TSTP Solution File: KRS161+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS161+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sat Sep 17 17:45:01 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS161+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.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 : Thu Sep 1 09:43:12 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.
% 0.20/0.49 % SZS status Theorem
% 0.20/0.49 % SZS output start Proof
% 0.20/0.49 tff(cC74xcomp_type, type, (
% 0.20/0.49 cC74xcomp: $i > $o)).
% 0.20/0.49 tff(iV16453_type, type, (
% 0.20/0.49 iV16453: $i)).
% 0.20/0.49 tff(cC62_type, type, (
% 0.20/0.49 cC62: $i > $o)).
% 0.20/0.49 tff(cC60_type, type, (
% 0.20/0.49 cC60: $i > $o)).
% 0.20/0.49 tff(cC58xcomp_type, type, (
% 0.20/0.49 cC58xcomp: $i > $o)).
% 0.20/0.49 tff(rR1_type, type, (
% 0.20/0.49 rR1: ( $i * $i ) > $o)).
% 0.20/0.49 tff(cC12xcomp_type, type, (
% 0.20/0.49 cC12xcomp: $i > $o)).
% 0.20/0.49 tff(tptp_fun_Y_70_type, type, (
% 0.20/0.49 tptp_fun_Y_70: $i > $i)).
% 0.20/0.49 tff(iV16461_type, type, (
% 0.20/0.49 iV16461: $i)).
% 0.20/0.49 tff(cC76_type, type, (
% 0.20/0.49 cC76: $i > $o)).
% 0.20/0.49 tff(cC42_type, type, (
% 0.20/0.49 cC42: $i > $o)).
% 0.20/0.49 tff(iV16455_type, type, (
% 0.20/0.49 iV16455: $i)).
% 0.20/0.49 tff(cC8xcomp_type, type, (
% 0.20/0.49 cC8xcomp: $i > $o)).
% 0.20/0.49 tff(tptp_fun_Y_50_type, type, (
% 0.20/0.49 tptp_fun_Y_50: $i > $i)).
% 0.20/0.49 tff(iV16460_type, type, (
% 0.20/0.49 iV16460: $i)).
% 0.20/0.49 tff(cC44_type, type, (
% 0.20/0.49 cC44: $i > $o)).
% 0.20/0.49 tff(cC40xcomp_type, type, (
% 0.20/0.49 cC40xcomp: $i > $o)).
% 0.20/0.49 tff(cC56_type, type, (
% 0.20/0.49 cC56: $i > $o)).
% 0.20/0.49 tff(cC54xcomp_type, type, (
% 0.20/0.49 cC54xcomp: $i > $o)).
% 0.20/0.49 tff(cC38_type, type, (
% 0.20/0.49 cC38: $i > $o)).
% 0.20/0.49 tff(iV16465_type, type, (
% 0.20/0.49 iV16465: $i)).
% 0.20/0.49 tff(iV16464_type, type, (
% 0.20/0.49 iV16464: $i)).
% 0.20/0.49 tff(iV16463_type, type, (
% 0.20/0.49 iV16463: $i)).
% 0.20/0.49 tff(iV16440_type, type, (
% 0.20/0.49 iV16440: $i)).
% 0.20/0.49 tff(iV16462_type, type, (
% 0.20/0.49 iV16462: $i)).
% 0.20/0.49 tff(cC68_type, type, (
% 0.20/0.49 cC68: $i > $o)).
% 0.20/0.49 tff(iV16459_type, type, (
% 0.20/0.49 iV16459: $i)).
% 0.20/0.49 tff(cC66xcomp_type, type, (
% 0.20/0.49 cC66xcomp: $i > $o)).
% 0.20/0.49 tff(cC64xcomp_type, type, (
% 0.20/0.49 cC64xcomp: $i > $o)).
% 0.20/0.49 tff(cC34_type, type, (
% 0.20/0.49 cC34: $i > $o)).
% 0.20/0.49 tff(cC32xcomp_type, type, (
% 0.20/0.49 cC32xcomp: $i > $o)).
% 0.20/0.49 tff(cC30xcomp_type, type, (
% 0.20/0.49 cC30xcomp: $i > $o)).
% 0.20/0.49 tff(cC88_type, type, (
% 0.20/0.49 cC88: $i > $o)).
% 0.20/0.49 tff(cC86xcomp_type, type, (
% 0.20/0.49 cC86xcomp: $i > $o)).
% 0.20/0.49 tff(cC84xcomp_type, type, (
% 0.20/0.49 cC84xcomp: $i > $o)).
% 0.20/0.49 tff(cC50_type, type, (
% 0.20/0.49 cC50: $i > $o)).
% 0.20/0.49 tff(cC48xcomp_type, type, (
% 0.20/0.49 cC48xcomp: $i > $o)).
% 0.20/0.49 tff(cC46xcomp_type, type, (
% 0.20/0.49 cC46xcomp: $i > $o)).
% 0.20/0.49 tff(iV16457_type, type, (
% 0.20/0.49 iV16457: $i)).
% 0.20/0.49 tff(cTOP_type, type, (
% 0.20/0.49 cTOP: $i > $o)).
% 0.20/0.49 tff(cC36xcomp_type, type, (
% 0.20/0.49 cC36xcomp: $i > $o)).
% 0.20/0.49 tff(cC104_type, type, (
% 0.20/0.49 cC104: $i > $o)).
% 0.20/0.49 tff(iV16439_type, type, (
% 0.20/0.49 iV16439: $i)).
% 0.20/0.49 tff(cC100xcomp_type, type, (
% 0.20/0.49 cC100xcomp: $i > $o)).
% 0.20/0.49 tff(cC106_type, type, (
% 0.20/0.49 cC106: $i > $o)).
% 0.20/0.49 tff(cC28_type, type, (
% 0.20/0.49 cC28: $i > $o)).
% 0.20/0.49 tff(cC108_type, type, (
% 0.20/0.49 cC108: $i > $o)).
% 0.20/0.49 tff(cC130_type, type, (
% 0.20/0.49 cC130: $i > $o)).
% 0.20/0.49 tff(cTEST_type, type, (
% 0.20/0.49 cTEST: $i > $o)).
% 0.20/0.49 tff(iV16448_type, type, (
% 0.20/0.49 iV16448: $i)).
% 0.20/0.49 tff(cC82_type, type, (
% 0.20/0.49 cC82: $i > $o)).
% 0.20/0.49 tff(cC96xcomp_type, type, (
% 0.20/0.49 cC96xcomp: $i > $o)).
% 0.20/0.49 tff(cC98_type, type, (
% 0.20/0.49 cC98: $i > $o)).
% 0.20/0.49 tff(cC80_type, type, (
% 0.20/0.49 cC80: $i > $o)).
% 0.20/0.49 tff(cC78xcomp_type, type, (
% 0.20/0.49 cC78xcomp: $i > $o)).
% 0.20/0.49 tff(cowlThing_type, type, (
% 0.20/0.49 cowlThing: $i > $o)).
% 0.20/0.49 tff(xsd_integer_type, type, (
% 0.20/0.49 xsd_integer: $i > $o)).
% 0.20/0.49 tff(xsd_string_type, type, (
% 0.20/0.49 xsd_string: $i > $o)).
% 0.20/0.49 tff(cowlNothing_type, type, (
% 0.20/0.49 cowlNothing: $i > $o)).
% 0.20/0.49 tff(1,assumption,((~((~cC60(iV16453)) | (~((~rR1(iV16453, tptp_fun_Y_70(iV16453))) | (~cC12xcomp(tptp_fun_Y_70(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))))), introduced(assumption)).
% 0.20/0.49 tff(2,plain,
% 0.20/0.49 (^[X: $i] : refl((~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(3,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.49 tff(4,plain,
% 0.20/0.49 (^[X: $i] : rewrite((~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[5, 3])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (^[X: $i] : trans(monotonicity(rewrite(((~cC60(X)) | (rR1(X, tptp_fun_Y_70(X)) & cC12xcomp(tptp_fun_Y_70(X)))) <=> ((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))), rewrite((cC60(X) | ![Y: $i] : (~(rR1(X, Y) & cC12xcomp(Y)))) <=> (cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))), ((((~cC60(X)) | (rR1(X, tptp_fun_Y_70(X)) & cC12xcomp(tptp_fun_Y_70(X)))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & cC12xcomp(Y))))) <=> (((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X)))))) & (cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X)))))) & (cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC60(X)) | (rR1(X, tptp_fun_Y_70(X)) & cC12xcomp(tptp_fun_Y_70(X)))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & cC12xcomp(Y))))) <=> (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (![X: $i] : (((~cC60(X)) | (rR1(X, tptp_fun_Y_70(X)) & cC12xcomp(tptp_fun_Y_70(X)))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & cC12xcomp(Y))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & cC12xcomp(Y))) <=> ![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & cC12xcomp(Y)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(10,axiom,(![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & cC12xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_91')).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & cC12xcomp(Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.20/0.49 tff(12,plain,(
% 0.20/0.49 ![X: $i] : (((~cC60(X)) | (rR1(X, tptp_fun_Y_70(X)) & cC12xcomp(tptp_fun_Y_70(X)))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & cC12xcomp(Y)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[11])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 ((~![X: $i] : (~((~((~cC60(X)) | (~((~rR1(X, tptp_fun_Y_70(X))) | (~cC12xcomp(tptp_fun_Y_70(X))))))) | (~(cC60(X) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC60(iV16453)) | (~((~rR1(iV16453, tptp_fun_Y_70(iV16453))) | (~cC12xcomp(tptp_fun_Y_70(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.20/0.49 tff(17,plain,(~((~((~cC60(iV16453)) | (~((~rR1(iV16453, tptp_fun_Y_70(iV16453))) | (~cC12xcomp(tptp_fun_Y_70(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (((~((~cC60(iV16453)) | (~((~rR1(iV16453, tptp_fun_Y_70(iV16453))) | (~cC12xcomp(tptp_fun_Y_70(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))))) | (cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.20/0.49 tff(20,assumption,(![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))), introduced(assumption)).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (cC12xcomp(iV16461) <=> cC12xcomp(iV16461)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(22,axiom,(cC12xcomp(iV16461)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_237')).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (cC12xcomp(iV16461)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (rR1(iV16453, iV16461) <=> rR1(iV16453, iV16461)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(25,axiom,(rR1(iV16453, iV16461)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_182')).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (rR1(iV16453, iV16461)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (((~![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))) | ((~cC12xcomp(iV16461)) | (~rR1(iV16453, iV16461)))) <=> ((~![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))) | (~cC12xcomp(iV16461)) | (~rR1(iV16453, iV16461)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 ((~![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))) | ((~cC12xcomp(iV16461)) | (~rR1(iV16453, iV16461)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 ((~![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))) | (~cC12xcomp(iV16461)) | (~rR1(iV16453, iV16461))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[29, 26, 23, 20])).
% 0.20/0.49 tff(31,plain,(~![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 ((~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y))))) | cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 ((~(cC60(iV16453) | ![Y: $i] : ((~cC12xcomp(Y)) | (~rR1(iV16453, Y))))) | cC60(iV16453)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (cC60(iV16453)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (cC58xcomp(iV16453) <=> cC58xcomp(iV16453)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(36,axiom,(cC58xcomp(iV16453)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_181')).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 (cC58xcomp(iV16453)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 ((~((~cC58xcomp(iV16453)) | (~cC60(iV16453)))) | (~cC58xcomp(iV16453)) | (~cC60(iV16453))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 ((~((~cC58xcomp(iV16453)) | (~cC60(iV16453)))) | (~cC60(iV16453))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (~((~cC58xcomp(iV16453)) | (~cC60(iV16453)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (^[X: $i] : refl((cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X))))) <=> (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X))))) <=> ![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[41])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (^[X: $i] : rewrite((cC62(X) <=> (cC60(X) & cC58xcomp(X))) <=> (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X))) <=> ![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[43])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X))) <=> ![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(46,axiom,(![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_92')).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.49 tff(48,plain,(
% 0.20/0.49 ![X: $i] : (cC62(X) <=> (cC60(X) & cC58xcomp(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[47])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 ((~![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))) | (cC62(iV16453) <=> (~((~cC58xcomp(iV16453)) | (~cC60(iV16453)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (cC62(iV16453) <=> (~((~cC58xcomp(iV16453)) | (~cC60(iV16453))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.49 tff(53,plain,
% 0.20/0.49 ((~(cC62(iV16453) <=> (~((~cC58xcomp(iV16453)) | (~cC60(iV16453)))))) | cC62(iV16453) | ((~cC58xcomp(iV16453)) | (~cC60(iV16453)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 (cC62(iV16453) | ((~cC58xcomp(iV16453)) | (~cC60(iV16453)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (cC62(iV16453)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (cC74xcomp(iV16453) <=> cC74xcomp(iV16453)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(57,axiom,(cC74xcomp(iV16453)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_174')).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (cC74xcomp(iV16453)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 ((~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))) | (~cC62(iV16453)) | (~cC74xcomp(iV16453))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 ((~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))) | (~cC62(iV16453))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 (~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.20/0.49 tff(62,assumption,((~((~cC42(iV16455)) | (~((~rR1(iV16455, tptp_fun_Y_50(iV16455))) | (~cC8xcomp(tptp_fun_Y_50(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))))), introduced(assumption)).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (^[X: $i] : refl((~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (^[X: $i] : rewrite((~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))) <=> (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (^[X: $i] : trans(monotonicity(rewrite(((~cC42(X)) | (rR1(X, tptp_fun_Y_50(X)) & cC8xcomp(tptp_fun_Y_50(X)))) <=> ((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))), rewrite((cC42(X) | ![Y: $i] : (~(rR1(X, Y) & cC8xcomp(Y)))) <=> (cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))), ((((~cC42(X)) | (rR1(X, tptp_fun_Y_50(X)) & cC8xcomp(tptp_fun_Y_50(X)))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & cC8xcomp(Y))))) <=> (((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X)))))) & (cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))))), rewrite((((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X)))))) & (cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y))))) <=> (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))), ((((~cC42(X)) | (rR1(X, tptp_fun_Y_50(X)) & cC8xcomp(tptp_fun_Y_50(X)))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & cC8xcomp(Y))))) <=> (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![X: $i] : (((~cC42(X)) | (rR1(X, tptp_fun_Y_50(X)) & cC8xcomp(tptp_fun_Y_50(X)))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & cC8xcomp(Y))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & cC8xcomp(Y))) <=> ![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & cC8xcomp(Y)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(71,axiom,(![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & cC8xcomp(Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_65')).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & cC8xcomp(Y)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.49 tff(73,plain,(
% 0.20/0.49 ![X: $i] : (((~cC42(X)) | (rR1(X, tptp_fun_Y_50(X)) & cC8xcomp(tptp_fun_Y_50(X)))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & cC8xcomp(Y)))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[72])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 ((~![X: $i] : (~((~((~cC42(X)) | (~((~rR1(X, tptp_fun_Y_50(X))) | (~cC8xcomp(tptp_fun_Y_50(X))))))) | (~(cC42(X) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(X, Y)))))))) | (~((~((~cC42(iV16455)) | (~((~rR1(iV16455, tptp_fun_Y_50(iV16455))) | (~cC8xcomp(tptp_fun_Y_50(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[76, 75, 62])).
% 0.20/0.49 tff(78,plain,(~((~((~cC42(iV16455)) | (~((~rR1(iV16455, tptp_fun_Y_50(iV16455))) | (~cC8xcomp(tptp_fun_Y_50(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 (((~((~cC42(iV16455)) | (~((~rR1(iV16455, tptp_fun_Y_50(iV16455))) | (~cC8xcomp(tptp_fun_Y_50(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))))) | (cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.20/0.49 tff(81,assumption,(![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))), introduced(assumption)).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 (cC8xcomp(iV16460) <=> cC8xcomp(iV16460)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,axiom,(cC8xcomp(iV16460)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_227')).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 (cC8xcomp(iV16460)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 (rR1(iV16455, iV16460) <=> rR1(iV16455, iV16460)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(86,axiom,(rR1(iV16455, iV16460)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_193')).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (rR1(iV16455, iV16460)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (((~![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))) | ((~cC8xcomp(iV16460)) | (~rR1(iV16455, iV16460)))) <=> ((~![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))) | (~cC8xcomp(iV16460)) | (~rR1(iV16455, iV16460)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 ((~![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))) | ((~cC8xcomp(iV16460)) | (~rR1(iV16455, iV16460)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 ((~![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))) | (~cC8xcomp(iV16460)) | (~rR1(iV16455, iV16460))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[90, 87, 84, 81])).
% 0.20/0.49 tff(92,plain,(~![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y))))) | cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 ((~(cC42(iV16455) | ![Y: $i] : ((~cC8xcomp(Y)) | (~rR1(iV16455, Y))))) | cC42(iV16455)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (cC42(iV16455)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[94, 80])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (cC40xcomp(iV16455) <=> cC40xcomp(iV16455)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(97,axiom,(cC40xcomp(iV16455)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_185')).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 (cC40xcomp(iV16455)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 ((~((~cC40xcomp(iV16455)) | (~cC42(iV16455)))) | (~cC40xcomp(iV16455)) | (~cC42(iV16455))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((~((~cC40xcomp(iV16455)) | (~cC42(iV16455)))) | (~cC42(iV16455))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (~((~cC40xcomp(iV16455)) | (~cC42(iV16455)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (^[X: $i] : refl((cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X))))) <=> (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X))))) <=> ![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (^[X: $i] : rewrite((cC44(X) <=> (cC40xcomp(X) & cC42(X))) <=> (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X))) <=> ![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X))) <=> ![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(107,axiom,(![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_66')).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.49 tff(109,plain,(
% 0.20/0.49 ![X: $i] : (cC44(X) <=> (cC40xcomp(X) & cC42(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[108])).
% 0.20/0.49 tff(110,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 ((~![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))) | (cC44(iV16455) <=> (~((~cC40xcomp(iV16455)) | (~cC42(iV16455)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(113,plain,
% 0.20/0.49 (cC44(iV16455) <=> (~((~cC40xcomp(iV16455)) | (~cC42(iV16455))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 ((~(cC44(iV16455) <=> (~((~cC40xcomp(iV16455)) | (~cC42(iV16455)))))) | cC44(iV16455) | ((~cC40xcomp(iV16455)) | (~cC42(iV16455)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (cC44(iV16455) | ((~cC40xcomp(iV16455)) | (~cC42(iV16455)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (cC44(iV16455)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 (cC54xcomp(iV16455) <=> cC54xcomp(iV16455)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(118,axiom,(cC54xcomp(iV16455)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_190')).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (cC54xcomp(iV16455)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 ((~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))) | (~cC44(iV16455)) | (~cC54xcomp(iV16455))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 ((~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))) | (~cC44(iV16455))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (^[X: $i] : refl((cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X))))) <=> (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X))))) <=> ![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (^[X: $i] : rewrite((cC56(X) <=> (cC54xcomp(X) & cC44(X))) <=> (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X))) <=> ![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X))) <=> ![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(128,axiom,(![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_82')).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.20/0.49 tff(130,plain,(
% 0.20/0.49 ![X: $i] : (cC56(X) <=> (cC54xcomp(X) & cC44(X)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[129])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 ((cC56(iV16455) <=> (~((~cC54xcomp(iV16455)) | (~cC44(iV16455))))) <=> (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC54xcomp(iV16455)) | (~cC44(iV16455)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[134])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC54xcomp(iV16455)) | (~cC44(iV16455)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[135, 133])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC54xcomp(iV16455)) | (~cC44(iV16455)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 (cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[138, 132])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ((~(cC56(iV16455) <=> (~((~cC44(iV16455)) | (~cC54xcomp(iV16455)))))) | cC56(iV16455) | ((~cC44(iV16455)) | (~cC54xcomp(iV16455)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (cC56(iV16455) | ((~cC44(iV16455)) | (~cC54xcomp(iV16455)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (cC56(iV16455)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[141, 122])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 (rR1(iV16464, iV16465) <=> rR1(iV16464, iV16465)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(144,axiom,(rR1(iV16464, iV16465)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_274')).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (rR1(iV16464, iV16465)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (^[X: $i] : refl((cC38(X) | (~rR1(iV16464, X))) <=> (cC38(X) | (~rR1(iV16464, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16464, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[146])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16464, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16464, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16464, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16464, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.50 tff(151,axiom,(![X: $i] : (rR1(iV16464, X) => cC38(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_265')).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.20/0.50 tff(154,plain,(
% 0.20/0.50 ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[153])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | (cC38(iV16465) | (~rR1(iV16464, iV16465)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | cC38(iV16465) | (~rR1(iV16464, iV16465)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | (cC38(iV16465) | (~rR1(iV16464, iV16465)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | cC38(iV16465) | (~rR1(iV16464, iV16465))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 (cC38(iV16465)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[158, 155, 145])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 ((cC56(iV16464) <=> (~((~cC54xcomp(iV16464)) | (~cC44(iV16464))))) <=> (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC54xcomp(iV16464)) | (~cC44(iV16464)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[161])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC54xcomp(iV16464)) | (~cC44(iV16464)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[162, 160])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC54xcomp(iV16464)) | (~cC44(iV16464)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 (cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[165, 132])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (rR1(iV16463, iV16464) <=> rR1(iV16463, iV16464)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(168,axiom,(rR1(iV16463, iV16464)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_263')).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (rR1(iV16463, iV16464)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (^[X: $i] : refl((cC56(X) | (~rR1(iV16463, X))) <=> (cC56(X) | (~rR1(iV16463, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16463, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.50 tff(172,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16463, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16463, X) => cC56(X)) <=> (cC56(X) | (~rR1(iV16463, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16463, X) => cC56(X)) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.50 tff(175,axiom,(![X: $i] : (rR1(iV16463, X) => cC56(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_261')).
% 0.20/0.50 tff(176,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[176, 172])).
% 0.20/0.50 tff(178,plain,(
% 0.20/0.50 ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[177])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[178, 171])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | (cC56(iV16464) | (~rR1(iV16463, iV16464)))) <=> ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | cC56(iV16464) | (~rR1(iV16463, iV16464)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | (cC56(iV16464) | (~rR1(iV16463, iV16464)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | cC56(iV16464) | (~rR1(iV16463, iV16464))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (cC56(iV16464)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[182, 179, 169])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 ((~(cC56(iV16464) <=> (~((~cC44(iV16464)) | (~cC54xcomp(iV16464)))))) | (~cC56(iV16464)) | (~((~cC44(iV16464)) | (~cC54xcomp(iV16464))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 (~((~cC44(iV16464)) | (~cC54xcomp(iV16464)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[184, 183, 166])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (((~cC44(iV16464)) | (~cC54xcomp(iV16464))) | cC44(iV16464)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (cC44(iV16464)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 ((~![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))) | (cC44(iV16464) <=> (~((~cC40xcomp(iV16464)) | (~cC42(iV16464)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (cC44(iV16464) <=> (~((~cC40xcomp(iV16464)) | (~cC42(iV16464))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[188, 111])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 ((~(cC44(iV16464) <=> (~((~cC40xcomp(iV16464)) | (~cC42(iV16464)))))) | (~cC44(iV16464)) | (~((~cC40xcomp(iV16464)) | (~cC42(iV16464))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (~((~cC40xcomp(iV16464)) | (~cC42(iV16464)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[190, 187, 189])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 (((~cC40xcomp(iV16464)) | (~cC42(iV16464))) | cC42(iV16464)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (cC42(iV16464)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 ((~![X: $i] : (cC62(X) <=> (~((~cC58xcomp(X)) | (~cC60(X)))))) | (cC62(iV16463) <=> (~((~cC58xcomp(iV16463)) | (~cC60(iV16463)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(195,plain,
% 0.20/0.50 (cC62(iV16463) <=> (~((~cC58xcomp(iV16463)) | (~cC60(iV16463))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[194, 50])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (^[X: $i] : refl((cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X))))) <=> (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X))))) <=> ![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 (^[X: $i] : rewrite((cC76(X) <=> (cC74xcomp(X) & cC62(X))) <=> (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X))) <=> ![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[198])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X))) <=> ![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(201,axiom,(![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_112')).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.20/0.50 tff(203,plain,(
% 0.20/0.50 ![X: $i] : (cC76(X) <=> (cC74xcomp(X) & cC62(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[202])).
% 0.20/0.50 tff(204,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 ((cC76(iV16463) <=> (~((~cC74xcomp(iV16463)) | (~cC62(iV16463))))) <=> (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC74xcomp(iV16463)) | (~cC62(iV16463)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[207])).
% 0.20/0.50 tff(209,plain,
% 0.20/0.50 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC74xcomp(iV16463)) | (~cC62(iV16463)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[208, 206])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC74xcomp(iV16463)) | (~cC62(iV16463)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(211,plain,
% 0.20/0.50 ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.50 tff(212,plain,
% 0.20/0.50 (cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.20/0.50 tff(213,plain,
% 0.20/0.50 (rR1(iV16440, iV16463) <=> rR1(iV16440, iV16463)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(214,axiom,(rR1(iV16440, iV16463)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_159')).
% 0.20/0.50 tff(215,plain,
% 0.20/0.50 (rR1(iV16440, iV16463)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.20/0.50 tff(216,plain,
% 0.20/0.50 (^[X: $i] : refl((cC76(X) | (~rR1(iV16440, X))) <=> (cC76(X) | (~rR1(iV16440, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(217,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X))) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[216])).
% 0.20/0.50 tff(218,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X))) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(219,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16440, X) => cC76(X)) <=> (cC76(X) | (~rR1(iV16440, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(220,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16440, X) => cC76(X)) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.50 tff(221,axiom,(![X: $i] : (rR1(iV16440, X) => cC76(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_156')).
% 0.20/0.50 tff(222,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.20/0.50 tff(223,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.20/0.50 tff(224,plain,(
% 0.20/0.50 ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[223])).
% 0.20/0.50 tff(225,plain,
% 0.20/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.20/0.50 tff(226,plain,
% 0.20/0.50 (((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | (cC76(iV16463) | (~rR1(iV16440, iV16463)))) <=> ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | cC76(iV16463) | (~rR1(iV16440, iV16463)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(227,plain,
% 0.20/0.50 ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | (cC76(iV16463) | (~rR1(iV16440, iV16463)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(228,plain,
% 0.20/0.50 ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | cC76(iV16463) | (~rR1(iV16440, iV16463))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.20/0.50 tff(229,plain,
% 0.20/0.50 (cC76(iV16463)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[228, 225, 215])).
% 0.20/0.50 tff(230,plain,
% 0.20/0.50 ((~(cC76(iV16463) <=> (~((~cC62(iV16463)) | (~cC74xcomp(iV16463)))))) | (~cC76(iV16463)) | (~((~cC62(iV16463)) | (~cC74xcomp(iV16463))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(231,plain,
% 0.20/0.50 (~((~cC62(iV16463)) | (~cC74xcomp(iV16463)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[230, 229, 212])).
% 0.20/0.50 tff(232,plain,
% 0.20/0.50 (((~cC62(iV16463)) | (~cC74xcomp(iV16463))) | cC62(iV16463)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(233,plain,
% 0.20/0.50 (cC62(iV16463)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[232, 231])).
% 0.20/0.50 tff(234,plain,
% 0.20/0.50 ((~(cC62(iV16463) <=> (~((~cC58xcomp(iV16463)) | (~cC60(iV16463)))))) | (~cC62(iV16463)) | (~((~cC58xcomp(iV16463)) | (~cC60(iV16463))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(235,plain,
% 0.20/0.50 (~((~cC58xcomp(iV16463)) | (~cC60(iV16463)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[234, 233, 195])).
% 0.20/0.50 tff(236,plain,
% 0.20/0.50 (((~cC58xcomp(iV16463)) | (~cC60(iV16463))) | cC60(iV16463)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(237,plain,
% 0.20/0.50 (cC60(iV16463)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.20/0.50 tff(238,plain,
% 0.20/0.50 (rR1(iV16461, iV16462) <=> rR1(iV16461, iV16462)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(239,axiom,(rR1(iV16461, iV16462)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_243')).
% 0.20/0.50 tff(240,plain,
% 0.20/0.50 (rR1(iV16461, iV16462)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.20/0.50 tff(241,plain,
% 0.20/0.50 (^[X: $i] : refl((cC38(X) | (~rR1(iV16461, X))) <=> (cC38(X) | (~rR1(iV16461, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(242,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[241])).
% 0.20/0.50 tff(243,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(244,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16461, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16461, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16461, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[244])).
% 0.20/0.50 tff(246,axiom,(![X: $i] : (rR1(iV16461, X) => cC38(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_241')).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.20/0.50 tff(248,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.20/0.50 tff(249,plain,(
% 0.20/0.50 ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[248])).
% 0.20/0.50 tff(250,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.20/0.50 tff(251,plain,
% 0.20/0.50 (((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | (cC38(iV16462) | (~rR1(iV16461, iV16462)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | cC38(iV16462) | (~rR1(iV16461, iV16462)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(252,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | (cC38(iV16462) | (~rR1(iV16461, iV16462)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(253,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | cC38(iV16462) | (~rR1(iV16461, iV16462))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.20/0.50 tff(254,plain,
% 0.20/0.50 (cC38(iV16462)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[253, 250, 240])).
% 0.20/0.50 tff(255,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(256,plain,
% 0.20/0.50 ((cC56(iV16461) <=> (~((~cC54xcomp(iV16461)) | (~cC44(iV16461))))) <=> (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(257,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC54xcomp(iV16461)) | (~cC44(iV16461)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[256])).
% 0.20/0.50 tff(258,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC54xcomp(iV16461)) | (~cC44(iV16461)))))) <=> ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[257, 255])).
% 0.20/0.50 tff(259,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC54xcomp(iV16461)) | (~cC44(iV16461)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(260,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) <=> (~((~cC54xcomp(X)) | (~cC44(X)))))) | (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.20/0.50 tff(261,plain,
% 0.20/0.50 (cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[260, 132])).
% 0.20/0.50 tff(262,plain,
% 0.20/0.50 (^[X: $i] : refl((cC56(X) | (~rR1(iV16453, X))) <=> (cC56(X) | (~rR1(iV16453, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(263,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[262])).
% 0.20/0.50 tff(264,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(265,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16453, X) => cC56(X)) <=> (cC56(X) | (~rR1(iV16453, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(266,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16453, X) => cC56(X)) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.50 tff(267,axiom,(![X: $i] : (rR1(iV16453, X) => cC56(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_178')).
% 0.20/0.50 tff(268,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.50 tff(269,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[268, 264])).
% 0.20/0.50 tff(270,plain,(
% 0.20/0.50 ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[269])).
% 0.20/0.50 tff(271,plain,
% 0.20/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[270, 263])).
% 0.20/0.50 tff(272,plain,
% 0.20/0.50 (((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | (cC56(iV16461) | (~rR1(iV16453, iV16461)))) <=> ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | cC56(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(273,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | (cC56(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(274,plain,
% 0.20/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | cC56(iV16461) | (~rR1(iV16453, iV16461))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[273, 272])).
% 0.20/0.50 tff(275,plain,
% 0.20/0.50 (cC56(iV16461)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[274, 271, 26])).
% 0.20/0.50 tff(276,plain,
% 0.20/0.50 ((~(cC56(iV16461) <=> (~((~cC44(iV16461)) | (~cC54xcomp(iV16461)))))) | (~cC56(iV16461)) | (~((~cC44(iV16461)) | (~cC54xcomp(iV16461))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(277,plain,
% 0.20/0.50 (~((~cC44(iV16461)) | (~cC54xcomp(iV16461)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[276, 275, 261])).
% 0.20/0.50 tff(278,plain,
% 0.20/0.50 (((~cC44(iV16461)) | (~cC54xcomp(iV16461))) | cC44(iV16461)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(279,plain,
% 0.20/0.50 (cC44(iV16461)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[278, 277])).
% 0.20/0.50 tff(280,plain,
% 0.20/0.50 ((~![X: $i] : (cC44(X) <=> (~((~cC40xcomp(X)) | (~cC42(X)))))) | (cC44(iV16461) <=> (~((~cC40xcomp(iV16461)) | (~cC42(iV16461)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(281,plain,
% 0.20/0.50 (cC44(iV16461) <=> (~((~cC40xcomp(iV16461)) | (~cC42(iV16461))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[280, 111])).
% 0.20/0.50 tff(282,plain,
% 0.20/0.50 ((~(cC44(iV16461) <=> (~((~cC40xcomp(iV16461)) | (~cC42(iV16461)))))) | (~cC44(iV16461)) | (~((~cC40xcomp(iV16461)) | (~cC42(iV16461))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(283,plain,
% 0.20/0.50 (~((~cC40xcomp(iV16461)) | (~cC42(iV16461)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[282, 279, 281])).
% 0.20/0.50 tff(284,plain,
% 0.20/0.50 (((~cC40xcomp(iV16461)) | (~cC42(iV16461))) | cC42(iV16461)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(285,plain,
% 0.20/0.50 (cC42(iV16461)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.20/0.50 tff(286,plain,
% 0.20/0.50 (^[X: $i] : refl((cC38(X) | (~rR1(iV16455, X))) <=> (cC38(X) | (~rR1(iV16455, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(287,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16455, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[286])).
% 0.20/0.50 tff(288,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16455, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(289,plain,
% 0.20/0.50 (^[X: $i] : rewrite((rR1(iV16455, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16455, X))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(290,plain,
% 0.20/0.50 (![X: $i] : (rR1(iV16455, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[289])).
% 0.20/0.50 tff(291,axiom,(![X: $i] : (rR1(iV16455, X) => cC38(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_188')).
% 0.20/0.50 tff(292,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.20/0.50 tff(293,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[292, 288])).
% 0.20/0.50 tff(294,plain,(
% 0.20/0.50 ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[293])).
% 0.20/0.50 tff(295,plain,
% 0.20/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[294, 287])).
% 0.20/0.50 tff(296,plain,
% 0.20/0.50 (((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | (cC38(iV16460) | (~rR1(iV16455, iV16460)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | cC38(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(297,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | (cC38(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(298,plain,
% 0.20/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | cC38(iV16460) | (~rR1(iV16455, iV16460))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.20/0.50 tff(299,plain,
% 0.20/0.50 (cC38(iV16460)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[298, 295, 87])).
% 0.20/0.50 tff(300,plain,
% 0.20/0.50 (^[X: $i] : refl((cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X))))) <=> (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(301,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X))))) <=> ![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[300])).
% 0.20/0.50 tff(302,plain,
% 0.20/0.50 (^[X: $i] : rewrite((cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X))) <=> (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(303,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X))) <=> ![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[302])).
% 0.20/0.50 tff(304,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X))) <=> ![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(305,axiom,(![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_100')).
% 0.20/0.50 tff(306,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[305, 304])).
% 0.20/0.50 tff(307,plain,(
% 0.20/0.50 ![X: $i] : (cC68(X) <=> (cC64xcomp(X) & cC66xcomp(X)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[306])).
% 0.20/0.50 tff(308,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[307, 303])).
% 0.20/0.50 tff(309,plain,
% 0.20/0.50 (![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[308, 301])).
% 0.20/0.50 tff(310,plain,
% 0.20/0.50 ((~![X: $i] : (cC68(X) <=> (~((~cC64xcomp(X)) | (~cC66xcomp(X)))))) | (cC68(iV16459) <=> (~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(311,plain,
% 0.20/0.50 (cC68(iV16459) <=> (~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[310, 309])).
% 0.20/0.50 tff(312,plain,
% 0.20/0.50 (cC66xcomp(iV16459) <=> cC66xcomp(iV16459)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(313,axiom,(cC66xcomp(iV16459)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_221')).
% 0.20/0.50 tff(314,plain,
% 0.20/0.50 (cC66xcomp(iV16459)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.50 tff(315,plain,
% 0.20/0.50 (cC64xcomp(iV16459) <=> cC64xcomp(iV16459)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(316,axiom,(cC64xcomp(iV16459)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_213')).
% 0.20/0.50 tff(317,plain,
% 0.20/0.50 (cC64xcomp(iV16459)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.50 tff(318,plain,
% 0.20/0.50 ((~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))) | (~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(319,plain,
% 0.20/0.50 (~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[318, 317, 314])).
% 0.20/0.50 tff(320,plain,
% 0.20/0.50 ((~(cC68(iV16459) <=> (~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))))) | cC68(iV16459) | ((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(321,plain,
% 0.20/0.50 ((~(cC68(iV16459) <=> (~((~cC64xcomp(iV16459)) | (~cC66xcomp(iV16459)))))) | cC68(iV16459)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[320, 319])).
% 0.20/0.50 tff(322,plain,
% 0.20/0.50 (cC68(iV16459)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[321, 311])).
% 0.20/0.50 tff(323,plain,
% 0.20/0.50 (^[X: $i] : refl((cC34(X) <=> (~((~cC30xcomp(X)) | (~cC32xcomp(X))))) <=> (cC34(X) <=> (~((~cC30xcomp(X)) | (~cC32xcomp(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(324,plain,
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% 0.20/0.50 inference(quant_intro,[status(thm)],[323])).
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% 0.20/0.50 inference(bind,[status(th)],[])).
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% 0.20/0.50 inference(quant_intro,[status(thm)],[325])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(328,axiom,(![X: $i] : (cC34(X) <=> (cC30xcomp(X) & cC32xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_52')).
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% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
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% 0.20/0.50 inference(modus_ponens,[status(thm)],[336, 335])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
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% 0.20/0.50 inference(tautology,[status(thm)],[])).
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[344, 334])).
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% 0.20/0.50 inference(bind,[status(th)],[])).
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% 0.20/0.50 inference(quant_intro,[status(thm)],[346])).
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% 0.20/0.50 inference(bind,[status(th)],[])).
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% 0.20/0.50 inference(quant_intro,[status(thm)],[348])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(351,axiom,(![X: $i] : (cC88(X) <=> (cC84xcomp(X) & cC86xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_128')).
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% 0.20/0.50 (![X: $i] : (cC88(X) <=> (cC84xcomp(X) & cC86xcomp(X)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[351, 350])).
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% 0.20/0.50 inference(skolemize,[status(sab)],[352])).
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% 0.20/0.50 inference(modus_ponens,[status(thm)],[353, 349])).
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% 0.20/0.50 (![X: $i] : (cC88(X) <=> (~((~cC84xcomp(X)) | (~cC86xcomp(X)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[354, 347])).
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% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(357,plain,
% 0.20/0.50 (cC88(iV16459) <=> (~((~cC84xcomp(iV16459)) | (~cC86xcomp(iV16459))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[356, 355])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(359,axiom,(cC86xcomp(iV16459)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_215')).
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% 0.20/0.50 inference(modus_ponens,[status(thm)],[359, 358])).
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% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(362,axiom,(cC84xcomp(iV16459)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_210')).
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% 0.20/0.50 inference(modus_ponens,[status(thm)],[362, 361])).
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% 0.20/0.50 inference(tautology,[status(thm)],[])).
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[364, 363, 360])).
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% 0.20/0.50 inference(tautology,[status(thm)],[])).
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[366, 365])).
% 0.20/0.50 tff(368,plain,
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% 0.20/0.50 inference(unit_resolution,[status(thm)],[367, 357])).
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% 0.20/0.50 (^[X: $i] : refl((cC50(X) <=> (~((~cC46xcomp(X)) | (~cC48xcomp(X))))) <=> (cC50(X) <=> (~((~cC46xcomp(X)) | (~cC48xcomp(X))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
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% 0.20/0.50 inference(quant_intro,[status(thm)],[369])).
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% 0.20/0.51 inference(bind,[status(th)],[])).
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% 0.20/0.51 (![X: $i] : (cC50(X) <=> (cC46xcomp(X) & cC48xcomp(X))) <=> ![X: $i] : (cC50(X) <=> (~((~cC46xcomp(X)) | (~cC48xcomp(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[371])).
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% 0.20/0.51 (![X: $i] : (cC50(X) <=> (cC46xcomp(X) & cC48xcomp(X))) <=> ![X: $i] : (cC50(X) <=> (cC46xcomp(X) & cC48xcomp(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(374,axiom,(![X: $i] : (cC50(X) <=> (cC46xcomp(X) & cC48xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_73')).
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% 0.20/0.51 (![X: $i] : (cC50(X) <=> (cC46xcomp(X) & cC48xcomp(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[374, 373])).
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% 0.20/0.51 inference(skolemize,[status(sab)],[375])).
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% 0.20/0.51 (![X: $i] : (cC50(X) <=> (~((~cC46xcomp(X)) | (~cC48xcomp(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[376, 372])).
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% 0.20/0.51 (![X: $i] : (cC50(X) <=> (~((~cC46xcomp(X)) | (~cC48xcomp(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[377, 370])).
% 0.20/0.51 tff(379,plain,
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(380,plain,
% 0.20/0.51 (cC50(iV16459) <=> (~((~cC46xcomp(iV16459)) | (~cC48xcomp(iV16459))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[379, 378])).
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% 0.20/0.51 (cC48xcomp(iV16459) <=> cC48xcomp(iV16459)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(382,axiom,(cC48xcomp(iV16459)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_217')).
% 0.20/0.51 tff(383,plain,
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[382, 381])).
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[385, 384])).
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% 0.20/0.51 ((~((~cC46xcomp(iV16459)) | (~cC48xcomp(iV16459)))) | (~cC46xcomp(iV16459)) | (~cC48xcomp(iV16459))),
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[387, 386, 383])).
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% 0.20/0.51 tff(391,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[390, 380])).
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% 0.20/0.51 tff(394,plain,
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% 0.20/0.51 (![X: $i] : (cC38(X) <=> (cTOP(X) & cC36xcomp(X))) <=> ![X: $i] : (cC38(X) <=> (cTOP(X) & cC36xcomp(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(397,axiom,(![X: $i] : (cC38(X) <=> (cTOP(X) & cC36xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_57')).
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% 0.20/0.51 (![X: $i] : (cC38(X) <=> (cTOP(X) & cC36xcomp(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[397, 396])).
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% 0.20/0.51 inference(skolemize,[status(sab)],[398])).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[399, 395])).
% 0.20/0.51 tff(401,plain,
% 0.20/0.51 (![X: $i] : (cC38(X) <=> (~((~cC36xcomp(X)) | (~cTOP(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[400, 393])).
% 0.20/0.51 tff(402,plain,
% 0.20/0.51 ((~![X: $i] : (cC38(X) <=> (~((~cC36xcomp(X)) | (~cTOP(X)))))) | (cC38(iV16457) <=> (~((~cC36xcomp(iV16457)) | (~cTOP(iV16457)))))),
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% 0.20/0.51 tff(403,plain,
% 0.20/0.51 (cC38(iV16457) <=> (~((~cC36xcomp(iV16457)) | (~cTOP(iV16457))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[402, 401])).
% 0.20/0.51 tff(404,plain,
% 0.20/0.51 (cC36xcomp(iV16457) <=> cC36xcomp(iV16457)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(405,axiom,(cC36xcomp(iV16457)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_201')).
% 0.20/0.51 tff(406,plain,
% 0.20/0.51 (cC36xcomp(iV16457)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[405, 404])).
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% 0.20/0.51 (cTOP(iV16457) <=> cTOP(iV16457)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(408,axiom,(cTOP(iV16457)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_197')).
% 0.20/0.51 tff(409,plain,
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[408, 407])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(411,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[410, 409, 406])).
% 0.20/0.51 tff(412,plain,
% 0.20/0.51 ((~(cC38(iV16457) <=> (~((~cC36xcomp(iV16457)) | (~cTOP(iV16457)))))) | cC38(iV16457) | ((~cC36xcomp(iV16457)) | (~cTOP(iV16457)))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(413,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[412, 411])).
% 0.20/0.51 tff(414,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[413, 403])).
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% 0.20/0.51 (^[X: $i] : refl((cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X))))) <=> (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(416,plain,
% 0.20/0.51 (![X: $i] : (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X))))) <=> ![X: $i] : (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[415])).
% 0.20/0.51 tff(417,plain,
% 0.20/0.51 (^[X: $i] : rewrite((cC106(X) <=> (cC104(X) & cC100xcomp(X))) <=> (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(418,plain,
% 0.20/0.51 (![X: $i] : (cC106(X) <=> (cC104(X) & cC100xcomp(X))) <=> ![X: $i] : (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[417])).
% 0.20/0.51 tff(419,plain,
% 0.20/0.51 (![X: $i] : (cC106(X) <=> (cC104(X) & cC100xcomp(X))) <=> ![X: $i] : (cC106(X) <=> (cC104(X) & cC100xcomp(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(420,axiom,(![X: $i] : (cC106(X) <=> (cC104(X) & cC100xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_11')).
% 0.20/0.51 tff(421,plain,
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.20/0.51 tff(422,plain,(
% 0.20/0.51 ![X: $i] : (cC106(X) <=> (cC104(X) & cC100xcomp(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[421])).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[422, 418])).
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% 0.20/0.51 (![X: $i] : (cC106(X) <=> (~((~cC100xcomp(X)) | (~cC104(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[423, 416])).
% 0.20/0.51 tff(425,plain,
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(426,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[425, 424])).
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% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(428,plain,
% 0.20/0.51 (![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))) <=> ![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[427])).
% 0.20/0.51 tff(429,plain,
% 0.20/0.51 (^[X: $i] : rewrite((cC108(X) <=> (cC28(X) & cC106(X))) <=> (cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(430,plain,
% 0.20/0.51 (![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X))) <=> ![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[429])).
% 0.20/0.51 tff(431,plain,
% 0.20/0.51 (![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X))) <=> ![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(432,axiom,(![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_12')).
% 0.20/0.51 tff(433,plain,
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[432, 431])).
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% 0.20/0.51 ![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[433])).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[434, 430])).
% 0.20/0.51 tff(436,plain,
% 0.20/0.51 (![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[435, 428])).
% 0.20/0.51 tff(437,plain,
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(438,plain,
% 0.20/0.51 ((cC108(iV16439) <=> (~((~cC28(iV16439)) | (~cC106(iV16439))))) <=> (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(439,plain,
% 0.20/0.51 (((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC28(iV16439)) | (~cC106(iV16439)))))) <=> ((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439))))))),
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% 0.20/0.51 inference(transitivity,[status(thm)],[439, 437])).
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(442,plain,
% 0.20/0.51 ((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[441, 440])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[442, 436])).
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% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(445,plain,
% 0.20/0.51 (![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))) <=> ![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[444])).
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% 0.20/0.51 (^[X: $i] : rewrite((cTEST(X) <=> (cC108(X) & cC130(X))) <=> (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(447,plain,
% 0.20/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X))) <=> ![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[446])).
% 0.20/0.51 tff(448,plain,
% 0.20/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X))) <=> ![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(449,axiom,(![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_145')).
% 0.20/0.51 tff(450,plain,
% 0.20/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.20/0.51 tff(451,plain,(
% 0.20/0.51 ![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[450])).
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% 0.20/0.51 (![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[451, 447])).
% 0.20/0.51 tff(453,plain,
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[452, 445])).
% 0.20/0.51 tff(454,plain,
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% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(455,plain,
% 0.20/0.51 (cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[454, 453])).
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(457,axiom,(cTEST(iV16439)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_149')).
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% 0.20/0.51 inference(modus_ponens,[status(thm)],[457, 456])).
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% 0.20/0.51 ((~(cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439)))))) | (~cTEST(iV16439)) | (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(460,plain,
% 0.20/0.51 ((~(cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439)))))) | (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[459, 458])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[460, 455])).
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% 0.20/0.51 (((~cC108(iV16439)) | (~cC130(iV16439))) | cC108(iV16439)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(463,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[462, 461])).
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% 0.20/0.51 ((~(cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))) | (~cC108(iV16439)) | (~((~cC106(iV16439)) | (~cC28(iV16439))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
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% 0.20/0.51 ((~(cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))) | (~((~cC106(iV16439)) | (~cC28(iV16439))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[464, 463])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[465, 443])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(468,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[467, 466])).
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% 0.20/0.51 ((~(cC106(iV16439) <=> (~((~cC100xcomp(iV16439)) | (~cC104(iV16439)))))) | (~cC106(iV16439)) | (~((~cC100xcomp(iV16439)) | (~cC104(iV16439))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(470,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[469, 468, 426])).
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% 0.20/0.51 tff(472,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[471, 470])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[473, 401])).
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% 0.20/0.51 inference(rewrite,[status(thm)],[])).
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[481, 480, 477])).
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% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(484,plain,
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% 0.20/0.51 tff(485,plain,
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% 0.20/0.51 inference(unit_resolution,[status(thm)],[484, 474])).
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% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(489,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X))) <=> ![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[488])).
% 0.20/0.51 tff(490,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X))) <=> ![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(491,axiom,(![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_143')).
% 0.20/0.51 tff(492,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.20/0.51 tff(493,plain,(
% 0.20/0.51 ![X: $i] : (cC98(X) <=> (cC96xcomp(X) & cC82(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[492])).
% 0.20/0.51 tff(494,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[493, 489])).
% 0.20/0.51 tff(495,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[494, 487])).
% 0.20/0.51 tff(496,plain,
% 0.20/0.51 (((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440)))))) <=> ((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(497,plain,
% 0.20/0.51 ((cC98(iV16440) <=> (~((~cC96xcomp(iV16440)) | (~cC82(iV16440))))) <=> (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(498,plain,
% 0.20/0.51 (((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC96xcomp(iV16440)) | (~cC82(iV16440)))))) <=> ((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[497])).
% 0.20/0.51 tff(499,plain,
% 0.20/0.51 (((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC96xcomp(iV16440)) | (~cC82(iV16440)))))) <=> ((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[498, 496])).
% 0.20/0.51 tff(500,plain,
% 0.20/0.51 ((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC96xcomp(iV16440)) | (~cC82(iV16440)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(501,plain,
% 0.20/0.51 ((~![X: $i] : (cC98(X) <=> (~((~cC96xcomp(X)) | (~cC82(X)))))) | (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[500, 499])).
% 0.20/0.51 tff(502,plain,
% 0.20/0.51 (cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[501, 495])).
% 0.20/0.51 tff(503,plain,
% 0.20/0.51 (rR1(iV16439, iV16440) <=> rR1(iV16439, iV16440)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(504,axiom,(rR1(iV16439, iV16440)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_150')).
% 0.20/0.51 tff(505,plain,
% 0.20/0.51 (rR1(iV16439, iV16440)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[504, 503])).
% 0.20/0.51 tff(506,plain,
% 0.20/0.51 (^[X: $i] : refl((cC98(X) | (~rR1(iV16439, X))) <=> (cC98(X) | (~rR1(iV16439, X))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(507,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) | (~rR1(iV16439, X))) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[506])).
% 0.20/0.51 tff(508,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) | (~rR1(iV16439, X))) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(509,plain,
% 0.20/0.51 (^[X: $i] : rewrite((rR1(iV16439, X) => cC98(X)) <=> (cC98(X) | (~rR1(iV16439, X))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(510,plain,
% 0.20/0.51 (![X: $i] : (rR1(iV16439, X) => cC98(X)) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[509])).
% 0.20/0.51 tff(511,axiom,(![X: $i] : (rR1(iV16439, X) => cC98(X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_146')).
% 0.20/0.51 tff(512,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.20/0.51 tff(513,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[512, 508])).
% 0.20/0.51 tff(514,plain,(
% 0.20/0.51 ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[513])).
% 0.20/0.51 tff(515,plain,
% 0.20/0.51 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[514, 507])).
% 0.20/0.51 tff(516,plain,
% 0.20/0.51 (((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | (cC98(iV16440) | (~rR1(iV16439, iV16440)))) <=> ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | cC98(iV16440) | (~rR1(iV16439, iV16440)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(517,plain,
% 0.20/0.51 ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | (cC98(iV16440) | (~rR1(iV16439, iV16440)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(518,plain,
% 0.20/0.51 ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | cC98(iV16440) | (~rR1(iV16439, iV16440))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.20/0.51 tff(519,plain,
% 0.20/0.51 (cC98(iV16440)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[518, 515, 505])).
% 0.20/0.51 tff(520,plain,
% 0.20/0.51 ((~(cC98(iV16440) <=> (~((~cC82(iV16440)) | (~cC96xcomp(iV16440)))))) | (~cC98(iV16440)) | (~((~cC82(iV16440)) | (~cC96xcomp(iV16440))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(521,plain,
% 0.20/0.51 (~((~cC82(iV16440)) | (~cC96xcomp(iV16440)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[520, 519, 502])).
% 0.20/0.51 tff(522,plain,
% 0.20/0.51 (((~cC82(iV16440)) | (~cC96xcomp(iV16440))) | cC82(iV16440)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(523,plain,
% 0.20/0.51 (cC82(iV16440)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[522, 521])).
% 0.20/0.51 tff(524,plain,
% 0.20/0.51 (^[X: $i] : refl((cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X))))) <=> (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(525,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X))))) <=> ![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[524])).
% 0.20/0.51 tff(526,plain,
% 0.20/0.51 (^[X: $i] : rewrite((cC82(X) <=> (cC80(X) & cC78xcomp(X))) <=> (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(527,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X))) <=> ![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[526])).
% 0.20/0.51 tff(528,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X))) <=> ![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(529,axiom,(![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axiom_120')).
% 0.20/0.51 tff(530,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.20/0.51 tff(531,plain,(
% 0.20/0.51 ![X: $i] : (cC82(X) <=> (cC80(X) & cC78xcomp(X)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[530])).
% 0.20/0.51 tff(532,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.20/0.51 tff(533,plain,
% 0.20/0.51 (![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[532, 525])).
% 0.20/0.51 tff(534,plain,
% 0.20/0.51 ((~![X: $i] : (cC82(X) <=> (~((~cC78xcomp(X)) | (~cC80(X)))))) | (cC82(iV16440) <=> (~((~cC78xcomp(iV16440)) | (~cC80(iV16440)))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(535,plain,
% 0.20/0.51 (cC82(iV16440) <=> (~((~cC78xcomp(iV16440)) | (~cC80(iV16440))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[534, 533])).
% 0.20/0.51 tff(536,plain,
% 0.20/0.51 ((~(cC82(iV16440) <=> (~((~cC78xcomp(iV16440)) | (~cC80(iV16440)))))) | (~cC82(iV16440)) | (~((~cC78xcomp(iV16440)) | (~cC80(iV16440))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(537,plain,
% 0.20/0.51 (~((~cC78xcomp(iV16440)) | (~cC80(iV16440)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[536, 523, 535])).
% 0.20/0.51 tff(538,plain,
% 0.20/0.51 (((~cC78xcomp(iV16440)) | (~cC80(iV16440))) | cC80(iV16440)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(539,plain,
% 0.20/0.51 (cC80(iV16440)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.20/0.51 tff(540,plain,
% 0.20/0.51 (((~cC106(iV16439)) | (~cC28(iV16439))) | cC28(iV16439)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(541,plain,
% 0.20/0.51 (cC28(iV16439)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[540, 466])).
% 0.20/0.51 tff(542,plain,
% 0.20/0.51 (((~cC108(iV16439)) | (~cC130(iV16439))) | cC130(iV16439)),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(543,plain,
% 0.20/0.51 (cC130(iV16439)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[542, 461])).
% 0.20/0.51 tff(544,plain,
% 0.20/0.51 ((~(~((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465))))) <=> ((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(545,plain,
% 0.20/0.51 ((cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465)) <=> (~((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(546,plain,
% 0.20/0.52 ((~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465))) <=> (~(~((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[545])).
% 0.20/0.52 tff(547,plain,
% 0.20/0.52 ((~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465))) <=> ((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[546, 544])).
% 0.20/0.52 tff(548,plain,
% 0.20/0.52 ((~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465))) <=> (~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(549,plain,
% 0.20/0.52 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465))) <=> (~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(550,plain,
% 0.20/0.52 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(551,plain,
% 0.20/0.52 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[550])).
% 0.20/0.52 tff(552,plain,
% 0.20/0.52 ((~((((((((((((((((((((((((((((((((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC130(iV16439)) & cC108(iV16439)) & cC104(iV16439)) & cC106(iV16439)) & cC28(iV16439)) & cowlThing(iV16439)) & cC98(iV16440)) & cC80(iV16440)) & cC82(iV16440)) & cowlThing(iV16440)) & cC38(iV16448)) & cowlThing(iV16448)) & cC76(iV16453)) & cC62(iV16453)) & cowlThing(iV16453)) & cC60(iV16453)) & cC56(iV16455)) & cC44(iV16455)) & cC42(iV16455)) & cowlThing(iV16455)) & cC38(iV16457)) & cowlThing(iV16457)) & cC50(iV16459)) & cC88(iV16459)) & cC34(iV16459)) & cC68(iV16459)) & cowlThing(iV16459)) & cC38(iV16460)) & cowlThing(iV16460)) & cC42(iV16461)) & cC56(iV16461)) & cC44(iV16461)) & cowlThing(iV16461)) & cC38(iV16462)) & cowlThing(iV16462)) & cC76(iV16463)) & cC62(iV16463)) & cowlThing(iV16463)) & cC60(iV16463)) & cC56(iV16464)) & cC42(iV16464)) & cC44(iV16464)) & cowlThing(iV16464)) & cC38(iV16465)) & cowlThing(iV16465))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(553,axiom,(~((((((((((((((((((((((((((((((((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC130(iV16439)) & cC108(iV16439)) & cC104(iV16439)) & cC106(iV16439)) & cC28(iV16439)) & cowlThing(iV16439)) & cC98(iV16440)) & cC80(iV16440)) & cC82(iV16440)) & cowlThing(iV16440)) & cC38(iV16448)) & cowlThing(iV16448)) & cC76(iV16453)) & cC62(iV16453)) & cowlThing(iV16453)) & cC60(iV16453)) & cC56(iV16455)) & cC44(iV16455)) & cC42(iV16455)) & cowlThing(iV16455)) & cC38(iV16457)) & cowlThing(iV16457)) & cC50(iV16459)) & cC88(iV16459)) & cC34(iV16459)) & cC68(iV16459)) & cowlThing(iV16459)) & cC38(iV16460)) & cowlThing(iV16460)) & cC42(iV16461)) & cC56(iV16461)) & cC44(iV16461)) & cowlThing(iV16461)) & cC38(iV16462)) & cowlThing(iV16462)) & cC76(iV16463)) & cC62(iV16463)) & cowlThing(iV16463)) & cC60(iV16463)) & cC56(iV16464)) & cC42(iV16464)) & cC44(iV16464)) & cowlThing(iV16464)) & cC38(iV16465)) & cowlThing(iV16465))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','the_axiom')).
% 0.20/0.52 tff(554,plain,
% 0.20/0.52 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[553, 552])).
% 0.20/0.52 tff(555,plain,
% 0.20/0.52 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cowlThing(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cowlThing(iV16440) & cC38(iV16448) & cowlThing(iV16448) & cC76(iV16453) & cC62(iV16453) & cowlThing(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cowlThing(iV16455) & cC38(iV16457) & cowlThing(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cowlThing(iV16459) & cC38(iV16460) & cowlThing(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cowlThing(iV16461) & cC38(iV16462) & cowlThing(iV16462) & cC76(iV16463) & cC62(iV16463) & cowlThing(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cowlThing(iV16464) & cC38(iV16465) & cowlThing(iV16465))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[554, 551])).
% 0.20/0.52 tff(556,plain,
% 0.20/0.52 (~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[555, 549])).
% 0.20/0.52 tff(557,plain,
% 0.20/0.52 (~(cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC106(iV16439) & cC28(iV16439) & cC98(iV16440) & cC80(iV16440) & cC82(iV16440) & cC38(iV16448) & cC76(iV16453) & cC62(iV16453) & cC60(iV16453) & cC56(iV16455) & cC44(iV16455) & cC42(iV16455) & cC38(iV16457) & cC50(iV16459) & cC88(iV16459) & cC34(iV16459) & cC68(iV16459) & cC38(iV16460) & cC42(iV16461) & cC56(iV16461) & cC44(iV16461) & cC38(iV16462) & cC76(iV16463) & cC62(iV16463) & cC60(iV16463) & cC56(iV16464) & cC42(iV16464) & cC44(iV16464) & cC38(iV16465))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[556, 548])).
% 0.20/0.52 tff(558,plain,
% 0.20/0.52 ((~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC106(iV16439)) | (~cC28(iV16439)) | (~cC98(iV16440)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC38(iV16448)) | (~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC50(iV16459)) | (~cC88(iV16459)) | (~cC34(iV16459)) | (~cC68(iV16459)) | (~cC38(iV16460)) | (~cC42(iV16461)) | (~cC56(iV16461)) | (~cC44(iV16461)) | (~cC38(iV16462)) | (~cC76(iV16463)) | (~cC62(iV16463)) | (~cC60(iV16463)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC44(iV16464)) | (~cC38(iV16465))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[557, 547])).
% 0.20/0.52 tff(559,plain,
% 0.20/0.52 ((~cC76(iV16453)) | (~cC62(iV16453)) | (~cC60(iV16453)) | (~cC56(iV16455)) | (~cC44(iV16455)) | (~cC42(iV16455))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[558, 463, 543, 541, 519, 539, 523, 485, 468, 472, 414, 391, 368, 345, 322, 299, 285, 275, 279, 254, 229, 233, 237, 183, 193, 187, 159])).
% 0.20/0.52 tff(560,plain,
% 0.20/0.52 (~cC76(iV16453)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[559, 55, 34, 142, 116, 95])).
% 0.20/0.52 tff(561,plain,
% 0.20/0.52 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(562,plain,
% 0.20/0.53 ((cC76(iV16453) <=> (~((~cC74xcomp(iV16453)) | (~cC62(iV16453))))) <=> (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(563,plain,
% 0.20/0.53 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC74xcomp(iV16453)) | (~cC62(iV16453)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[562])).
% 0.20/0.53 tff(564,plain,
% 0.20/0.53 (((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC74xcomp(iV16453)) | (~cC62(iV16453)))))) <=> ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[563, 561])).
% 0.20/0.53 tff(565,plain,
% 0.20/0.53 ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC74xcomp(iV16453)) | (~cC62(iV16453)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(566,plain,
% 0.20/0.53 ((~![X: $i] : (cC76(X) <=> (~((~cC74xcomp(X)) | (~cC62(X)))))) | (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.20/0.53 tff(567,plain,
% 0.20/0.53 (cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[566, 205])).
% 0.20/0.53 tff(568,plain,
% 0.20/0.53 ((~(cC76(iV16453) <=> (~((~cC62(iV16453)) | (~cC74xcomp(iV16453)))))) | cC76(iV16453) | ((~cC62(iV16453)) | (~cC74xcomp(iV16453)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(569,plain,
% 0.20/0.53 (cC76(iV16453) | ((~cC62(iV16453)) | (~cC74xcomp(iV16453)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[568, 567])).
% 0.20/0.53 tff(570,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[569, 560, 61])).
% 0.20/0.53 % SZS output end Proof
%------------------------------------------------------------------------------