TSTP Solution File: NUN073+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 13:27:54 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN073+2 : TPTP v8.1.0. Released v7.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.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 16:18:14 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.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 tff(tptp_fun_Y1_20_type, type, (
% 0.20/0.40 tptp_fun_Y1_20: $i)).
% 0.20/0.40 tff(tptp_fun_Y24_0_type, type, (
% 0.20/0.40 tptp_fun_Y24_0: $i)).
% 0.20/0.40 tff(tptp_fun_Y21_1_type, type, (
% 0.20/0.40 tptp_fun_Y21_1: $i > $i)).
% 0.20/0.40 tff(tptp_fun_Y4_22_type, type, (
% 0.20/0.40 tptp_fun_Y4_22: $i)).
% 0.20/0.40 tff(r2_type, type, (
% 0.20/0.40 r2: ( $i * $i ) > $o)).
% 0.20/0.40 tff(tptp_fun_Y2_21_type, type, (
% 0.20/0.40 tptp_fun_Y2_21: $i)).
% 0.20/0.40 tff(tptp_fun_Y3_23_type, type, (
% 0.20/0.40 tptp_fun_Y3_23: $i)).
% 0.20/0.40 tff(tptp_fun_Y5_24_type, type, (
% 0.20/0.40 tptp_fun_Y5_24: $i)).
% 0.20/0.40 tff(r1_type, type, (
% 0.20/0.40 r1: $i > $o)).
% 0.20/0.40 tff(1,plain,
% 0.20/0.40 ((((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) & (r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))) <=> ((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))) & r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(2,plain,
% 0.20/0.40 (((~(~r2(Y3!23, Y1!20))) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23))))) <=> (r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(3,plain,
% 0.20/0.40 (((~(~(Y2!21 = Y1!20))) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) <=> ((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(4,plain,
% 0.20/0.40 ((((~(~(Y2!21 = Y1!20))) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) & ((~(~r2(Y3!23, Y1!20))) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))) <=> (((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) & (r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23))))))),
% 0.20/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.20/0.40 tff(5,plain,
% 0.20/0.40 ((((~(~(Y2!21 = Y1!20))) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) & ((~(~r2(Y3!23, Y1!20))) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))) <=> ((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))) & r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))))),
% 0.20/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.20/0.40 tff(6,plain,
% 0.20/0.40 ((~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(7,plain,
% 0.20/0.40 ((~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~(Y2 = Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(8,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~(Y2 = Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','oneuneqtwo')).
% 0.20/0.40 tff(9,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.40 tff(10,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.20/0.40 tff(11,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.40 tff(12,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.20/0.40 tff(13,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.20/0.40 tff(14,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.40 tff(15,plain,
% 0.20/0.40 (~![Y1: $i] : (![Y2: $i] : ((~(Y2 = Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.20/0.40 tff(16,plain,
% 0.20/0.40 ((Y2!21 = Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))) & r2(Y3!23, Y1!20) & (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.20/0.40 tff(17,plain,
% 0.20/0.40 (Y2!21 = Y1!20),
% 0.20/0.40 inference(and_elim,[status(thm)],[16])).
% 0.20/0.40 tff(18,plain,
% 0.20/0.40 (Y1!20 = Y2!21),
% 0.20/0.40 inference(symmetry,[status(thm)],[17])).
% 0.20/0.40 tff(19,plain,
% 0.20/0.40 (r2(Y4!22, Y1!20) <=> r2(Y4!22, Y2!21)),
% 0.20/0.40 inference(monotonicity,[status(thm)],[18])).
% 0.20/0.40 tff(20,plain,
% 0.20/0.40 (r2(Y4!22, Y2!21) <=> r2(Y4!22, Y1!20)),
% 0.20/0.40 inference(symmetry,[status(thm)],[19])).
% 0.20/0.40 tff(21,plain,
% 0.20/0.40 (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[16])).
% 0.20/0.40 tff(22,plain,
% 0.20/0.40 (r2(Y4!22, Y2!21)),
% 0.20/0.40 inference(or_elim,[status(thm)],[21])).
% 0.20/0.40 tff(23,plain,
% 0.20/0.40 (r2(Y4!22, Y1!20)),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.20/0.40 tff(24,plain,
% 0.20/0.40 ((r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22))) | (~r2(Y4!22, Y1!20))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(25,plain,
% 0.20/0.40 (r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.20/0.40 tff(26,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(27,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.40 tff(28,plain,
% 0.20/0.40 (^[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)))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(29,plain,
% 0.20/0.40 (![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))))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.40 tff(30,plain,
% 0.20/0.40 (![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))))),
% 0.20/0.40 inference(pull_quant,[status(thm)],[])).
% 0.20/0.40 tff(31,plain,
% 0.20/0.40 (![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)))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(32,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_2')).
% 0.20/0.40 tff(33,plain,
% 0.20/0.40 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = Y21))) | (r2(X11, X12) & (X12 = Y21)))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.40 tff(34,plain,(
% 0.20/0.40 ![X11: $i] : ![X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.20/0.40 inference(skolemize,[status(sab)],[33])).
% 0.20/0.40 tff(35,plain,
% 0.20/0.40 (![X11: $i, X12: $i] : (((~r2(X11, X12)) & (~(X12 = tptp_fun_Y21_1(X11)))) | (r2(X11, X12) & (X12 = tptp_fun_Y21_1(X11))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[34, 30])).
% 0.20/0.40 tff(36,plain,
% 0.20/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[35, 29])).
% 0.20/0.40 tff(37,plain,
% 0.20/0.40 (![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[36, 27])).
% 0.20/0.40 tff(38,plain,
% 0.20/0.40 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22))))))),
% 0.20/0.40 inference(rewrite,[status(thm)],[])).
% 0.20/0.40 tff(39,plain,
% 0.20/0.40 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22))))))),
% 0.20/0.40 inference(quant_inst,[status(thm)],[])).
% 0.20/0.40 tff(40,plain,
% 0.20/0.40 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22)))))),
% 0.20/0.40 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.40 tff(41,plain,
% 0.20/0.40 ((~(r2(Y4!22, Y1!20) | (Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22)))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[40, 37])).
% 0.20/0.40 tff(42,plain,
% 0.20/0.40 (~((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22))))),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[41, 25])).
% 0.20/0.40 tff(43,plain,
% 0.20/0.40 (((~r2(Y4!22, Y1!20)) | (~(Y1!20 = tptp_fun_Y21_1(Y4!22)))) | (Y1!20 = tptp_fun_Y21_1(Y4!22))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(44,plain,
% 0.20/0.40 (Y1!20 = tptp_fun_Y21_1(Y4!22)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.40 tff(45,plain,
% 0.20/0.40 (tptp_fun_Y21_1(Y4!22) = Y1!20),
% 0.20/0.40 inference(symmetry,[status(thm)],[44])).
% 0.20/0.40 tff(46,plain,
% 0.20/0.40 (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))),
% 0.20/0.40 inference(and_elim,[status(thm)],[16])).
% 0.20/0.40 tff(47,plain,
% 0.20/0.40 (r1(Y5!24)),
% 0.20/0.40 inference(or_elim,[status(thm)],[46])).
% 0.20/0.40 tff(48,plain,
% 0.20/0.40 ((r1(Y5!24) | (Y5!24 = Y24!0)) | (~r1(Y5!24))),
% 0.20/0.40 inference(tautology,[status(thm)],[])).
% 0.20/0.40 tff(49,plain,
% 0.20/0.40 (r1(Y5!24) | (Y5!24 = Y24!0)),
% 0.20/0.40 inference(unit_resolution,[status(thm)],[48, 47])).
% 0.20/0.40 tff(50,plain,
% 0.20/0.40 (^[X19: $i] : refl(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(51,plain,
% 0.20/0.40 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[50])).
% 0.20/0.40 tff(52,plain,
% 0.20/0.40 (^[X19: $i] : trans(monotonicity(rewrite((r1(X19) & (X19 = Y24!0)) <=> (~((~r1(X19)) | (~(X19 = Y24!0))))), rewrite(((~r1(X19)) & (~(X19 = Y24!0))) <=> (~(r1(X19) | (X19 = Y24!0)))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))))), rewrite(((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))), (((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))))),
% 0.20/0.40 inference(bind,[status(th)],[])).
% 0.20/0.40 tff(53,plain,
% 0.20/0.40 (![X19: $i] : ((r1(X19) & (X19 = Y24!0)) | ((~r1(X19)) & (~(X19 = Y24!0)))) <=> ![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.40 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.41 tff(54,plain,
% 0.20/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24)))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(55,plain,
% 0.20/0.41 (^[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))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(56,plain,
% 0.20/0.41 (?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24))) <=> ?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.41 tff(57,axiom,(?[Y24: $i] : ![X19: $i] : (((~r1(X19)) & (~(X19 = Y24))) | (r1(X19) & (X19 = Y24)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_1')).
% 0.20/0.41 tff(58,plain,
% 0.20/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.41 tff(59,plain,
% 0.20/0.41 (?[Y24: $i] : ![X19: $i] : ((r1(X19) & (X19 = Y24)) | ((~r1(X19)) & (~(X19 = Y24))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.41 tff(60,plain,(
% 0.20/0.41 $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)))))),
% 0.20/0.41 inference(transitivity,[status(sab)],[59])).
% 0.20/0.41 tff(61,plain,
% 0.20/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.41 tff(62,plain,
% 0.20/0.41 (![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.41 tff(63,plain,
% 0.20/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y5!24)) | (~(Y5!24 = Y24!0)))) | (~(r1(Y5!24) | (Y5!24 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y5!24)) | (~(Y5!24 = Y24!0)))) | (~(r1(Y5!24) | (Y5!24 = Y24!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(64,plain,
% 0.20/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y5!24)) | (~(Y5!24 = Y24!0)))) | (~(r1(Y5!24) | (Y5!24 = Y24!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(65,plain,
% 0.20/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y5!24)) | (~(Y5!24 = Y24!0)))) | (~(r1(Y5!24) | (Y5!24 = Y24!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.41 tff(66,plain,
% 0.20/0.41 (~((~r1(Y5!24)) | (~(Y5!24 = Y24!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[65, 62, 49])).
% 0.20/0.41 tff(67,plain,
% 0.20/0.41 (((~r1(Y5!24)) | (~(Y5!24 = Y24!0))) | (Y5!24 = Y24!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(68,plain,
% 0.20/0.41 (Y5!24 = Y24!0),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[67, 66])).
% 0.20/0.41 tff(69,plain,
% 0.20/0.41 (Y24!0 = Y5!24),
% 0.20/0.41 inference(symmetry,[status(thm)],[68])).
% 0.20/0.41 tff(70,plain,
% 0.20/0.41 (r1(Y4!22)),
% 0.20/0.41 inference(or_elim,[status(thm)],[21])).
% 0.20/0.41 tff(71,plain,
% 0.20/0.41 ((r1(Y4!22) | (Y4!22 = Y24!0)) | (~r1(Y4!22))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(72,plain,
% 0.20/0.41 (r1(Y4!22) | (Y4!22 = Y24!0)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.41 tff(73,plain,
% 0.20/0.41 (((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y4!22)) | (~(Y4!22 = Y24!0)))) | (~(r1(Y4!22) | (Y4!22 = Y24!0))))) <=> ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y4!22)) | (~(Y4!22 = Y24!0)))) | (~(r1(Y4!22) | (Y4!22 = Y24!0))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(74,plain,
% 0.20/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | ((~((~r1(Y4!22)) | (~(Y4!22 = Y24!0)))) | (~(r1(Y4!22) | (Y4!22 = Y24!0))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(75,plain,
% 0.20/0.41 ((~![X19: $i] : ((~((~r1(X19)) | (~(X19 = Y24!0)))) | (~(r1(X19) | (X19 = Y24!0))))) | (~((~r1(Y4!22)) | (~(Y4!22 = Y24!0)))) | (~(r1(Y4!22) | (Y4!22 = Y24!0)))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.20/0.41 tff(76,plain,
% 0.20/0.41 (~((~r1(Y4!22)) | (~(Y4!22 = Y24!0)))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[75, 62, 72])).
% 0.20/0.41 tff(77,plain,
% 0.20/0.41 (((~r1(Y4!22)) | (~(Y4!22 = Y24!0))) | (Y4!22 = Y24!0)),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(78,plain,
% 0.20/0.41 (Y4!22 = Y24!0),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[77, 76])).
% 0.20/0.41 tff(79,plain,
% 0.20/0.41 (Y4!22 = Y5!24),
% 0.20/0.41 inference(transitivity,[status(thm)],[78, 69])).
% 0.20/0.41 tff(80,plain,
% 0.20/0.41 (tptp_fun_Y21_1(Y4!22) = tptp_fun_Y21_1(Y5!24)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.41 tff(81,plain,
% 0.20/0.41 (tptp_fun_Y21_1(Y5!24) = tptp_fun_Y21_1(Y4!22)),
% 0.20/0.41 inference(symmetry,[status(thm)],[80])).
% 0.20/0.41 tff(82,plain,
% 0.20/0.41 (r2(Y5!24, Y3!23)),
% 0.20/0.41 inference(or_elim,[status(thm)],[46])).
% 0.20/0.41 tff(83,plain,
% 0.20/0.41 ((r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24))) | (~r2(Y5!24, Y3!23))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(84,plain,
% 0.20/0.41 (r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.20/0.41 tff(85,plain,
% 0.20/0.41 (((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24)))) | (~((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24))))))) <=> ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24)))) | (~((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24))))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(86,plain,
% 0.20/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | ((~(r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24)))) | (~((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24))))))),
% 0.20/0.41 inference(quant_inst,[status(thm)],[])).
% 0.20/0.41 tff(87,plain,
% 0.20/0.41 ((~![X11: $i, X12: $i] : ((~(r2(X11, X12) | (X12 = tptp_fun_Y21_1(X11)))) | (~((~r2(X11, X12)) | (~(X12 = tptp_fun_Y21_1(X11))))))) | (~(r2(Y5!24, Y3!23) | (Y3!23 = tptp_fun_Y21_1(Y5!24)))) | (~((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.41 tff(88,plain,
% 0.20/0.41 (~((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24))))),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[87, 37, 84])).
% 0.20/0.41 tff(89,plain,
% 0.20/0.41 (((~r2(Y5!24, Y3!23)) | (~(Y3!23 = tptp_fun_Y21_1(Y5!24)))) | (Y3!23 = tptp_fun_Y21_1(Y5!24))),
% 0.20/0.41 inference(tautology,[status(thm)],[])).
% 0.20/0.41 tff(90,plain,
% 0.20/0.41 (Y3!23 = tptp_fun_Y21_1(Y5!24)),
% 0.20/0.41 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.20/0.41 tff(91,plain,
% 0.20/0.41 (r2(Y3!23, Y1!20)),
% 0.20/0.41 inference(and_elim,[status(thm)],[16])).
% 0.20/0.41 tff(92,plain,
% 0.20/0.41 (^[X3: $i, X10: $i, Y12: $i, Y13: $i] : trans(monotonicity(rewrite(((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))), (((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))))), rewrite(((X3 = X10) | ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))), (((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(93,plain,
% 0.20/0.41 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[92])).
% 0.20/0.41 tff(94,plain,
% 0.20/0.41 (^[X3: $i, X10: $i, Y12: $i, Y13: $i] : refl(((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(95,plain,
% 0.20/0.41 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[94])).
% 0.20/0.41 tff(96,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(pull_quant,[status(thm)],[])).
% 0.20/0.41 tff(97,plain,
% 0.20/0.41 (^[X3: $i, X10: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[Y12: $i] : pull_quant(((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i] : ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), pull_quant(![Y12: $i] : ![Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) <=> ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))))), pull_quant(((X3 = X10) | ![Y12: $i, Y13: $i] : ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), (((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(98,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ![Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[97])).
% 0.20/0.41 tff(99,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[98, 96])).
% 0.20/0.41 tff(100,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[99, 95])).
% 0.20/0.41 tff(101,plain,
% 0.20/0.41 (^[X3: $i, X10: $i] : rewrite(((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(102,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.41 tff(103,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(transitivity,[status(thm)],[102, 100])).
% 0.20/0.41 tff(104,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(105,plain,
% 0.20/0.41 (^[X3: $i, X10: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y12: $i] : trans(monotonicity(quant_intro(proof_bind(^[Y13: $i] : rewrite(((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ((~(Y13 = Y12)) | (~r2(X3, Y13))))), (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) <=> ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> (![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))))), rewrite((![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) <=> ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))), ((![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13))))))), (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) <=> ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> (![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) | (X3 = X10)))), rewrite((![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))), ((![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))))),
% 0.20/0.41 inference(bind,[status(th)],[])).
% 0.20/0.41 tff(106,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10)) <=> ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.41 tff(107,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~r2(X3, Y13)) | (~(Y13 = Y12))) | (~r2(X10, Y12))) | (X3 = X10))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_3a')).
% 0.20/0.41 tff(108,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.41 tff(109,plain,
% 0.20/0.41 (![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.41 tff(110,plain,(
% 0.20/0.41 ![X3: $i, X10: $i] : ((X3 = X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(skolemize,[status(sab)],[109])).
% 0.20/0.41 tff(111,plain,
% 0.20/0.41 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((X3 = X10) | ((~r2(X10, Y12)) | ((~(Y13 = Y12)) | (~r2(X3, Y13)))))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.41 tff(112,plain,
% 0.20/0.41 (![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))),
% 0.20/0.41 inference(modus_ponens,[status(thm)],[111, 93])).
% 0.20/0.41 tff(113,plain,
% 0.20/0.41 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(114,plain,
% 0.20/0.41 (($false | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)) <=> ((~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(115,plain,
% 0.20/0.41 ((~$true) <=> $false),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(116,plain,
% 0.20/0.41 ((Y1!20 = Y1!20) <=> $true),
% 0.20/0.41 inference(rewrite,[status(thm)],[])).
% 0.20/0.41 tff(117,plain,
% 0.20/0.41 ((~(Y1!20 = Y1!20)) <=> (~$true)),
% 0.20/0.41 inference(monotonicity,[status(thm)],[116])).
% 0.20/0.41 tff(118,plain,
% 0.20/0.41 ((~(Y1!20 = Y1!20)) <=> $false),
% 0.20/0.41 inference(transitivity,[status(thm)],[117, 115])).
% 0.20/0.41 tff(119,plain,
% 0.20/0.41 (((~(Y1!20 = Y1!20)) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)) <=> ($false | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[118])).
% 0.20/0.42 tff(120,plain,
% 0.20/0.42 (((~(Y1!20 = Y1!20)) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)) <=> ((~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.42 inference(transitivity,[status(thm)],[119, 114])).
% 0.20/0.42 tff(121,plain,
% 0.20/0.42 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(Y1!20 = Y1!20)) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)))),
% 0.20/0.42 inference(monotonicity,[status(thm)],[120])).
% 0.20/0.42 tff(122,plain,
% 0.20/0.42 (((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(Y1!20 = Y1!20)) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))) <=> ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.42 inference(transitivity,[status(thm)],[121, 113])).
% 0.20/0.42 tff(123,plain,
% 0.20/0.42 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | ((~(Y1!20 = Y1!20)) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(124,plain,
% 0.20/0.42 ((~![X3: $i, X10: $i, Y12: $i, Y13: $i] : ((~(Y13 = Y12)) | (~r2(X3, Y13)) | (~r2(X10, Y12)) | (X3 = X10))) | (~r2(Y3!23, Y1!20)) | (~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.20/0.42 tff(125,plain,
% 0.20/0.42 ((~r2(Y4!22, Y1!20)) | (Y3!23 = Y4!22)),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[124, 112, 91])).
% 0.20/0.42 tff(126,plain,
% 0.20/0.42 (Y3!23 = Y4!22),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[125, 23])).
% 0.20/0.42 tff(127,plain,
% 0.20/0.42 (Y4!22 = Y3!23),
% 0.20/0.42 inference(symmetry,[status(thm)],[126])).
% 0.20/0.42 tff(128,plain,
% 0.20/0.42 (Y24!0 = Y4!22),
% 0.20/0.42 inference(symmetry,[status(thm)],[78])).
% 0.20/0.42 tff(129,plain,
% 0.20/0.42 (Y24!0 = Y1!20),
% 0.20/0.42 inference(transitivity,[status(thm)],[128, 127, 90, 81, 45])).
% 0.20/0.42 tff(130,plain,
% 0.20/0.42 (r1(Y24!0) <=> r1(Y4!22)),
% 0.20/0.42 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.42 tff(131,plain,
% 0.20/0.42 (r1(Y4!22) <=> r1(Y24!0)),
% 0.20/0.42 inference(symmetry,[status(thm)],[130])).
% 0.20/0.42 tff(132,plain,
% 0.20/0.42 (r1(Y24!0)),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[70, 131])).
% 0.20/0.42 tff(133,plain,
% 0.20/0.42 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(134,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.42 tff(135,plain,
% 0.20/0.42 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(136,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.42 tff(137,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(transitivity,[status(thm)],[136, 134])).
% 0.20/0.42 tff(138,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(139,plain,
% 0.20/0.42 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(140,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.42 tff(141,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox/benchmark/Axioms/NUM008+0.ax','axiom_7a')).
% 0.20/0.42 tff(142,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.42 tff(143,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[142, 138])).
% 0.20/0.42 tff(144,plain,(
% 0.20/0.42 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[143])).
% 0.20/0.42 tff(145,plain,
% 0.20/0.42 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[144, 137])).
% 0.20/0.42 tff(146,plain,
% 0.20/0.42 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y3!23, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y3!23, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(147,plain,
% 0.20/0.42 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | ((~r2(Y3!23, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(148,plain,
% 0.20/0.42 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y10))))) | (~r2(Y3!23, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.20/0.42 tff(149,plain,
% 0.20/0.42 (![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[148, 145, 91])).
% 0.20/0.42 tff(150,plain,
% 0.20/0.42 (((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | ((~r1(Y24!0)) | (~(Y24!0 = Y1!20)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y24!0)) | (~(Y24!0 = Y1!20)))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(151,plain,
% 0.20/0.42 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | ((~r1(Y24!0)) | (~(Y24!0 = Y1!20)))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(152,plain,
% 0.20/0.42 ((~![Y20: $i] : ((~r1(Y20)) | (~(Y20 = Y1!20)))) | (~r1(Y24!0)) | (~(Y24!0 = Y1!20))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.42 tff(153,plain,
% 0.20/0.42 ((~r1(Y24!0)) | (~(Y24!0 = Y1!20))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[152, 149])).
% 0.20/0.42 tff(154,plain,
% 0.20/0.42 ($false),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[153, 132, 129])).
% 0.20/0.42 % SZS output end Proof
%------------------------------------------------------------------------------