.56 tptp_fun_Y21_1: $i > $i)).
% 0.50/0.56 tff(tptp_fun_Y22_2_type, type, (
% 0.50/0.56 tptp_fun_Y22_2: ( $i * $i ) > $i)).
% 0.50/0.56 tff(tptp_fun_Y16_13_type, type, (
% 0.50/0.56 tptp_fun_Y16_13: $i > $i)).
% 0.50/0.56 tff(tptp_fun_Y9_12_type, type, (
% 0.50/0.56 tptp_fun_Y9_12: $i > $i)).
% 0.50/0.56 tff(1,plain,
% 0.50/0.56 (^[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))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(2,plain,
% 0.50/0.56 (![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)))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[1])).
% 0.50/0.56 tff(3,plain,
% 0.50/0.56 (^[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)))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(4,plain,
% 0.50/0.56 (![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)))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[3])).
% 0.50/0.56 tff(5,plain,
% 0.50/0.56 (![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)))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(6,axiom,(![X1: $i, X8: $i] : ?[Y4: $i] : (?[Y5: $i] : (?[Y15: $i] : (r2(X8, Y15) & r3(X1, Y15, Y5)) & (Y5 = Y4)) & ?[Y7: $i] : (r2(Y7, Y4) & r3(X1, X8, Y7)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1a')).
% 0.50/0.56 tff(7,plain,
% 0.50/0.56 (![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)))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.50/0.56 tff(8,plain,(
% 0.50/0.56 ![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))))),
% 0.50/0.56 inference(skolemize,[status(sab)],[7])).
% 0.50/0.56 tff(9,plain,
% 0.50/0.56 (![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)))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.50/0.56 tff(10,plain,
% 0.50/0.56 (![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)))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.50/0.56 tff(11,plain,
% 0.50/0.56 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(12,plain,
% 0.50/0.56 ((~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) <=> (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(13,plain,
% 0.50/0.56 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.56 inference(monotonicity,[status(thm)],[12])).
% 0.50/0.56 tff(14,plain,
% 0.50/0.56 (((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))) <=> ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.56 inference(transitivity,[status(thm)],[13, 11])).
% 0.50/0.56 tff(15,plain,
% 0.50/0.56 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(16,plain,
% 0.50/0.57 ((~![X1: $i, X8: $i] : (~((~r2(X8, tptp_fun_Y15_6(X8, X1))) | (~r3(X1, tptp_fun_Y15_6(X8, X1), tptp_fun_Y5_5(X8, X1))) | (~(tptp_fun_Y5_5(X8, X1) = tptp_fun_Y4_4(X8, X1))) | (~r2(tptp_fun_Y7_7(X8, X1), tptp_fun_Y4_4(X8, X1))) | (~r3(X1, X8, tptp_fun_Y7_7(X8, X1)))))) | (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.50/0.57 tff(17,plain,
% 0.50/0.57 (~((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[16, 10])).
% 0.50/0.57 tff(18,plain,
% 0.50/0.57 (((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(19,plain,
% 0.50/0.57 (tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.50/0.57 tff(20,plain,
% 0.50/0.57 (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.57 inference(symmetry,[status(thm)],[19])).
% 0.50/0.57 tff(21,plain,
% 0.50/0.57 (((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(22,plain,
% 0.50/0.57 (r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[21, 17])).
% 0.50/0.57 tff(23,plain,
% 0.50/0.57 ((r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(24,plain,
% 0.50/0.57 (r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.50/0.57 tff(25,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(26,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[25])).
% 0.50/0.57 tff(27,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(28,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[27])).
% 0.50/0.57 tff(29,plain,
% 0.50/0.57 (![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))))),
% 0.50/0.57 inference(pull_quant,[status(thm)],[])).
% 0.50/0.57 tff(30,plain,
% 0.50/0.57 (![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)))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(31,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.50/0.57 tff(32,plain,
% 0.50/0.57 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.50/0.57 tff(33,plain,(
% 0.50/0.57 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.50/0.57 inference(skolemize,[status(sab)],[32])).
% 0.50/0.57 tff(34,plain,
% 0.50/0.57 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.50/0.57 tff(35,plain,
% 0.50/0.57 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.50/0.57 tff(36,plain,
% 0.50/0.57 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.50/0.57 tff(37,plain,
% 0.50/0.57 (((~![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_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(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_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(38,plain,
% 0.50/0.57 ((~![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_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(39,plain,
% 0.50/0.57 ((~![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_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.50/0.57 tff(40,plain,
% 0.50/0.57 (~((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[39, 36, 24])).
% 0.50/0.57 tff(41,plain,
% 0.50/0.57 (((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))))) | (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(42,plain,
% 0.50/0.57 (tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[41, 40])).
% 0.50/0.57 tff(43,plain,
% 0.50/0.57 (tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.57 inference(symmetry,[status(thm)],[42])).
% 0.50/0.57 tff(44,plain,
% 0.50/0.57 (((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(45,plain,
% 0.50/0.57 (r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[44, 17])).
% 0.50/0.57 tff(46,plain,
% 0.50/0.57 ((r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(47,plain,
% 0.50/0.57 (r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.50/0.57 tff(48,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(49,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[48])).
% 0.50/0.57 tff(50,plain,
% 0.50/0.57 (^[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)))))))),
% 0.50/0.57 inference(bind,[status(th)],[])).
% 0.50/0.57 tff(51,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(quant_intro,[status(thm)],[50])).
% 0.50/0.57 tff(52,plain,
% 0.50/0.57 (![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))))),
% 0.50/0.57 inference(pull_quant,[status(thm)],[])).
% 0.50/0.57 tff(53,plain,
% 0.50/0.57 (![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)))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(54,axiom,(![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_3')).
% 0.50/0.57 tff(55,plain,
% 0.50/0.57 (![X13: $i, X14: $i] : ?[Y22: $i] : ![X15: $i] : (((~r3(X13, X14, X15)) & (~(X15 = Y22))) | (r3(X13, X14, X15) & (X15 = Y22)))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.50/0.57 tff(56,plain,(
% 0.50/0.57 ![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))))),
% 0.50/0.57 inference(skolemize,[status(sab)],[55])).
% 0.50/0.57 tff(57,plain,
% 0.50/0.57 (![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))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.50/0.57 tff(58,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.50/0.57 tff(59,plain,
% 0.50/0.57 (![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))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[58, 49])).
% 0.50/0.57 tff(60,plain,
% 0.50/0.57 (((~![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_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(61,plain,
% 0.50/0.57 ((~![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_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(62,plain,
% 0.50/0.57 ((~![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_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.50/0.57 tff(63,plain,
% 0.50/0.57 (~((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[62, 59, 47])).
% 0.50/0.57 tff(64,plain,
% 0.50/0.57 (((~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(65,plain,
% 0.50/0.57 (tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.50/0.57 tff(66,plain,
% 0.50/0.57 (tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.57 inference(symmetry,[status(thm)],[65])).
% 0.50/0.57 tff(67,plain,
% 0.50/0.57 ((~![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)))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(68,plain,
% 0.50/0.57 (~((~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))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[67, 10])).
% 0.50/0.58 tff(69,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(70,plain,
% 0.50/0.58 (r2(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[69, 68])).
% 0.50/0.58 tff(71,plain,
% 0.50/0.58 ((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)))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(72,plain,
% 0.50/0.58 (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))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.50/0.58 tff(73,plain,
% 0.50/0.58 (((~![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))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(74,plain,
% 0.50/0.58 ((~![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))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(75,plain,
% 0.50/0.58 ((~![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)))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.50/0.58 tff(76,plain,
% 0.50/0.58 (~((~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))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[75, 36, 72])).
% 0.50/0.58 tff(77,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(78,plain,
% 0.50/0.58 (tptp_fun_Y15_6(Y24!0, Y24!0) = tptp_fun_Y21_1(Y24!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.50/0.58 tff(79,plain,
% 0.50/0.58 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[78])).
% 0.50/0.58 tff(80,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(81,plain,
% 0.50/0.58 (r3(Y24!0, Y24!0, tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[80, 68])).
% 0.50/0.58 tff(82,plain,
% 0.50/0.58 ((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)))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(83,plain,
% 0.50/0.58 (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))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.50/0.58 tff(84,plain,
% 0.50/0.58 (((~![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))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(85,plain,
% 0.50/0.58 ((~![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))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(86,plain,
% 0.50/0.58 ((~![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)))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.50/0.58 tff(87,plain,
% 0.50/0.58 (~((~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))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[86, 59, 83])).
% 0.50/0.58 tff(88,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(89,plain,
% 0.50/0.58 (tptp_fun_Y7_7(Y24!0, Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.50/0.58 tff(90,plain,
% 0.50/0.58 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y7_7(Y24!0, Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[89])).
% 0.50/0.58 tff(91,plain,
% 0.50/0.58 (^[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)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(92,plain,
% 0.50/0.58 (![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))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[91])).
% 0.50/0.58 tff(93,plain,
% 0.50/0.58 (^[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)))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(94,plain,
% 0.50/0.58 (![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))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[93])).
% 0.50/0.58 tff(95,plain,
% 0.50/0.58 (![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))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(96,axiom,(![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_4a')).
% 0.50/0.58 tff(97,plain,
% 0.50/0.58 (![X4: $i] : ?[Y9: $i] : (?[Y16: $i] : (r1(Y16) & r3(X4, Y16, Y9)) & (Y9 = X4))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.50/0.58 tff(98,plain,(
% 0.50/0.58 ![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))),
% 0.50/0.58 inference(skolemize,[status(sab)],[97])).
% 0.50/0.58 tff(99,plain,
% 0.50/0.58 (![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))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.50/0.58 tff(100,plain,
% 0.50/0.58 (![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))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.50/0.58 tff(101,plain,
% 0.50/0.58 ((~![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))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(102,plain,
% 0.50/0.58 (~((~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)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.50/0.58 tff(103,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(104,plain,
% 0.50/0.58 (r1(tptp_fun_Y16_13(Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.50/0.58 tff(105,plain,
% 0.50/0.58 ((r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)) | (~r1(tptp_fun_Y16_13(Y24!0)))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(106,plain,
% 0.50/0.58 (r1(tptp_fun_Y16_13(Y24!0)) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.50/0.58 tff(107,plain,
% 0.50/0.58 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(108,plain,
% 0.50/0.58 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[107])).
% 0.50/0.58 tff(109,plain,
% 0.50/0.58 (^[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))))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(110,plain,
% 0.50/0.58 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[109])).
% 0.50/0.58 tff(111,plain,
% 0.50/0.58 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(112,plain,
% 0.50/0.58 (^[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))))))),
% 0.50/0.58 inference(bind,[status(th)],[])).
% 0.50/0.58 tff(113,plain,
% 0.50/0.58 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.50/0.58 inference(quant_intro,[status(thm)],[112])).
% 0.50/0.58 tff(114,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.50/0.58 tff(115,plain,
% 0.50/0.58 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.50/0.58 tff(116,plain,
% 0.50/0.58 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.50/0.58 tff(117,plain,(
% 0.50/0.58 $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)))))),
% 0.50/0.58 inference(transitivity,[status(sab)],[116])).
% 0.50/0.58 tff(118,plain,
% 0.50/0.58 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.50/0.58 tff(119,plain,
% 0.50/0.58 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[118, 108])).
% 0.50/0.58 tff(120,plain,
% 0.50/0.58 (((~![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))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(121,plain,
% 0.50/0.58 ((~![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))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(122,plain,
% 0.50/0.58 ((~![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)))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.50/0.58 tff(123,plain,
% 0.50/0.58 (~((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[122, 119, 106])).
% 0.50/0.58 tff(124,plain,
% 0.50/0.58 (((~r1(tptp_fun_Y16_13(Y24!0))) | (~(tptp_fun_Y16_13(Y24!0) = Y24!0))) | (tptp_fun_Y16_13(Y24!0) = Y24!0)),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(125,plain,
% 0.50/0.58 (tptp_fun_Y16_13(Y24!0) = Y24!0),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.50/0.58 tff(126,plain,
% 0.50/0.58 (Y24!0 = tptp_fun_Y16_13(Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[125])).
% 0.50/0.58 tff(127,plain,
% 0.50/0.58 (tptp_fun_Y22_2(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.50/0.58 inference(monotonicity,[status(thm)],[126])).
% 0.50/0.58 tff(128,plain,
% 0.50/0.58 (tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0) = tptp_fun_Y22_2(Y24!0, Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[127])).
% 0.50/0.58 tff(129,plain,
% 0.50/0.58 (((~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)),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(130,plain,
% 0.50/0.58 (tptp_fun_Y9_12(Y24!0) = Y24!0),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[129, 102])).
% 0.50/0.58 tff(131,plain,
% 0.50/0.58 (Y24!0 = tptp_fun_Y9_12(Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[130])).
% 0.50/0.58 tff(132,plain,
% 0.50/0.58 (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))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[131])).
% 0.50/0.58 tff(133,plain,
% 0.50/0.58 (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)),
% 0.50/0.58 inference(symmetry,[status(thm)],[132])).
% 0.50/0.58 tff(134,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(135,plain,
% 0.50/0.58 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), tptp_fun_Y9_12(Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[134, 102])).
% 0.50/0.58 tff(136,plain,
% 0.50/0.58 (r3(Y24!0, tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[135, 133])).
% 0.50/0.58 tff(137,plain,
% 0.50/0.58 (((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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(138,plain,
% 0.50/0.58 ((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)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.50/0.58 tff(139,plain,
% 0.50/0.58 (((~![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))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(140,plain,
% 0.50/0.58 (((~(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))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(141,plain,
% 0.50/0.58 (((~![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)))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[140])).
% 0.50/0.58 tff(142,plain,
% 0.50/0.58 (((~![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))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[141, 139])).
% 0.50/0.58 tff(143,plain,
% 0.50/0.58 ((~![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))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(144,plain,
% 0.50/0.58 ((~![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)))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.50/0.58 tff(145,plain,
% 0.50/0.58 ((~((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)))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[144, 59])).
% 0.50/0.58 tff(146,plain,
% 0.50/0.58 (~((~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))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[145, 138])).
% 0.50/0.58 tff(147,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(148,plain,
% 0.50/0.58 (Y24!0 = tptp_fun_Y22_2(tptp_fun_Y16_13(Y24!0), Y24!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.50/0.58 tff(149,plain,
% 0.50/0.58 (Y24!0 = tptp_fun_Y7_7(Y24!0, Y24!0)),
% 0.50/0.58 inference(transitivity,[status(thm)],[148, 128, 90])).
% 0.50/0.58 tff(150,plain,
% 0.50/0.58 (tptp_fun_Y21_1(Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[149])).
% 0.50/0.58 tff(151,plain,
% 0.50/0.58 (tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0)) = tptp_fun_Y21_1(Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[150])).
% 0.50/0.58 tff(152,plain,
% 0.50/0.58 (((~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))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(153,plain,
% 0.50/0.58 (r2(tptp_fun_Y7_7(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[152, 68])).
% 0.50/0.58 tff(154,plain,
% 0.50/0.58 ((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)))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(155,plain,
% 0.50/0.58 (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)))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.50/0.58 tff(156,plain,
% 0.50/0.58 (((~![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)))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(157,plain,
% 0.50/0.58 ((~![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)))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(158,plain,
% 0.50/0.58 ((~![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))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.50/0.58 tff(159,plain,
% 0.50/0.58 (~((~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)))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[158, 36, 155])).
% 0.50/0.58 tff(160,plain,
% 0.50/0.58 (((~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)))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(161,plain,
% 0.50/0.58 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(Y24!0, Y24!0))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.50/0.58 tff(162,plain,
% 0.50/0.58 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y15_6(Y24!0, Y24!0)),
% 0.50/0.58 inference(transitivity,[status(thm)],[161, 151, 79])).
% 0.50/0.58 tff(163,plain,
% 0.50/0.58 (tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)),
% 0.50/0.58 inference(monotonicity,[status(thm)],[162])).
% 0.50/0.58 tff(164,plain,
% 0.50/0.58 (tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0) = tptp_fun_Y22_2(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[163])).
% 0.50/0.58 tff(165,plain,
% 0.50/0.58 (((~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)))) | (tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.58 inference(tautology,[status(thm)],[])).
% 0.50/0.58 tff(166,plain,
% 0.50/0.58 (tptp_fun_Y5_5(Y24!0, Y24!0) = tptp_fun_Y4_4(Y24!0, Y24!0)),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[165, 68])).
% 0.50/0.58 tff(167,plain,
% 0.50/0.58 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y5_5(Y24!0, Y24!0)),
% 0.50/0.58 inference(symmetry,[status(thm)],[166])).
% 0.50/0.58 tff(168,plain,
% 0.50/0.58 (r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) <=> r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[167])).
% 0.50/0.58 tff(169,plain,
% 0.50/0.58 (r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0)) <=> r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.58 inference(symmetry,[status(thm)],[168])).
% 0.50/0.58 tff(170,plain,
% 0.50/0.58 (((~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, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(171,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y5_5(Y24!0, Y24!0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[170, 68])).
% 0.50/0.59 tff(172,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[171, 169])).
% 0.50/0.59 tff(173,plain,
% 0.50/0.59 ((r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(174,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[173, 172])).
% 0.50/0.59 tff(175,plain,
% 0.50/0.59 (((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))))))) <=> ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(176,plain,
% 0.50/0.59 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | ((~(r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(177,plain,
% 0.50/0.59 ((~![X13: $i, X14: $i, X15: $i] : ((~(r3(X13, X14, X15) | (X15 = tptp_fun_Y22_2(X14, X13)))) | (~((~r3(X13, X14, X15)) | (~(X15 = tptp_fun_Y22_2(X14, X13))))))) | (~(r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.50/0.59 tff(178,plain,
% 0.50/0.59 ((~(r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0)) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[177, 59])).
% 0.50/0.59 tff(179,plain,
% 0.50/0.59 (~((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[178, 174])).
% 0.50/0.59 tff(180,plain,
% 0.50/0.59 (((~r3(Y24!0, tptp_fun_Y15_6(Y24!0, Y24!0), tptp_fun_Y4_4(Y24!0, Y24!0))) | (~(tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)))) | (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(181,plain,
% 0.50/0.59 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y22_2(tptp_fun_Y15_6(Y24!0, Y24!0), Y24!0)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.50/0.59 tff(182,plain,
% 0.50/0.59 (tptp_fun_Y4_4(Y24!0, Y24!0) = tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.59 inference(transitivity,[status(thm)],[181, 164, 66])).
% 0.50/0.59 tff(183,plain,
% 0.50/0.59 (tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[182])).
% 0.50/0.59 tff(184,plain,
% 0.50/0.59 (tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) = tptp_fun_Y21_1(tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.59 inference(symmetry,[status(thm)],[183])).
% 0.50/0.59 tff(185,plain,
% 0.50/0.59 (((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(186,plain,
% 0.50/0.59 (r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[185, 17])).
% 0.50/0.59 tff(187,plain,
% 0.50/0.59 ((r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(188,plain,
% 0.50/0.59 (r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.50/0.59 tff(189,plain,
% 0.50/0.59 (((~![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(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) | (~((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, 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(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) | (~((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(190,plain,
% 0.50/0.59 ((~![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(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) | (~((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(191,plain,
% 0.50/0.59 ((~![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(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) | (~((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.50/0.59 tff(192,plain,
% 0.50/0.59 (~((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[191, 36, 188])).
% 0.50/0.59 tff(193,plain,
% 0.50/0.59 (((~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))))) | (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(194,plain,
% 0.50/0.59 (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y21_1(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.50/0.59 tff(195,plain,
% 0.50/0.59 (tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)),
% 0.50/0.59 inference(transitivity,[status(thm)],[194, 184, 43])).
% 0.50/0.59 tff(196,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) <=> r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[195, 20])).
% 0.50/0.59 tff(197,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) <=> r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(symmetry,[status(thm)],[196])).
% 0.50/0.59 tff(198,plain,
% 0.50/0.59 (((~r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r3(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~(tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)))) | r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(199,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y15_6(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y5_5(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[198, 17])).
% 0.50/0.59 tff(200,plain,
% 0.50/0.59 (r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[199, 197])).
% 0.50/0.59 tff(201,plain,
% 0.50/0.59 (^[Y1: $i, Y2: $i, Y3: $i] : rewrite(((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(202,plain,
% 0.50/0.59 (![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[201])).
% 0.50/0.59 tff(203,plain,
% 0.50/0.59 (^[Y1: $i, Y2: $i, Y3: $i] : rewrite(((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))) <=> ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(204,plain,
% 0.50/0.59 (![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))) <=> ![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[203])).
% 0.50/0.59 tff(205,plain,
% 0.50/0.59 ((~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))) <=> (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(206,axiom,(~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','xplustwoeqy')).
% 0.50/0.59 tff(207,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.50/0.59 tff(208,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[207, 205])).
% 0.50/0.59 tff(209,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[208, 205])).
% 0.50/0.59 tff(210,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[209, 205])).
% 0.50/0.59 tff(211,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[210, 205])).
% 0.50/0.59 tff(212,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[211, 205])).
% 0.50/0.59 tff(213,plain,
% 0.50/0.59 (~?[Y1: $i, Y2: $i, Y3: $i] : ((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[212, 205])).
% 0.50/0.59 tff(214,plain,
% 0.50/0.59 (^[Y1: $i, Y2: $i, Y3: $i] : nnf_neg(refl($oeq((~(Y3 = Y2)), (~(Y3 = Y2)))), nnf_neg(proof_bind(^[Y4: $i] : nnf_neg(refl($oeq((~r3(Y1, Y4, Y3)), (~r3(Y1, Y4, Y3)))), nnf_neg(proof_bind(^[Y5: $i] : nnf_neg(refl($oeq((~r2(Y5, Y4)), (~r2(Y5, Y4)))), nnf_neg(proof_bind(^[Y6: $i] : refl($oeq((~(r1(Y6) & r2(Y6, Y5))), (~(r1(Y6) & r2(Y6, Y5)))))), $oeq((~?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))), ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))), $oeq((~(r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))), ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))))), $oeq((~?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))), ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))), $oeq((~(r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))), ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5)))))))), $oeq((~?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5))))), ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))))), $oeq((~((Y3 = Y2) & ?[Y4: $i] : (r3(Y1, Y4, Y3) & ?[Y5: $i] : (r2(Y5, Y4) & ?[Y6: $i] : (r1(Y6) & r2(Y6, Y5)))))), ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(215,plain,(
% 0.50/0.59 ![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : (~(r1(Y6) & r2(Y6, Y5))))))),
% 0.50/0.59 inference(nnf-neg,[status(sab)],[213, 214])).
% 0.50/0.59 tff(216,plain,
% 0.50/0.59 (![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[215, 204])).
% 0.50/0.59 tff(217,plain,
% 0.50/0.59 (![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[216, 202])).
% 0.50/0.59 tff(218,plain,
% 0.50/0.59 (((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(219,plain,
% 0.50/0.59 (($false | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(220,plain,
% 0.50/0.59 ((~$true) <=> $false),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(221,plain,
% 0.50/0.59 ((tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) <=> $true),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(222,plain,
% 0.50/0.59 ((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) <=> (~$true)),
% 0.50/0.59 inference(monotonicity,[status(thm)],[221])).
% 0.50/0.59 tff(223,plain,
% 0.50/0.59 ((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) <=> $false),
% 0.50/0.59 inference(transitivity,[status(thm)],[222, 220])).
% 0.50/0.59 tff(224,plain,
% 0.50/0.59 (((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ($false | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[223])).
% 0.50/0.59 tff(225,plain,
% 0.50/0.59 (((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[224, 219])).
% 0.50/0.59 tff(226,plain,
% 0.50/0.59 (((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[225])).
% 0.50/0.59 tff(227,plain,
% 0.50/0.59 (((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) <=> ((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[226, 218])).
% 0.50/0.60 tff(228,plain,
% 0.50/0.60 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ((~(tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0) = tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(229,plain,
% 0.50/0.60 ((~![Y1: $i, Y2: $i, Y3: $i] : ((~(Y3 = Y2)) | ![Y4: $i] : ((~r3(Y1, Y4, Y3)) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))))) | ![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.50/0.60 tff(230,plain,
% 0.50/0.60 (![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[229, 217])).
% 0.50/0.60 tff(231,plain,
% 0.50/0.60 (((~![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | ((~r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) <=> ((~![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | (~r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(232,plain,
% 0.50/0.60 ((~![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | ((~r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(233,plain,
% 0.50/0.60 ((~![Y4: $i] : ((~r3(Y24!0, Y4, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, Y4)) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5)))))) | (~r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.50/0.60 tff(234,plain,
% 0.50/0.60 ((~r3(Y24!0, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[233, 230])).
% 0.50/0.60 tff(235,plain,
% 0.50/0.60 (![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[234, 200])).
% 0.50/0.60 tff(236,plain,
% 0.50/0.60 (r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) <=> r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[182])).
% 0.50/0.60 tff(237,plain,
% 0.50/0.60 (r2(tptp_fun_Y7_7(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0)) <=> r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.60 inference(symmetry,[status(thm)],[236])).
% 0.50/0.60 tff(238,plain,
% 0.50/0.60 (r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[186, 237])).
% 0.50/0.60 tff(239,plain,
% 0.50/0.60 (((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | ((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0)))))) <=> ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(240,plain,
% 0.50/0.60 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | ((~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0)))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(241,plain,
% 0.50/0.60 ((~![Y5: $i] : ((~r2(Y5, tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, Y5))))) | (~r2(tptp_fun_Y4_4(Y24!0, Y24!0), tptp_fun_Y4_4(tptp_fun_Y4_4(Y24!0, Y24!0), Y24!0))) | ![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[240, 239])).
% 0.50/0.60 tff(242,plain,
% 0.50/0.60 (![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[241, 238, 235])).
% 0.50/0.60 tff(243,plain,
% 0.50/0.60 (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))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[149])).
% 0.50/0.60 tff(244,plain,
% 0.50/0.60 (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))),
% 0.50/0.60 inference(symmetry,[status(thm)],[243])).
% 0.50/0.60 tff(245,plain,
% 0.50/0.60 (r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[153, 244])).
% 0.50/0.60 tff(246,plain,
% 0.50/0.60 (((~![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))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(247,plain,
% 0.50/0.60 ((r1(Y24!0) | $false) <=> r1(Y24!0)),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(248,plain,
% 0.50/0.60 ((r1(Y24!0) | $true) <=> $true),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(249,plain,
% 0.50/0.60 ((Y24!0 = Y24!0) <=> $true),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(250,plain,
% 0.50/0.60 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> (r1(Y24!0) | $true)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[249])).
% 0.50/0.60 tff(251,plain,
% 0.50/0.60 ((r1(Y24!0) | (Y24!0 = Y24!0)) <=> $true),
% 0.50/0.60 inference(transitivity,[status(thm)],[250, 248])).
% 0.50/0.60 tff(252,plain,
% 0.50/0.60 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> (~$true)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[251])).
% 0.50/0.60 tff(253,plain,
% 0.50/0.60 ((~(r1(Y24!0) | (Y24!0 = Y24!0))) <=> $false),
% 0.50/0.60 inference(transitivity,[status(thm)],[252, 220])).
% 0.50/0.60 tff(254,plain,
% 0.50/0.60 ((~(~r1(Y24!0))) <=> r1(Y24!0)),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(255,plain,
% 0.50/0.60 (((~r1(Y24!0)) | $false) <=> (~r1(Y24!0))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(256,plain,
% 0.50/0.60 ((~(Y24!0 = Y24!0)) <=> (~$true)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[249])).
% 0.50/0.60 tff(257,plain,
% 0.50/0.60 ((~(Y24!0 = Y24!0)) <=> $false),
% 0.50/0.60 inference(transitivity,[status(thm)],[256, 220])).
% 0.50/0.60 tff(258,plain,
% 0.50/0.60 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> ((~r1(Y24!0)) | $false)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[257])).
% 0.50/0.60 tff(259,plain,
% 0.50/0.60 (((~r1(Y24!0)) | (~(Y24!0 = Y24!0))) <=> (~r1(Y24!0))),
% 0.50/0.60 inference(transitivity,[status(thm)],[258, 255])).
% 0.50/0.60 tff(260,plain,
% 0.50/0.60 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> (~(~r1(Y24!0)))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[259])).
% 0.50/0.60 tff(261,plain,
% 0.50/0.60 ((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.50/0.60 inference(transitivity,[status(thm)],[260, 254])).
% 0.50/0.60 tff(262,plain,
% 0.50/0.60 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> (r1(Y24!0) | $false)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[261, 253])).
% 0.50/0.60 tff(263,plain,
% 0.50/0.60 (((~((~r1(Y24!0)) | (~(Y24!0 = Y24!0)))) | (~(r1(Y24!0) | (Y24!0 = Y24!0)))) <=> r1(Y24!0)),
% 0.50/0.60 inference(transitivity,[status(thm)],[262, 247])).
% 0.50/0.60 tff(264,plain,
% 0.50/0.60 (((~![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))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[263])).
% 0.50/0.60 tff(265,plain,
% 0.50/0.60 (((~![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))),
% 0.50/0.60 inference(transitivity,[status(thm)],[264, 246])).
% 0.50/0.60 tff(266,plain,
% 0.50/0.60 ((~![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))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(267,plain,
% 0.50/0.60 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | r1(Y24!0)),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.50/0.60 tff(268,plain,
% 0.50/0.60 (r1(Y24!0)),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[267, 119])).
% 0.50/0.60 tff(269,plain,
% 0.50/0.60 (((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))))) <=> ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(270,plain,
% 0.50/0.60 ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))) | ((~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(271,plain,
% 0.50/0.60 ((~![Y6: $i] : ((~r1(Y6)) | (~r2(Y6, tptp_fun_Y4_4(Y24!0, Y24!0))))) | (~r1(Y24!0)) | (~r2(Y24!0, tptp_fun_Y4_4(Y24!0, Y24!0)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.50/0.60 tff(272,plain,
% 0.50/0.60 ($false),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[271, 268, 245, 242])).
% 0.50/0.60 % SZS output end Proof
%------------------------------------------------------------------------------