TSTP Solution File: NUN089+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN089+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:27:59 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN089+1 : 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 : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 16:44:54 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 tff(id_type, type, (
% 0.19/0.40 id: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_Y1_20_type, type, (
% 0.19/0.40 tptp_fun_Y1_20: $i)).
% 0.19/0.40 tff(tptp_fun_Y4_23_type, type, (
% 0.19/0.40 tptp_fun_Y4_23: $i)).
% 0.19/0.40 tff(r1_type, type, (
% 0.19/0.40 r1: $i > $o)).
% 0.19/0.40 tff(r2_type, type, (
% 0.19/0.40 r2: ( $i * $i ) > $o)).
% 0.19/0.40 tff(tptp_fun_Y2_21_type, type, (
% 0.19/0.40 tptp_fun_Y2_21: $i)).
% 0.19/0.40 tff(tptp_fun_Y3_22_type, type, (
% 0.19/0.40 tptp_fun_Y3_22: $i)).
% 0.19/0.40 tff(1,plain,
% 0.19/0.40 (((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(2,plain,
% 0.19/0.40 ((~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))) <=> (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(3,plain,
% 0.19/0.40 (((~(~r2(Y2!21, Y1!20))) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) <=> (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(4,plain,
% 0.19/0.40 ((((~(~r2(Y2!21, Y1!20))) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> ((r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.40 tff(5,plain,
% 0.19/0.40 ((((~(~r2(Y2!21, Y1!20))) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21))))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))) <=> (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.40 tff(6,plain,
% 0.19/0.40 ((~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(7,plain,
% 0.19/0.40 ((~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4)))))),
% 0.19/0.40 inference(rewrite,[status(thm)],[])).
% 0.19/0.40 tff(8,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2))) | (~r2(Y2, Y1))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','zerounidtwo')).
% 0.19/0.40 tff(9,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.40 tff(10,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.40 tff(11,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.40 tff(12,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.40 tff(13,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.19/0.40 tff(14,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.40 tff(15,plain,
% 0.19/0.40 (~![Y1: $i] : (![Y2: $i] : ((~r2(Y2, Y1)) | ![Y3: $i] : ((~r1(Y3)) | (~r2(Y3, Y2)))) | ![Y4: $i] : ((~id(Y4, Y1)) | (~r1(Y4))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.40 tff(16,plain,
% 0.19/0.40 (r2(Y2!21, Y1!20) & (~((~r1(Y3!22)) | (~r2(Y3!22, Y2!21)))) & (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.40 tff(17,plain,
% 0.19/0.40 (~((~id(Y4!23, Y1!20)) | (~r1(Y4!23)))),
% 0.19/0.41 inference(and_elim,[status(thm)],[16])).
% 0.19/0.41 tff(18,plain,
% 0.19/0.41 (id(Y4!23, Y1!20)),
% 0.19/0.41 inference(or_elim,[status(thm)],[17])).
% 0.19/0.41 tff(19,plain,
% 0.19/0.41 (^[X21: $i, X22: $i] : refl(((~id(X21, X22)) | id(X22, X21)) <=> ((~id(X21, X22)) | id(X22, X21)))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(20,plain,
% 0.19/0.41 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.41 tff(21,plain,
% 0.19/0.41 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(22,axiom,(![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_6')).
% 0.19/0.41 tff(23,plain,
% 0.19/0.41 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.19/0.41 tff(24,plain,(
% 0.19/0.41 ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.41 inference(skolemize,[status(sab)],[23])).
% 0.19/0.41 tff(25,plain,
% 0.19/0.41 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.19/0.41 tff(26,plain,
% 0.19/0.41 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(27,plain,
% 0.19/0.41 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(28,plain,
% 0.19/0.41 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!23, Y1!20)) | id(Y1!20, Y4!23)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.41 tff(29,plain,
% 0.19/0.41 (id(Y1!20, Y4!23)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[28, 25, 18])).
% 0.19/0.41 tff(30,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(31,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(32,plain,
% 0.19/0.41 (^[X23: $i, X24: $i, X25: $i] : rewrite((((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(33,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25))) <=> ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.19/0.41 tff(34,axiom,(![X23: $i, X24: $i, X25: $i] : (((~id(X23, X24)) | id(X23, X25)) | (~id(X24, X25)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_7')).
% 0.19/0.41 tff(35,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.19/0.41 tff(36,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.19/0.41 tff(37,plain,(
% 0.19/0.41 ![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(skolemize,[status(sab)],[36])).
% 0.19/0.41 tff(38,plain,
% 0.19/0.41 (![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.19/0.41 tff(39,plain,
% 0.19/0.41 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(40,plain,
% 0.19/0.41 (((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23))) <=> ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20)))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[40])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))) <=> ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20))),
% 0.19/0.41 inference(transitivity,[status(thm)],[41, 39])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | ((~id(Y4!23, Y1!20)) | id(Y1!20, Y1!20) | (~id(Y1!20, Y4!23)))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(44,plain,
% 0.19/0.41 ((~![X23: $i, X24: $i, X25: $i] : ((~id(X24, X25)) | id(X23, X25) | (~id(X23, X24)))) | (~id(Y4!23, Y1!20)) | (~id(Y1!20, Y4!23)) | id(Y1!20, Y1!20)),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.19/0.41 tff(45,plain,
% 0.19/0.41 (id(Y1!20, Y1!20)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[44, 38, 18, 29])).
% 0.19/0.41 tff(46,plain,
% 0.19/0.41 (r2(Y2!21, Y1!20)),
% 0.19/0.41 inference(and_elim,[status(thm)],[16])).
% 0.19/0.41 tff(47,plain,
% 0.19/0.41 (^[X7: $i, Y10: $i] : refl(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(48,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.41 tff(49,plain,
% 0.19/0.41 (^[X7: $i, Y10: $i] : rewrite(((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(50,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.19/0.41 tff(51,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.19/0.41 tff(52,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(53,plain,
% 0.19/0.41 (^[X7: $i, Y10: $i] : rewrite((![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(54,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10))) <=> ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[53])).
% 0.19/0.41 tff(55,axiom,(![X7: $i, Y10: $i] : (![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))) | (~r2(X7, Y10)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_7a')).
% 0.19/0.41 tff(56,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.41 tff(57,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.19/0.41 tff(58,plain,(
% 0.19/0.41 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(skolemize,[status(sab)],[57])).
% 0.19/0.41 tff(59,plain,
% 0.19/0.41 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.19/0.41 tff(60,plain,
% 0.19/0.41 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(61,plain,
% 0.19/0.41 (((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20)))) <=> ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(62,plain,
% 0.19/0.41 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[61])).
% 0.19/0.41 tff(63,plain,
% 0.19/0.41 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20))))),
% 0.19/0.41 inference(transitivity,[status(thm)],[62, 60])).
% 0.19/0.41 tff(64,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~id(Y20, Y1!20)) | (~r1(Y20))))),
% 0.19/0.41 inference(quant_inst,[status(thm)],[])).
% 0.19/0.41 tff(65,plain,
% 0.19/0.41 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y2!21, Y1!20)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))),
% 0.19/0.41 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.19/0.41 tff(66,plain,
% 0.19/0.41 (![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[65, 59, 46])).
% 0.19/0.41 tff(67,plain,
% 0.19/0.41 (r1(Y4!23)),
% 0.19/0.41 inference(or_elim,[status(thm)],[17])).
% 0.19/0.41 tff(68,plain,
% 0.19/0.41 ((r1(Y1!20) | r1(Y4!23)) | (~r1(Y4!23))),
% 0.19/0.41 inference(tautology,[status(thm)],[])).
% 0.19/0.41 tff(69,plain,
% 0.19/0.41 (r1(Y1!20) | r1(Y4!23)),
% 0.19/0.41 inference(unit_resolution,[status(thm)],[68, 67])).
% 0.19/0.41 tff(70,plain,
% 0.19/0.41 (^[X26: $i, X27: $i] : refl(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(71,plain,
% 0.19/0.41 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[70])).
% 0.19/0.41 tff(72,plain,
% 0.19/0.41 (^[X26: $i, X27: $i] : trans(monotonicity(rewrite((r1(X26) & r1(X27)) <=> (~((~r1(X27)) | (~r1(X26))))), rewrite(((~r1(X26)) & (~r1(X27))) <=> (~(r1(X27) | r1(X26)))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))))), rewrite(((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))), (((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))))),
% 0.19/0.41 inference(bind,[status(th)],[])).
% 0.19/0.41 tff(73,plain,
% 0.19/0.41 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.19/0.41 inference(quant_intro,[status(thm)],[72])).
% 0.19/0.41 tff(74,plain,
% 0.19/0.41 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(75,plain,
% 0.19/0.41 (^[X26: $i, X27: $i] : rewrite((((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27)))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(76,plain,
% 0.19/0.42 (![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27))) <=> ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.19/0.42 tff(77,axiom,(![X26: $i, X27: $i] : (((~id(X26, X27)) | ((~r1(X26)) & (~r1(X27)))) | (r1(X26) & r1(X27)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_8')).
% 0.19/0.42 tff(78,plain,
% 0.19/0.42 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.19/0.42 tff(79,plain,
% 0.19/0.42 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.19/0.42 tff(80,plain,(
% 0.19/0.42 ![X26: $i, X27: $i] : ((~id(X26, X27)) | (r1(X26) & r1(X27)) | ((~r1(X26)) & (~r1(X27))))),
% 0.19/0.42 inference(skolemize,[status(sab)],[79])).
% 0.19/0.42 tff(81,plain,
% 0.19/0.42 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.19/0.42 tff(82,plain,
% 0.19/0.42 (![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[81, 71])).
% 0.19/0.42 tff(83,plain,
% 0.19/0.42 (((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))) <=> ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(84,plain,
% 0.19/0.42 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | ((~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(85,plain,
% 0.19/0.42 ((~![X26: $i, X27: $i] : ((~id(X26, X27)) | (~((~r1(X27)) | (~r1(X26)))) | (~(r1(X27) | r1(X26))))) | (~id(Y4!23, Y1!20)) | (~((~r1(Y1!20)) | (~r1(Y4!23)))) | (~(r1(Y1!20) | r1(Y4!23)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.19/0.42 tff(86,plain,
% 0.19/0.42 (~((~r1(Y1!20)) | (~r1(Y4!23)))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[85, 82, 18, 69])).
% 0.19/0.42 tff(87,plain,
% 0.19/0.42 (((~r1(Y1!20)) | (~r1(Y4!23))) | r1(Y1!20)),
% 0.19/0.42 inference(tautology,[status(thm)],[])).
% 0.19/0.42 tff(88,plain,
% 0.19/0.42 (r1(Y1!20)),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.19/0.42 tff(89,plain,
% 0.19/0.42 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | ((~r1(Y1!20)) | (~id(Y1!20, Y1!20)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | (~r1(Y1!20)) | (~id(Y1!20, Y1!20)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(90,plain,
% 0.19/0.42 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | ((~r1(Y1!20)) | (~id(Y1!20, Y1!20)))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(91,plain,
% 0.19/0.42 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y1!20)))) | (~r1(Y1!20)) | (~id(Y1!20, Y1!20))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.42 tff(92,plain,
% 0.19/0.42 ($false),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[91, 88, 66, 45])).
% 0.19/0.42 % SZS output end Proof
%------------------------------------------------------------------------------