TSTP Solution File: NUN073+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUN073+1 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:27:54 EDT 2022
% Result : Theorem 0.19s 0.48s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUN073+1 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 16:23:48 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.48 % SZS status Theorem
% 0.19/0.48 % SZS output start Proof
% 0.19/0.48 tff(r2_type, type, (
% 0.19/0.48 r2: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_Y4_22_type, type, (
% 0.19/0.48 tptp_fun_Y4_22: $i)).
% 0.19/0.48 tff(id_type, type, (
% 0.19/0.48 id: ( $i * $i ) > $o)).
% 0.19/0.48 tff(tptp_fun_Y1_20_type, type, (
% 0.19/0.48 tptp_fun_Y1_20: $i)).
% 0.19/0.48 tff(tptp_fun_Y3_23_type, type, (
% 0.19/0.48 tptp_fun_Y3_23: $i)).
% 0.19/0.48 tff(r1_type, type, (
% 0.19/0.48 r1: $i > $o)).
% 0.19/0.48 tff(tptp_fun_Y5_24_type, type, (
% 0.19/0.48 tptp_fun_Y5_24: $i)).
% 0.19/0.48 tff(tptp_fun_Y2_21_type, type, (
% 0.19/0.48 tptp_fun_Y2_21: $i)).
% 0.19/0.48 tff(tptp_fun_Y21_1_type, type, (
% 0.19/0.48 tptp_fun_Y21_1: $i > $i)).
% 0.19/0.48 tff(tptp_fun_Y24_0_type, type, (
% 0.19/0.48 tptp_fun_Y24_0: $i)).
% 0.19/0.48 tff(1,plain,
% 0.19/0.48 (((id(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)))))) <=> (id(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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(2,plain,
% 0.19/0.48 (((~(~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)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(3,plain,
% 0.19/0.48 (((~(~id(Y2!21, Y1!20))) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21))))) <=> (id(Y2!21, Y1!20) & (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(4,plain,
% 0.19/0.48 ((((~(~id(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)))))) <=> ((id(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))))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.48 tff(5,plain,
% 0.19/0.48 ((((~(~id(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)))))) <=> (id(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)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.48 tff(6,plain,
% 0.19/0.48 ((~![Y1: $i] : (![Y2: $i] : ((~id(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] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(7,plain,
% 0.19/0.48 ((~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~id(Y2, Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))) <=> (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(8,axiom,(~![Y1: $i] : (![Y2: $i] : (![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2))) | (~id(Y2, Y1))) | ![Y3: $i] : (![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3))) | (~r2(Y3, Y1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','oneunidtwo')).
% 0.19/0.48 tff(9,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.48 tff(10,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.48 tff(11,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.48 tff(12,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.48 tff(13,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[12, 6])).
% 0.19/0.48 tff(14,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.19/0.48 tff(15,plain,
% 0.19/0.48 (~![Y1: $i] : (![Y2: $i] : ((~id(Y2, Y1)) | ![Y4: $i] : ((~r1(Y4)) | (~r2(Y4, Y2)))) | ![Y3: $i] : ((~r2(Y3, Y1)) | ![Y5: $i] : ((~r1(Y5)) | (~r2(Y5, Y3)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[14, 6])).
% 0.19/0.48 tff(16,plain,
% 0.19/0.48 (id(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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.19/0.48 tff(17,plain,
% 0.19/0.48 (~((~r1(Y5!24)) | (~r2(Y5!24, Y3!23)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[16])).
% 0.19/0.48 tff(18,plain,
% 0.19/0.48 (r2(Y5!24, Y3!23)),
% 0.19/0.48 inference(or_elim,[status(thm)],[17])).
% 0.19/0.48 tff(19,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(20,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.48 tff(21,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 (^[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)))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.48 tff(27,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')).
% 0.19/0.48 tff(28,plain,
% 0.19/0.48 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.48 tff(29,plain,
% 0.19/0.48 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.48 tff(30,plain,(
% 0.19/0.48 ![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[29])).
% 0.19/0.48 tff(31,plain,
% 0.19/0.48 (![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.48 tff(32,plain,
% 0.19/0.48 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(33,plain,
% 0.19/0.48 (((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~id(Y20, Y3!23)) | (~r1(Y20)))) <=> ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(34,plain,
% 0.19/0.48 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~id(Y20, Y3!23)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))))),
% 0.19/0.48 inference(monotonicity,[status(thm)],[33])).
% 0.19/0.48 tff(35,plain,
% 0.19/0.48 (((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~id(Y20, Y3!23)) | (~r1(Y20))))) <=> ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[34, 32])).
% 0.19/0.48 tff(36,plain,
% 0.19/0.48 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | ((~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~id(Y20, Y3!23)) | (~r1(Y20))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(37,plain,
% 0.19/0.48 ((~![X7: $i, Y10: $i] : ((~r2(X7, Y10)) | ![Y20: $i] : ((~id(Y20, Y10)) | (~r1(Y20))))) | (~r2(Y5!24, Y3!23)) | ![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.19/0.48 tff(38,plain,
% 0.19/0.48 (![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[37, 31, 18])).
% 0.19/0.48 tff(39,plain,
% 0.19/0.48 (~((~r1(Y4!22)) | (~r2(Y4!22, Y2!21)))),
% 0.19/0.48 inference(and_elim,[status(thm)],[16])).
% 0.19/0.48 tff(40,plain,
% 0.19/0.48 (r1(Y4!22)),
% 0.19/0.48 inference(or_elim,[status(thm)],[39])).
% 0.19/0.48 tff(41,plain,
% 0.19/0.48 (((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))) | ((~r1(Y4!22)) | (~id(Y4!22, Y3!23)))) <=> ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))) | (~r1(Y4!22)) | (~id(Y4!22, Y3!23)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(42,plain,
% 0.19/0.48 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))) | ((~r1(Y4!22)) | (~id(Y4!22, Y3!23)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(43,plain,
% 0.19/0.48 ((~![Y20: $i] : ((~r1(Y20)) | (~id(Y20, Y3!23)))) | (~r1(Y4!22)) | (~id(Y4!22, Y3!23))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.19/0.48 tff(44,plain,
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% 0.19/0.48 inference(unit_resolution,[status(thm)],[43, 40, 38])).
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% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(46,plain,
% 0.19/0.48 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[45])).
% 0.19/0.48 tff(47,plain,
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% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(48,plain,
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% 0.19/0.48 inference(quant_intro,[status(thm)],[47])).
% 0.19/0.48 tff(49,plain,
% 0.19/0.48 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))))) <=> ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[48, 46])).
% 0.19/0.48 tff(50,plain,
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% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(51,plain,
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% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(52,plain,
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% 0.19/0.48 inference(quant_intro,[status(thm)],[51])).
% 0.19/0.48 tff(53,axiom,(![X3: $i, X10: $i] : (![Y12: $i] : (![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13))) | (~r2(X10, Y12))) | id(X3, X10))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_3a')).
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% 0.19/0.48 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.19/0.48 tff(55,plain,
% 0.19/0.48 (![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.19/0.48 tff(56,plain,(
% 0.19/0.48 ![X3: $i, X10: $i] : (id(X3, X10) | ![Y12: $i] : ((~r2(X10, Y12)) | ![Y13: $i] : ((~id(Y13, Y12)) | (~r2(X3, Y13)))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[55])).
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% 0.19/0.48 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.19/0.48 tff(58,plain,
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% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(59,plain,
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% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(60,plain,
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% 0.19/0.48 inference(modus_ponens,[status(thm)],[59, 58])).
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% 0.19/0.48 inference(unit_resolution,[status(thm)],[60, 57, 44])).
% 0.19/0.48 tff(62,plain,
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% 0.19/0.48 inference(and_elim,[status(thm)],[16])).
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% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(64,plain,
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% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(65,plain,
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% 0.19/0.49 inference(modus_ponens,[status(thm)],[64, 63])).
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% 0.19/0.49 inference(unit_resolution,[status(thm)],[65, 62, 61])).
% 0.19/0.49 tff(67,plain,
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% 0.19/0.49 inference(or_elim,[status(thm)],[39])).
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% 0.19/0.49 inference(tautology,[status(thm)],[])).
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% 0.19/0.49 inference(unit_resolution,[status(thm)],[68, 67])).
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% 0.19/0.49 inference(tautology,[status(thm)],[])).
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% 0.19/0.49 inference(unit_resolution,[status(thm)],[70, 40])).
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% 0.19/0.49 inference(bind,[status(th)],[])).
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% 0.19/0.49 inference(quant_intro,[status(thm)],[72])).
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% 0.19/0.49 inference(bind,[status(th)],[])).
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% 0.19/0.49 inference(quant_intro,[status(thm)],[74])).
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% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(77,axiom,(?[Y24: $i] : ![X19: $i] : ((id(X19, Y24) & r1(X19)) | ((~r1(X19)) & (~id(X19, Y24))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_1')).
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% 0.19/0.49 inference(transitivity,[status(sab)],[78])).
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% 0.19/0.49 inference(rewrite,[status(thm)],[])).
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% 0.19/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
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% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(90,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29)))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.49 tff(91,plain,
% 0.19/0.49 (^[X28: $i, X29: $i, X30: $i, X31: $i] : trans(monotonicity(rewrite((r2(X28, X29) & r2(X30, X31)) <=> (~((~r2(X30, X31)) | (~r2(X28, X29))))), rewrite(((~r2(X28, X29)) & (~r2(X30, X31))) <=> (~(r2(X30, X31) | r2(X28, X29)))), (((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))) | (~id(X29, X31)) | (~id(X28, X30))))), rewrite(((~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))), (((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(92,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.49 tff(93,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(94,plain,
% 0.19/0.49 (^[X28: $i, X29: $i, X30: $i, X31: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~id(X28, X30)) | (~id(X29, X31))) <=> ((~id(X29, X31)) | (~id(X28, X30)))), ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~id(X29, X31)) | (~id(X28, X30))) | ((~r2(X28, X29)) & (~r2(X30, X31)))))), rewrite((((~id(X29, X31)) | (~id(X28, X30))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))), ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) <=> (((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))))), (((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ((((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) | (r2(X28, X29) & r2(X30, X31))))), rewrite(((((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30))) | (r2(X28, X29) & r2(X30, X31))) <=> ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))), (((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(95,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31))) <=> ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.49 tff(96,axiom,(![X28: $i, X29: $i, X30: $i, X31: $i] : ((((~id(X28, X30)) | (~id(X29, X31))) | ((~r2(X28, X29)) & (~r2(X30, X31)))) | (r2(X28, X29) & r2(X30, X31)))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_9')).
% 0.19/0.49 tff(97,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.49 tff(98,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.49 tff(99,plain,(
% 0.19/0.49 ![X28: $i, X29: $i, X30: $i, X31: $i] : ((r2(X28, X29) & r2(X30, X31)) | ((~r2(X28, X29)) & (~r2(X30, X31))) | (~id(X29, X31)) | (~id(X28, X30)))),
% 0.19/0.49 inference(skolemize,[status(sab)],[98])).
% 0.19/0.49 tff(100,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.49 tff(101,plain,
% 0.19/0.49 (![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.19/0.49 tff(102,plain,
% 0.19/0.49 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y2!21, Y1!20)) | (~id(Y4!22, Y24!0)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21)))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, Y2!21))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y2!21, Y1!20)) | (~id(Y4!22, Y24!0)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21)))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, Y2!21))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(103,plain,
% 0.19/0.49 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y2!21, Y1!20)) | (~id(Y4!22, Y24!0)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21)))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, Y2!21))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(104,plain,
% 0.19/0.49 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y2!21, Y1!20)) | (~id(Y4!22, Y24!0)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21)))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, Y2!21)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.19/0.49 tff(105,plain,
% 0.19/0.49 (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[104, 101, 88, 87, 69])).
% 0.19/0.49 tff(106,plain,
% 0.19/0.49 (((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, Y2!21))) | r2(Y24!0, Y1!20)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(107,plain,
% 0.19/0.49 (r2(Y24!0, Y1!20)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.19/0.49 tff(108,plain,
% 0.19/0.49 ((r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(109,plain,
% 0.19/0.49 (r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.19/0.49 tff(110,plain,
% 0.19/0.49 (^[X11: $i, X12: $i] : refl(((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(111,plain,
% 0.19/0.49 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[110])).
% 0.19/0.49 tff(112,plain,
% 0.19/0.49 (^[X11: $i, X12: $i] : trans(monotonicity(rewrite((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) <=> (~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11)))))), rewrite(((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))) <=> (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))), (((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))))), rewrite(((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))), (((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(113,plain,
% 0.19/0.49 (![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[112])).
% 0.19/0.49 tff(114,plain,
% 0.19/0.49 (![X11: $i] : ![X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11))))) <=> ![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(pull_quant,[status(thm)],[])).
% 0.19/0.49 tff(115,plain,
% 0.19/0.49 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21)))) <=> ![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(116,axiom,(![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_2')).
% 0.19/0.49 tff(117,plain,
% 0.19/0.49 (![X11: $i] : ?[Y21: $i] : ![X12: $i] : ((id(X12, Y21) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, Y21))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.19/0.49 tff(118,plain,(
% 0.19/0.49 ![X11: $i] : ![X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(skolemize,[status(sab)],[117])).
% 0.19/0.49 tff(119,plain,
% 0.19/0.49 (![X11: $i, X12: $i] : ((id(X12, tptp_fun_Y21_1(X11)) & r2(X11, X12)) | ((~r2(X11, X12)) & (~id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.19/0.49 tff(120,plain,
% 0.19/0.49 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[119, 113])).
% 0.19/0.49 tff(121,plain,
% 0.19/0.49 (![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[120, 111])).
% 0.19/0.49 tff(122,plain,
% 0.19/0.49 (((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0)))))) <=> ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(123,plain,
% 0.19/0.49 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | ((~((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(124,plain,
% 0.19/0.49 ((~![X11: $i, X12: $i] : ((~((~r2(X11, X12)) | (~id(X12, tptp_fun_Y21_1(X11))))) | (~(r2(X11, X12) | id(X12, tptp_fun_Y21_1(X11)))))) | (~((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | id(Y1!20, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.19/0.49 tff(125,plain,
% 0.19/0.49 (~((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[124, 121, 109])).
% 0.19/0.49 tff(126,plain,
% 0.19/0.49 (((~r2(Y24!0, Y1!20)) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0)))) | id(Y1!20, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(127,plain,
% 0.19/0.49 (id(Y1!20, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.49 tff(128,plain,
% 0.19/0.49 (^[X21: $i, X22: $i] : refl(((~id(X21, X22)) | id(X22, X21)) <=> ((~id(X21, X22)) | id(X22, X21)))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(129,plain,
% 0.19/0.49 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.49 tff(130,plain,
% 0.19/0.49 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21)) <=> ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(131,axiom,(![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))), file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax','axiom_6')).
% 0.19/0.49 tff(132,plain,
% 0.19/0.49 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.49 tff(133,plain,(
% 0.19/0.49 ![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.49 inference(skolemize,[status(sab)],[132])).
% 0.19/0.49 tff(134,plain,
% 0.19/0.49 (![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[133, 129])).
% 0.19/0.49 tff(135,plain,
% 0.19/0.49 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | id(tptp_fun_Y21_1(Y24!0), Y1!20))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | id(tptp_fun_Y21_1(Y24!0), Y1!20))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(136,plain,
% 0.19/0.49 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | id(tptp_fun_Y21_1(Y24!0), Y1!20))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(137,plain,
% 0.19/0.49 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | id(tptp_fun_Y21_1(Y24!0), Y1!20)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.19/0.49 tff(138,plain,
% 0.19/0.49 (id(tptp_fun_Y21_1(Y24!0), Y1!20)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[137, 134, 127])).
% 0.19/0.49 tff(139,plain,
% 0.19/0.49 ((r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(140,plain,
% 0.19/0.49 (r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[139, 107])).
% 0.19/0.49 tff(141,plain,
% 0.19/0.49 (((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!22, Y24!0)) | id(Y24!0, Y4!22))) <=> ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!22, Y24!0)) | id(Y24!0, Y4!22))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(142,plain,
% 0.19/0.49 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | ((~id(Y4!22, Y24!0)) | id(Y24!0, Y4!22))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(143,plain,
% 0.19/0.49 ((~![X21: $i, X22: $i] : ((~id(X21, X22)) | id(X22, X21))) | (~id(Y4!22, Y24!0)) | id(Y24!0, Y4!22)),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.49 tff(144,plain,
% 0.19/0.49 (id(Y24!0, Y4!22)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[143, 134, 87])).
% 0.19/0.49 tff(145,plain,
% 0.19/0.49 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(146,plain,
% 0.19/0.49 (((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) <=> ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(147,plain,
% 0.19/0.49 ((~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20))) <=> (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(148,plain,
% 0.19/0.49 ((~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) <=> (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(149,plain,
% 0.19/0.49 (((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) | (~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20)))) <=> ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[148, 147])).
% 0.19/0.49 tff(150,plain,
% 0.19/0.49 (((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) | (~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20)))) <=> ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[149, 146])).
% 0.19/0.49 tff(151,plain,
% 0.19/0.49 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) | (~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[150])).
% 0.19/0.49 tff(152,plain,
% 0.19/0.49 (((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) | (~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20))))) <=> ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0)))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[151, 145])).
% 0.19/0.50 tff(153,plain,
% 0.19/0.50 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | ((~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y4!22, tptp_fun_Y21_1(Y24!0))) | (~r2(Y24!0, Y1!20)))) | (~(r2(Y4!22, tptp_fun_Y21_1(Y24!0)) | r2(Y24!0, Y1!20))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(154,plain,
% 0.19/0.50 ((~![X28: $i, X29: $i, X30: $i, X31: $i] : ((~id(X29, X31)) | (~id(X28, X30)) | (~((~r2(X30, X31)) | (~r2(X28, X29)))) | (~(r2(X30, X31) | r2(X28, X29))))) | (~id(Y1!20, tptp_fun_Y21_1(Y24!0))) | (~id(Y24!0, Y4!22)) | (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) | (~(r2(Y24!0, Y1!20) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.19/0.50 tff(155,plain,
% 0.19/0.50 (~((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[154, 101, 144, 127, 140])).
% 0.19/0.50 tff(156,plain,
% 0.19/0.50 (((~r2(Y24!0, Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0)))) | r2(Y4!22, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(157,plain,
% 0.19/0.50 (r2(Y4!22, tptp_fun_Y21_1(Y24!0))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.19/0.50 tff(158,plain,
% 0.19/0.50 (((~![Y13: $i] : ((~id(Y13, Y1!20)) | (~r2(Y4!22, Y13)))) | ((~id(tptp_fun_Y21_1(Y24!0), Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))) <=> ((~![Y13: $i] : ((~id(Y13, Y1!20)) | (~r2(Y4!22, Y13)))) | (~id(tptp_fun_Y21_1(Y24!0), Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(159,plain,
% 0.19/0.50 ((~![Y13: $i] : ((~id(Y13, Y1!20)) | (~r2(Y4!22, Y13)))) | ((~id(tptp_fun_Y21_1(Y24!0), Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(160,plain,
% 0.19/0.50 ((~![Y13: $i] : ((~id(Y13, Y1!20)) | (~r2(Y4!22, Y13)))) | (~id(tptp_fun_Y21_1(Y24!0), Y1!20)) | (~r2(Y4!22, tptp_fun_Y21_1(Y24!0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.19/0.50 tff(161,plain,
% 0.19/0.50 ($false),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[160, 157, 138, 66])).
% 0.19/0.50 % SZS output end Proof
%------------------------------------------------------------------------------