TSTP Solution File: KRS153+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS153+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 17:44:59 EDT 2022
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS153+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 09:43:10 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(cC62_type, type, (
% 0.21/0.48 cC62: $i > $o)).
% 0.21/0.48 tff(iV16453_type, type, (
% 0.21/0.48 iV16453: $i)).
% 0.21/0.48 tff(cC74_type, type, (
% 0.21/0.48 cC74: $i > $o)).
% 0.21/0.48 tff(cC60_type, type, (
% 0.21/0.48 cC60: $i > $o)).
% 0.21/0.48 tff(cC58_type, type, (
% 0.21/0.48 cC58: $i > $o)).
% 0.21/0.48 tff(rR1_type, type, (
% 0.21/0.48 rR1: ( $i * $i ) > $o)).
% 0.21/0.48 tff(cC12_type, type, (
% 0.21/0.48 cC12: $i > $o)).
% 0.21/0.48 tff(tptp_fun_Y_18_type, type, (
% 0.21/0.48 tptp_fun_Y_18: $i > $i)).
% 0.21/0.48 tff(iV16461_type, type, (
% 0.21/0.48 iV16461: $i)).
% 0.21/0.48 tff(cC76_type, type, (
% 0.21/0.48 cC76: $i > $o)).
% 0.21/0.48 tff(cC42_type, type, (
% 0.21/0.48 cC42: $i > $o)).
% 0.21/0.48 tff(iV16455_type, type, (
% 0.21/0.48 iV16455: $i)).
% 0.21/0.48 tff(cC8_type, type, (
% 0.21/0.48 cC8: $i > $o)).
% 0.21/0.48 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.48 tptp_fun_Y_14: $i > $i)).
% 0.21/0.48 tff(iV16460_type, type, (
% 0.21/0.48 iV16460: $i)).
% 0.21/0.48 tff(cC56_type, type, (
% 0.21/0.48 cC56: $i > $o)).
% 0.21/0.48 tff(cC44_type, type, (
% 0.21/0.48 cC44: $i > $o)).
% 0.21/0.48 tff(cC54_type, type, (
% 0.21/0.48 cC54: $i > $o)).
% 0.21/0.48 tff(cC40_type, type, (
% 0.21/0.48 cC40: $i > $o)).
% 0.21/0.48 tff(cC38_type, type, (
% 0.21/0.48 cC38: $i > $o)).
% 0.21/0.48 tff(iV16465_type, type, (
% 0.21/0.48 iV16465: $i)).
% 0.21/0.48 tff(iV16464_type, type, (
% 0.21/0.48 iV16464: $i)).
% 0.21/0.48 tff(iV16463_type, type, (
% 0.21/0.48 iV16463: $i)).
% 0.21/0.48 tff(iV16440_type, type, (
% 0.21/0.48 iV16440: $i)).
% 0.21/0.48 tff(iV16462_type, type, (
% 0.21/0.48 iV16462: $i)).
% 0.21/0.48 tff(cC34_type, type, (
% 0.21/0.48 cC34: $i > $o)).
% 0.21/0.48 tff(iV16459_type, type, (
% 0.21/0.48 iV16459: $i)).
% 0.21/0.48 tff(cC32_type, type, (
% 0.21/0.48 cC32: $i > $o)).
% 0.21/0.48 tff(cC30_type, type, (
% 0.21/0.48 cC30: $i > $o)).
% 0.21/0.48 tff(cC50_type, type, (
% 0.21/0.48 cC50: $i > $o)).
% 0.21/0.48 tff(cC48_type, type, (
% 0.21/0.48 cC48: $i > $o)).
% 0.21/0.48 tff(cC46_type, type, (
% 0.21/0.48 cC46: $i > $o)).
% 0.21/0.48 tff(cC88_type, type, (
% 0.21/0.48 cC88: $i > $o)).
% 0.21/0.48 tff(cC86_type, type, (
% 0.21/0.48 cC86: $i > $o)).
% 0.21/0.48 tff(cC84_type, type, (
% 0.21/0.48 cC84: $i > $o)).
% 0.21/0.48 tff(cC68_type, type, (
% 0.21/0.48 cC68: $i > $o)).
% 0.21/0.48 tff(cC66_type, type, (
% 0.21/0.48 cC66: $i > $o)).
% 0.21/0.48 tff(cC64_type, type, (
% 0.21/0.48 cC64: $i > $o)).
% 0.21/0.48 tff(iV16457_type, type, (
% 0.21/0.48 iV16457: $i)).
% 0.21/0.48 tff(cTOP_type, type, (
% 0.21/0.48 cTOP: $i > $o)).
% 0.21/0.48 tff(cC36_type, type, (
% 0.21/0.48 cC36: $i > $o)).
% 0.21/0.48 tff(cC104_type, type, (
% 0.21/0.48 cC104: $i > $o)).
% 0.21/0.48 tff(iV16439_type, type, (
% 0.21/0.48 iV16439: $i)).
% 0.21/0.48 tff(cC100_type, type, (
% 0.21/0.48 cC100: $i > $o)).
% 0.21/0.48 tff(cC106_type, type, (
% 0.21/0.48 cC106: $i > $o)).
% 0.21/0.48 tff(cC28_type, type, (
% 0.21/0.48 cC28: $i > $o)).
% 0.21/0.48 tff(cC108_type, type, (
% 0.21/0.48 cC108: $i > $o)).
% 0.21/0.48 tff(cC130_type, type, (
% 0.21/0.48 cC130: $i > $o)).
% 0.21/0.48 tff(cTEST_type, type, (
% 0.21/0.48 cTEST: $i > $o)).
% 0.21/0.48 tff(iV16448_type, type, (
% 0.21/0.48 iV16448: $i)).
% 0.21/0.48 tff(cC98_type, type, (
% 0.21/0.48 cC98: $i > $o)).
% 0.21/0.48 tff(cC82_type, type, (
% 0.21/0.48 cC82: $i > $o)).
% 0.21/0.48 tff(cC96_type, type, (
% 0.21/0.48 cC96: $i > $o)).
% 0.21/0.48 tff(cC80_type, type, (
% 0.21/0.48 cC80: $i > $o)).
% 0.21/0.48 tff(cC78_type, type, (
% 0.21/0.48 cC78: $i > $o)).
% 0.21/0.48 tff(cowlThing_type, type, (
% 0.21/0.48 cowlThing: $i > $o)).
% 0.21/0.48 tff(xsd_integer_type, type, (
% 0.21/0.48 xsd_integer: $i > $o)).
% 0.21/0.48 tff(xsd_string_type, type, (
% 0.21/0.48 xsd_string: $i > $o)).
% 0.21/0.48 tff(cowlNothing_type, type, (
% 0.21/0.48 cowlNothing: $i > $o)).
% 0.21/0.48 tff(1,assumption,((~((~cC60(iV16453)) | (~(cC12(tptp_fun_Y_18(iV16453)) | (~rR1(iV16453, tptp_fun_Y_18(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))))), introduced(assumption)).
% 0.21/0.48 tff(2,plain,
% 0.21/0.48 (^[X: $i] : refl((~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(3,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[2])).
% 0.21/0.48 tff(4,plain,
% 0.21/0.48 (^[X: $i] : rewrite((~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(5,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[4])).
% 0.21/0.48 tff(6,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[5, 3])).
% 0.21/0.48 tff(7,plain,
% 0.21/0.48 (^[X: $i] : trans(monotonicity(rewrite(((~cC60(X)) | (rR1(X, tptp_fun_Y_18(X)) & (~cC12(tptp_fun_Y_18(X))))) <=> ((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))), rewrite((cC60(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC12(Y))))) <=> (cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))), ((((~cC60(X)) | (rR1(X, tptp_fun_Y_18(X)) & (~cC12(tptp_fun_Y_18(X))))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC12(Y)))))) <=> (((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X)))))) & (cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))))), rewrite((((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X)))))) & (cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y))))) <=> (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))), ((((~cC60(X)) | (rR1(X, tptp_fun_Y_18(X)) & (~cC12(tptp_fun_Y_18(X))))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC12(Y)))))) <=> (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(8,plain,
% 0.21/0.48 (![X: $i] : (((~cC60(X)) | (rR1(X, tptp_fun_Y_18(X)) & (~cC12(tptp_fun_Y_18(X))))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC12(Y)))))) <=> ![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[7])).
% 0.21/0.48 tff(9,plain,
% 0.21/0.48 (![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC12(Y)))) <=> ![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC12(Y))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(10,axiom,(![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC12(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_39')).
% 0.21/0.48 tff(11,plain,
% 0.21/0.48 (![X: $i] : (cC60(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC12(Y))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.21/0.48 tff(12,plain,(
% 0.21/0.48 ![X: $i] : (((~cC60(X)) | (rR1(X, tptp_fun_Y_18(X)) & (~cC12(tptp_fun_Y_18(X))))) & (cC60(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC12(Y))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[11])).
% 0.21/0.48 tff(13,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.21/0.48 tff(14,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.21/0.48 tff(15,plain,
% 0.21/0.48 ((~![X: $i] : (~((~((~cC60(X)) | (~(cC12(tptp_fun_Y_18(X)) | (~rR1(X, tptp_fun_Y_18(X))))))) | (~(cC60(X) | ![Y: $i] : (cC12(Y) | (~rR1(X, Y)))))))) | (~((~((~cC60(iV16453)) | (~(cC12(tptp_fun_Y_18(iV16453)) | (~rR1(iV16453, tptp_fun_Y_18(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(16,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[15, 14, 1])).
% 0.21/0.48 tff(17,plain,(~((~((~cC60(iV16453)) | (~(cC12(tptp_fun_Y_18(iV16453)) | (~rR1(iV16453, tptp_fun_Y_18(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(18,plain,
% 0.21/0.48 (((~((~cC60(iV16453)) | (~(cC12(tptp_fun_Y_18(iV16453)) | (~rR1(iV16453, tptp_fun_Y_18(iV16453))))))) | (~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))))) | (cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(19,plain,
% 0.21/0.48 (cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[18, 17])).
% 0.21/0.48 tff(20,assumption,(![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))), introduced(assumption)).
% 0.21/0.48 tff(21,plain,
% 0.21/0.48 ((~cC12(iV16461)) <=> (~cC12(iV16461))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(22,axiom,(~cC12(iV16461)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_151')).
% 0.21/0.48 tff(23,plain,
% 0.21/0.48 (~cC12(iV16461)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 (rR1(iV16453, iV16461) <=> rR1(iV16453, iV16461)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(25,axiom,(rR1(iV16453, iV16461)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_96')).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 (rR1(iV16453, iV16461)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 (((~![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))) | (cC12(iV16461) | (~rR1(iV16453, iV16461)))) <=> ((~![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))) | cC12(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(28,plain,
% 0.21/0.48 ((~![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))) | (cC12(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 ((~![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))) | cC12(iV16461) | (~rR1(iV16453, iV16461))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[29, 26, 23, 20])).
% 0.21/0.48 tff(31,plain,(~![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 ((~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y))))) | cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 ((~(cC60(iV16453) | ![Y: $i] : (cC12(Y) | (~rR1(iV16453, Y))))) | cC60(iV16453)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[32, 31])).
% 0.21/0.48 tff(34,plain,
% 0.21/0.48 (cC60(iV16453)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[33, 19])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 ((~cC58(iV16453)) <=> (~cC58(iV16453))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(36,axiom,(~cC58(iV16453)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_91')).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 (~cC58(iV16453)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 ((~(cC58(iV16453) | (~cC60(iV16453)))) | cC58(iV16453) | (~cC60(iV16453))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 ((~(cC58(iV16453) | (~cC60(iV16453)))) | (~cC60(iV16453))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 (~(cC58(iV16453) | (~cC60(iV16453)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[39, 34])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 (^[X: $i] : refl((cC62(X) <=> (~(cC58(X) | (~cC60(X))))) <=> (cC62(X) <=> (~(cC58(X) | (~cC60(X))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X))))) <=> ![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[41])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (^[X: $i] : rewrite((cC62(X) <=> (cC60(X) & (~cC58(X)))) <=> (cC62(X) <=> (~(cC58(X) | (~cC60(X))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X)))) <=> ![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X)))) <=> ![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(46,axiom,(![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_40')).
% 0.21/0.48 tff(47,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.48 tff(48,plain,(
% 0.21/0.48 ![X: $i] : (cC62(X) <=> (cC60(X) & (~cC58(X))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[47])).
% 0.21/0.48 tff(49,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.48 tff(50,plain,
% 0.21/0.48 (![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.48 tff(51,plain,
% 0.21/0.48 ((~![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))) | (cC62(iV16453) <=> (~(cC58(iV16453) | (~cC60(iV16453)))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(52,plain,
% 0.21/0.48 (cC62(iV16453) <=> (~(cC58(iV16453) | (~cC60(iV16453))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.21/0.48 tff(53,plain,
% 0.21/0.48 ((~(cC62(iV16453) <=> (~(cC58(iV16453) | (~cC60(iV16453)))))) | cC62(iV16453) | (cC58(iV16453) | (~cC60(iV16453)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(54,plain,
% 0.21/0.48 (cC62(iV16453) | (cC58(iV16453) | (~cC60(iV16453)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.48 tff(55,plain,
% 0.21/0.48 (cC62(iV16453)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.21/0.48 tff(56,plain,
% 0.21/0.48 ((~cC74(iV16453)) <=> (~cC74(iV16453))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(57,axiom,(~cC74(iV16453)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_92')).
% 0.21/0.48 tff(58,plain,
% 0.21/0.48 (~cC74(iV16453)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.48 tff(59,plain,
% 0.21/0.48 ((~(cC74(iV16453) | (~cC62(iV16453)))) | cC74(iV16453) | (~cC62(iV16453))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(60,plain,
% 0.21/0.48 ((~(cC74(iV16453) | (~cC62(iV16453)))) | (~cC62(iV16453))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.21/0.48 tff(61,plain,
% 0.21/0.48 (~(cC74(iV16453) | (~cC62(iV16453)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[60, 55])).
% 0.21/0.48 tff(62,assumption,((~((~cC42(iV16455)) | (~(cC8(tptp_fun_Y_14(iV16455)) | (~rR1(iV16455, tptp_fun_Y_14(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))))), introduced(assumption)).
% 0.21/0.48 tff(63,plain,
% 0.21/0.48 (^[X: $i] : refl((~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(64,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.48 tff(65,plain,
% 0.21/0.48 (^[X: $i] : rewrite((~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))) <=> (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(66,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[65])).
% 0.21/0.48 tff(67,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.21/0.48 tff(68,plain,
% 0.21/0.48 (^[X: $i] : trans(monotonicity(rewrite(((~cC42(X)) | (rR1(X, tptp_fun_Y_14(X)) & (~cC8(tptp_fun_Y_14(X))))) <=> ((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))), rewrite((cC42(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC8(Y))))) <=> (cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))), ((((~cC42(X)) | (rR1(X, tptp_fun_Y_14(X)) & (~cC8(tptp_fun_Y_14(X))))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC8(Y)))))) <=> (((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X)))))) & (cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))))), rewrite((((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X)))))) & (cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y))))) <=> (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))), ((((~cC42(X)) | (rR1(X, tptp_fun_Y_14(X)) & (~cC8(tptp_fun_Y_14(X))))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC8(Y)))))) <=> (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(69,plain,
% 0.21/0.48 (![X: $i] : (((~cC42(X)) | (rR1(X, tptp_fun_Y_14(X)) & (~cC8(tptp_fun_Y_14(X))))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC8(Y)))))) <=> ![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.48 tff(70,plain,
% 0.21/0.48 (![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC8(Y)))) <=> ![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC8(Y))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(71,axiom,(![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC8(Y))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_29')).
% 0.21/0.48 tff(72,plain,
% 0.21/0.48 (![X: $i] : (cC42(X) <=> ?[Y: $i] : (rR1(X, Y) & (~cC8(Y))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.48 tff(73,plain,(
% 0.21/0.48 ![X: $i] : (((~cC42(X)) | (rR1(X, tptp_fun_Y_14(X)) & (~cC8(tptp_fun_Y_14(X))))) & (cC42(X) | ![Y: $i] : (~(rR1(X, Y) & (~cC8(Y))))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[72])).
% 0.21/0.48 tff(74,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.21/0.48 tff(75,plain,
% 0.21/0.48 (![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[74, 67])).
% 0.21/0.48 tff(76,plain,
% 0.21/0.48 ((~![X: $i] : (~((~((~cC42(X)) | (~(cC8(tptp_fun_Y_14(X)) | (~rR1(X, tptp_fun_Y_14(X))))))) | (~(cC42(X) | ![Y: $i] : (cC8(Y) | (~rR1(X, Y)))))))) | (~((~((~cC42(iV16455)) | (~(cC8(tptp_fun_Y_14(iV16455)) | (~rR1(iV16455, tptp_fun_Y_14(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(77,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[76, 75, 62])).
% 0.21/0.48 tff(78,plain,(~((~((~cC42(iV16455)) | (~(cC8(tptp_fun_Y_14(iV16455)) | (~rR1(iV16455, tptp_fun_Y_14(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(79,plain,
% 0.21/0.48 (((~((~cC42(iV16455)) | (~(cC8(tptp_fun_Y_14(iV16455)) | (~rR1(iV16455, tptp_fun_Y_14(iV16455))))))) | (~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))))) | (cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(80,plain,
% 0.21/0.48 (cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[79, 78])).
% 0.21/0.48 tff(81,assumption,(![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))), introduced(assumption)).
% 0.21/0.48 tff(82,plain,
% 0.21/0.48 ((~cC8(iV16460)) <=> (~cC8(iV16460))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(83,axiom,(~cC8(iV16460)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_141')).
% 0.21/0.48 tff(84,plain,
% 0.21/0.48 (~cC8(iV16460)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.21/0.48 tff(85,plain,
% 0.21/0.48 (rR1(iV16455, iV16460) <=> rR1(iV16455, iV16460)),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(86,axiom,(rR1(iV16455, iV16460)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_107')).
% 0.21/0.48 tff(87,plain,
% 0.21/0.48 (rR1(iV16455, iV16460)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.21/0.48 tff(88,plain,
% 0.21/0.48 (((~![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))) | (cC8(iV16460) | (~rR1(iV16455, iV16460)))) <=> ((~![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))) | cC8(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(89,plain,
% 0.21/0.49 ((~![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))) | (cC8(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(90,plain,
% 0.21/0.49 ((~![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))) | cC8(iV16460) | (~rR1(iV16455, iV16460))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.49 tff(91,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[90, 87, 84, 81])).
% 0.21/0.49 tff(92,plain,(~![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.49 tff(93,plain,
% 0.21/0.49 ((~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y))))) | cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(94,plain,
% 0.21/0.49 ((~(cC42(iV16455) | ![Y: $i] : (cC8(Y) | (~rR1(iV16455, Y))))) | cC42(iV16455)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[93, 92])).
% 0.21/0.49 tff(95,plain,
% 0.21/0.49 (cC42(iV16455)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[94, 80])).
% 0.21/0.49 tff(96,plain,
% 0.21/0.49 ((~cC40(iV16455)) <=> (~cC40(iV16455))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(97,axiom,(~cC40(iV16455)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_98')).
% 0.21/0.49 tff(98,plain,
% 0.21/0.49 (~cC40(iV16455)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.21/0.49 tff(99,plain,
% 0.21/0.49 ((~(cC40(iV16455) | (~cC42(iV16455)))) | cC40(iV16455) | (~cC42(iV16455))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(100,plain,
% 0.21/0.49 ((~(cC40(iV16455) | (~cC42(iV16455)))) | (~cC42(iV16455))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.49 tff(101,plain,
% 0.21/0.49 (~(cC40(iV16455) | (~cC42(iV16455)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[100, 95])).
% 0.21/0.49 tff(102,plain,
% 0.21/0.49 (^[X: $i] : refl((cC44(X) <=> (~(cC40(X) | (~cC42(X))))) <=> (cC44(X) <=> (~(cC40(X) | (~cC42(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(103,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X))))) <=> ![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[102])).
% 0.21/0.49 tff(104,plain,
% 0.21/0.49 (^[X: $i] : rewrite((cC44(X) <=> ((~cC40(X)) & cC42(X))) <=> (cC44(X) <=> (~(cC40(X) | (~cC42(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(105,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X))) <=> ![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.21/0.49 tff(106,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X))) <=> ![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(107,axiom,(![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_30')).
% 0.21/0.49 tff(108,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.49 tff(109,plain,(
% 0.21/0.49 ![X: $i] : (cC44(X) <=> ((~cC40(X)) & cC42(X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[108])).
% 0.21/0.49 tff(110,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.21/0.49 tff(111,plain,
% 0.21/0.49 (![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.21/0.49 tff(112,plain,
% 0.21/0.49 ((~![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))) | (cC44(iV16455) <=> (~(cC40(iV16455) | (~cC42(iV16455)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(113,plain,
% 0.21/0.49 (cC44(iV16455) <=> (~(cC40(iV16455) | (~cC42(iV16455))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[112, 111])).
% 0.21/0.49 tff(114,plain,
% 0.21/0.49 ((~(cC44(iV16455) <=> (~(cC40(iV16455) | (~cC42(iV16455)))))) | cC44(iV16455) | (cC40(iV16455) | (~cC42(iV16455)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(115,plain,
% 0.21/0.49 (cC44(iV16455) | (cC40(iV16455) | (~cC42(iV16455)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.21/0.49 tff(116,plain,
% 0.21/0.49 (cC44(iV16455)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[115, 101])).
% 0.21/0.49 tff(117,plain,
% 0.21/0.49 ((~cC54(iV16455)) <=> (~cC54(iV16455))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(118,axiom,(~cC54(iV16455)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_103')).
% 0.21/0.49 tff(119,plain,
% 0.21/0.49 (~cC54(iV16455)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.21/0.49 tff(120,plain,
% 0.21/0.49 ((~(cC54(iV16455) | (~cC44(iV16455)))) | cC54(iV16455) | (~cC44(iV16455))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(121,plain,
% 0.21/0.49 ((~(cC54(iV16455) | (~cC44(iV16455)))) | (~cC44(iV16455))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[120, 119])).
% 0.21/0.49 tff(122,plain,
% 0.21/0.49 (~(cC54(iV16455) | (~cC44(iV16455)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[121, 116])).
% 0.21/0.49 tff(123,plain,
% 0.21/0.49 (^[X: $i] : refl((cC56(X) <=> (~(cC54(X) | (~cC44(X))))) <=> (cC56(X) <=> (~(cC54(X) | (~cC44(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(124,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X))))) <=> ![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[123])).
% 0.21/0.49 tff(125,plain,
% 0.21/0.49 (^[X: $i] : rewrite((cC56(X) <=> (cC44(X) & (~cC54(X)))) <=> (cC56(X) <=> (~(cC54(X) | (~cC44(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(126,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X)))) <=> ![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.49 tff(127,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X)))) <=> ![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(128,axiom,(![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_36')).
% 0.21/0.49 tff(129,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.21/0.49 tff(130,plain,(
% 0.21/0.49 ![X: $i] : (cC56(X) <=> (cC44(X) & (~cC54(X))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[129])).
% 0.21/0.49 tff(131,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[130, 126])).
% 0.21/0.49 tff(132,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.21/0.49 tff(133,plain,
% 0.21/0.49 ((~![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))) | (cC56(iV16455) <=> (~(cC54(iV16455) | (~cC44(iV16455)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(134,plain,
% 0.21/0.49 (cC56(iV16455) <=> (~(cC54(iV16455) | (~cC44(iV16455))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.21/0.49 tff(135,plain,
% 0.21/0.49 ((~(cC56(iV16455) <=> (~(cC54(iV16455) | (~cC44(iV16455)))))) | cC56(iV16455) | (cC54(iV16455) | (~cC44(iV16455)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(136,plain,
% 0.21/0.49 (cC56(iV16455) | (cC54(iV16455) | (~cC44(iV16455)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.21/0.49 tff(137,plain,
% 0.21/0.49 (cC56(iV16455)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[136, 122])).
% 0.21/0.49 tff(138,plain,
% 0.21/0.49 (rR1(iV16464, iV16465) <=> rR1(iV16464, iV16465)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(139,axiom,(rR1(iV16464, iV16465)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_188')).
% 0.21/0.49 tff(140,plain,
% 0.21/0.49 (rR1(iV16464, iV16465)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.49 tff(141,plain,
% 0.21/0.49 (^[X: $i] : refl((cC38(X) | (~rR1(iV16464, X))) <=> (cC38(X) | (~rR1(iV16464, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(142,plain,
% 0.21/0.49 (![X: $i] : (cC38(X) | (~rR1(iV16464, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[141])).
% 0.21/0.49 tff(143,plain,
% 0.21/0.49 (![X: $i] : (cC38(X) | (~rR1(iV16464, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(144,plain,
% 0.21/0.49 (^[X: $i] : rewrite((rR1(iV16464, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16464, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(145,plain,
% 0.21/0.49 (![X: $i] : (rR1(iV16464, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[144])).
% 0.21/0.49 tff(146,axiom,(![X: $i] : (rR1(iV16464, X) => cC38(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_182')).
% 0.21/0.49 tff(147,plain,
% 0.21/0.49 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.49 tff(148,plain,
% 0.21/0.49 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.21/0.49 tff(149,plain,(
% 0.21/0.49 ![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[148])).
% 0.21/0.49 tff(150,plain,
% 0.21/0.49 (![X: $i] : (cC38(X) | (~rR1(iV16464, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.21/0.49 tff(151,plain,
% 0.21/0.49 (((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | (cC38(iV16465) | (~rR1(iV16464, iV16465)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | cC38(iV16465) | (~rR1(iV16464, iV16465)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(152,plain,
% 0.21/0.49 ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | (cC38(iV16465) | (~rR1(iV16464, iV16465)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(153,plain,
% 0.21/0.49 ((~![X: $i] : (cC38(X) | (~rR1(iV16464, X)))) | cC38(iV16465) | (~rR1(iV16464, iV16465))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.21/0.49 tff(154,plain,
% 0.21/0.49 (cC38(iV16465)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[153, 150, 140])).
% 0.21/0.49 tff(155,plain,
% 0.21/0.49 ((~![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))) | (cC44(iV16464) <=> (~(cC40(iV16464) | (~cC42(iV16464)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(156,plain,
% 0.21/0.49 (cC44(iV16464) <=> (~(cC40(iV16464) | (~cC42(iV16464))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[155, 111])).
% 0.21/0.49 tff(157,plain,
% 0.21/0.49 ((~![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))) | (cC56(iV16464) <=> (~(cC54(iV16464) | (~cC44(iV16464)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(158,plain,
% 0.21/0.49 (cC56(iV16464) <=> (~(cC54(iV16464) | (~cC44(iV16464))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[157, 132])).
% 0.21/0.49 tff(159,plain,
% 0.21/0.49 (rR1(iV16463, iV16464) <=> rR1(iV16463, iV16464)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(160,axiom,(rR1(iV16463, iV16464)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_177')).
% 0.21/0.49 tff(161,plain,
% 0.21/0.49 (rR1(iV16463, iV16464)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.21/0.49 tff(162,plain,
% 0.21/0.49 (^[X: $i] : refl((cC56(X) | (~rR1(iV16463, X))) <=> (cC56(X) | (~rR1(iV16463, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(163,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) | (~rR1(iV16463, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[162])).
% 0.21/0.49 tff(164,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) | (~rR1(iV16463, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(165,plain,
% 0.21/0.49 (^[X: $i] : rewrite((rR1(iV16463, X) => cC56(X)) <=> (cC56(X) | (~rR1(iV16463, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(166,plain,
% 0.21/0.49 (![X: $i] : (rR1(iV16463, X) => cC56(X)) <=> ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[165])).
% 0.21/0.49 tff(167,axiom,(![X: $i] : (rR1(iV16463, X) => cC56(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_171')).
% 0.21/0.49 tff(168,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.49 tff(169,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[168, 164])).
% 0.21/0.49 tff(170,plain,(
% 0.21/0.49 ![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[169])).
% 0.21/0.49 tff(171,plain,
% 0.21/0.49 (![X: $i] : (cC56(X) | (~rR1(iV16463, X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.21/0.49 tff(172,plain,
% 0.21/0.49 (((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | (cC56(iV16464) | (~rR1(iV16463, iV16464)))) <=> ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | cC56(iV16464) | (~rR1(iV16463, iV16464)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(173,plain,
% 0.21/0.49 ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | (cC56(iV16464) | (~rR1(iV16463, iV16464)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(174,plain,
% 0.21/0.49 ((~![X: $i] : (cC56(X) | (~rR1(iV16463, X)))) | cC56(iV16464) | (~rR1(iV16463, iV16464))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.21/0.49 tff(175,plain,
% 0.21/0.49 (cC56(iV16464)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[174, 171, 161])).
% 0.21/0.49 tff(176,plain,
% 0.21/0.49 ((~(cC56(iV16464) <=> (~(cC54(iV16464) | (~cC44(iV16464)))))) | (~cC56(iV16464)) | (~(cC54(iV16464) | (~cC44(iV16464))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(177,plain,
% 0.21/0.49 (~(cC54(iV16464) | (~cC44(iV16464)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[176, 175, 158])).
% 0.21/0.49 tff(178,plain,
% 0.21/0.49 ((cC54(iV16464) | (~cC44(iV16464))) | cC44(iV16464)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(179,plain,
% 0.21/0.49 (cC44(iV16464)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.21/0.49 tff(180,plain,
% 0.21/0.49 ((~(cC44(iV16464) <=> (~(cC40(iV16464) | (~cC42(iV16464)))))) | (~cC44(iV16464)) | (~(cC40(iV16464) | (~cC42(iV16464))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(181,plain,
% 0.21/0.49 (~(cC40(iV16464) | (~cC42(iV16464)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[180, 179, 156])).
% 0.21/0.49 tff(182,plain,
% 0.21/0.49 ((cC40(iV16464) | (~cC42(iV16464))) | cC42(iV16464)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(183,plain,
% 0.21/0.49 (cC42(iV16464)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[182, 181])).
% 0.21/0.49 tff(184,plain,
% 0.21/0.49 ((~![X: $i] : (cC62(X) <=> (~(cC58(X) | (~cC60(X)))))) | (cC62(iV16463) <=> (~(cC58(iV16463) | (~cC60(iV16463)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(185,plain,
% 0.21/0.49 (cC62(iV16463) <=> (~(cC58(iV16463) | (~cC60(iV16463))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[184, 50])).
% 0.21/0.49 tff(186,plain,
% 0.21/0.49 (^[X: $i] : refl((cC76(X) <=> (~(cC74(X) | (~cC62(X))))) <=> (cC76(X) <=> (~(cC74(X) | (~cC62(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(187,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X))))) <=> ![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[186])).
% 0.21/0.49 tff(188,plain,
% 0.21/0.49 (^[X: $i] : rewrite((cC76(X) <=> ((~cC74(X)) & cC62(X))) <=> (cC76(X) <=> (~(cC74(X) | (~cC62(X))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(189,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X))) <=> ![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[188])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X))) <=> ![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(191,axiom,(![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_47')).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.21/0.49 tff(193,plain,(
% 0.21/0.49 ![X: $i] : (cC76(X) <=> ((~cC74(X)) & cC62(X)))),
% 0.21/0.49 inference(skolemize,[status(sab)],[192])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[194, 187])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 ((~![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))) | (cC76(iV16463) <=> (~(cC74(iV16463) | (~cC62(iV16463)))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (cC76(iV16463) <=> (~(cC74(iV16463) | (~cC62(iV16463))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (rR1(iV16440, iV16463) <=> rR1(iV16440, iV16463)),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(199,axiom,(rR1(iV16440, iV16463)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_73')).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 (rR1(iV16440, iV16463)),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 (^[X: $i] : refl((cC76(X) | (~rR1(iV16440, X))) <=> (cC76(X) | (~rR1(iV16440, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) | (~rR1(iV16440, X))) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[201])).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) | (~rR1(iV16440, X))) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (^[X: $i] : rewrite((rR1(iV16440, X) => cC76(X)) <=> (cC76(X) | (~rR1(iV16440, X))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (![X: $i] : (rR1(iV16440, X) => cC76(X)) <=> ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[204])).
% 0.21/0.49 tff(206,axiom,(![X: $i] : (rR1(iV16440, X) => cC76(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_67')).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.21/0.50 tff(208,plain,
% 0.21/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.21/0.50 tff(209,plain,(
% 0.21/0.50 ![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[208])).
% 0.21/0.50 tff(210,plain,
% 0.21/0.50 (![X: $i] : (cC76(X) | (~rR1(iV16440, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.21/0.50 tff(211,plain,
% 0.21/0.50 (((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | (cC76(iV16463) | (~rR1(iV16440, iV16463)))) <=> ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | cC76(iV16463) | (~rR1(iV16440, iV16463)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(212,plain,
% 0.21/0.50 ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | (cC76(iV16463) | (~rR1(iV16440, iV16463)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(213,plain,
% 0.21/0.50 ((~![X: $i] : (cC76(X) | (~rR1(iV16440, X)))) | cC76(iV16463) | (~rR1(iV16440, iV16463))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.21/0.50 tff(214,plain,
% 0.21/0.50 (cC76(iV16463)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[213, 210, 200])).
% 0.21/0.50 tff(215,plain,
% 0.21/0.50 ((~(cC76(iV16463) <=> (~(cC74(iV16463) | (~cC62(iV16463)))))) | (~cC76(iV16463)) | (~(cC74(iV16463) | (~cC62(iV16463))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(216,plain,
% 0.21/0.50 (~(cC74(iV16463) | (~cC62(iV16463)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[215, 214, 197])).
% 0.21/0.50 tff(217,plain,
% 0.21/0.50 ((cC74(iV16463) | (~cC62(iV16463))) | cC62(iV16463)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(218,plain,
% 0.21/0.50 (cC62(iV16463)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[217, 216])).
% 0.21/0.50 tff(219,plain,
% 0.21/0.50 ((~(cC62(iV16463) <=> (~(cC58(iV16463) | (~cC60(iV16463)))))) | (~cC62(iV16463)) | (~(cC58(iV16463) | (~cC60(iV16463))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(220,plain,
% 0.21/0.50 (~(cC58(iV16463) | (~cC60(iV16463)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[219, 218, 185])).
% 0.21/0.50 tff(221,plain,
% 0.21/0.50 ((cC58(iV16463) | (~cC60(iV16463))) | cC60(iV16463)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(222,plain,
% 0.21/0.50 (cC60(iV16463)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[221, 220])).
% 0.21/0.50 tff(223,plain,
% 0.21/0.50 (rR1(iV16461, iV16462) <=> rR1(iV16461, iV16462)),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(224,axiom,(rR1(iV16461, iV16462)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_157')).
% 0.21/0.50 tff(225,plain,
% 0.21/0.50 (rR1(iV16461, iV16462)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.21/0.50 tff(226,plain,
% 0.21/0.50 (^[X: $i] : refl((cC38(X) | (~rR1(iV16461, X))) <=> (cC38(X) | (~rR1(iV16461, X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(227,plain,
% 0.21/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[226])).
% 0.21/0.50 tff(228,plain,
% 0.21/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(229,plain,
% 0.21/0.50 (^[X: $i] : rewrite((rR1(iV16461, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16461, X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(230,plain,
% 0.21/0.50 (![X: $i] : (rR1(iV16461, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[229])).
% 0.21/0.50 tff(231,axiom,(![X: $i] : (rR1(iV16461, X) => cC38(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_154')).
% 0.21/0.50 tff(232,plain,
% 0.21/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.21/0.50 tff(233,plain,
% 0.21/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[232, 228])).
% 0.21/0.50 tff(234,plain,(
% 0.21/0.50 ![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[233])).
% 0.21/0.50 tff(235,plain,
% 0.21/0.50 (![X: $i] : (cC38(X) | (~rR1(iV16461, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[234, 227])).
% 0.21/0.50 tff(236,plain,
% 0.21/0.50 (((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | (cC38(iV16462) | (~rR1(iV16461, iV16462)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | cC38(iV16462) | (~rR1(iV16461, iV16462)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | (cC38(iV16462) | (~rR1(iV16461, iV16462)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 ((~![X: $i] : (cC38(X) | (~rR1(iV16461, X)))) | cC38(iV16462) | (~rR1(iV16461, iV16462))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.21/0.50 tff(239,plain,
% 0.21/0.50 (cC38(iV16462)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[238, 235, 225])).
% 0.21/0.50 tff(240,plain,
% 0.21/0.50 ((~![X: $i] : (cC44(X) <=> (~(cC40(X) | (~cC42(X)))))) | (cC44(iV16461) <=> (~(cC40(iV16461) | (~cC42(iV16461)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 (cC44(iV16461) <=> (~(cC40(iV16461) | (~cC42(iV16461))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[240, 111])).
% 0.21/0.50 tff(242,plain,
% 0.21/0.50 ((~![X: $i] : (cC56(X) <=> (~(cC54(X) | (~cC44(X)))))) | (cC56(iV16461) <=> (~(cC54(iV16461) | (~cC44(iV16461)))))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 (cC56(iV16461) <=> (~(cC54(iV16461) | (~cC44(iV16461))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[242, 132])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (^[X: $i] : refl((cC56(X) | (~rR1(iV16453, X))) <=> (cC56(X) | (~rR1(iV16453, X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[244])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X))) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(247,plain,
% 0.21/0.50 (^[X: $i] : rewrite((rR1(iV16453, X) => cC56(X)) <=> (cC56(X) | (~rR1(iV16453, X))))),
% 0.21/0.50 inference(bind,[status(th)],[])).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (![X: $i] : (rR1(iV16453, X) => cC56(X)) <=> ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(quant_intro,[status(thm)],[247])).
% 0.21/0.50 tff(249,axiom,(![X: $i] : (rR1(iV16453, X) => cC56(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_93')).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[249, 248])).
% 0.21/0.50 tff(251,plain,
% 0.21/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[250, 246])).
% 0.21/0.50 tff(252,plain,(
% 0.21/0.50 ![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(skolemize,[status(sab)],[251])).
% 0.21/0.50 tff(253,plain,
% 0.21/0.50 (![X: $i] : (cC56(X) | (~rR1(iV16453, X)))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[252, 245])).
% 0.21/0.50 tff(254,plain,
% 0.21/0.50 (((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | (cC56(iV16461) | (~rR1(iV16453, iV16461)))) <=> ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | cC56(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(255,plain,
% 0.21/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | (cC56(iV16461) | (~rR1(iV16453, iV16461)))),
% 0.21/0.50 inference(quant_inst,[status(thm)],[])).
% 0.21/0.50 tff(256,plain,
% 0.21/0.50 ((~![X: $i] : (cC56(X) | (~rR1(iV16453, X)))) | cC56(iV16461) | (~rR1(iV16453, iV16461))),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.21/0.50 tff(257,plain,
% 0.21/0.50 (cC56(iV16461)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[256, 253, 26])).
% 0.21/0.50 tff(258,plain,
% 0.21/0.50 ((~(cC56(iV16461) <=> (~(cC54(iV16461) | (~cC44(iV16461)))))) | (~cC56(iV16461)) | (~(cC54(iV16461) | (~cC44(iV16461))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(259,plain,
% 0.21/0.50 (~(cC54(iV16461) | (~cC44(iV16461)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[258, 257, 243])).
% 0.21/0.50 tff(260,plain,
% 0.21/0.50 ((cC54(iV16461) | (~cC44(iV16461))) | cC44(iV16461)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(261,plain,
% 0.21/0.50 (cC44(iV16461)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[260, 259])).
% 0.21/0.50 tff(262,plain,
% 0.21/0.50 ((~(cC44(iV16461) <=> (~(cC40(iV16461) | (~cC42(iV16461)))))) | (~cC44(iV16461)) | (~(cC40(iV16461) | (~cC42(iV16461))))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(263,plain,
% 0.21/0.50 (~(cC40(iV16461) | (~cC42(iV16461)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[262, 261, 241])).
% 0.21/0.50 tff(264,plain,
% 0.21/0.50 ((cC40(iV16461) | (~cC42(iV16461))) | cC42(iV16461)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(265,plain,
% 0.21/0.50 (cC42(iV16461)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.21/0.50 tff(266,plain,
% 0.21/0.50 (^[X: $i] : refl((cC38(X) | (~rR1(iV16455, X))) <=> (cC38(X) | (~rR1(iV16455, X))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(267,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) | (~rR1(iV16455, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[266])).
% 0.21/0.51 tff(268,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) | (~rR1(iV16455, X))) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(269,plain,
% 0.21/0.51 (^[X: $i] : rewrite((rR1(iV16455, X) => cC38(X)) <=> (cC38(X) | (~rR1(iV16455, X))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(270,plain,
% 0.21/0.51 (![X: $i] : (rR1(iV16455, X) => cC38(X)) <=> ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[269])).
% 0.21/0.51 tff(271,axiom,(![X: $i] : (rR1(iV16455, X) => cC38(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_106')).
% 0.21/0.51 tff(272,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.21/0.51 tff(273,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[272, 268])).
% 0.21/0.51 tff(274,plain,(
% 0.21/0.51 ![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[273])).
% 0.21/0.51 tff(275,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) | (~rR1(iV16455, X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[274, 267])).
% 0.21/0.51 tff(276,plain,
% 0.21/0.51 (((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | (cC38(iV16460) | (~rR1(iV16455, iV16460)))) <=> ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | cC38(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(277,plain,
% 0.21/0.51 ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | (cC38(iV16460) | (~rR1(iV16455, iV16460)))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(278,plain,
% 0.21/0.51 ((~![X: $i] : (cC38(X) | (~rR1(iV16455, X)))) | cC38(iV16460) | (~rR1(iV16455, iV16460))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.21/0.51 tff(279,plain,
% 0.21/0.51 (cC38(iV16460)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[278, 275, 87])).
% 0.21/0.51 tff(280,plain,
% 0.21/0.51 (^[X: $i] : refl((cC34(X) <=> (~(cC30(X) | cC32(X)))) <=> (cC34(X) <=> (~(cC30(X) | cC32(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(281,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X)))) <=> ![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[280])).
% 0.21/0.51 tff(282,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC34(X) <=> ((~cC32(X)) & (~cC30(X)))) <=> (cC34(X) <=> (~(cC30(X) | cC32(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(283,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X)))) <=> ![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[282])).
% 0.21/0.51 tff(284,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X)))) <=> ![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(285,axiom,(![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_25')).
% 0.21/0.51 tff(286,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.21/0.51 tff(287,plain,(
% 0.21/0.51 ![X: $i] : (cC34(X) <=> ((~cC32(X)) & (~cC30(X))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[286])).
% 0.21/0.51 tff(288,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[287, 283])).
% 0.21/0.51 tff(289,plain,
% 0.21/0.51 (![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.21/0.51 tff(290,plain,
% 0.21/0.51 ((~![X: $i] : (cC34(X) <=> (~(cC30(X) | cC32(X))))) | (cC34(iV16459) <=> (~(cC30(iV16459) | cC32(iV16459))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(291,plain,
% 0.21/0.51 (cC34(iV16459) <=> (~(cC30(iV16459) | cC32(iV16459)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.21/0.51 tff(292,plain,
% 0.21/0.51 ((~cC32(iV16459)) <=> (~cC32(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(293,axiom,(~cC32(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_135')).
% 0.21/0.51 tff(294,plain,
% 0.21/0.51 (~cC32(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[293, 292])).
% 0.21/0.51 tff(295,plain,
% 0.21/0.51 ((~cC30(iV16459)) <=> (~cC30(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(296,axiom,(~cC30(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_121')).
% 0.21/0.51 tff(297,plain,
% 0.21/0.51 (~cC30(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.21/0.51 tff(298,plain,
% 0.21/0.51 ((~(cC30(iV16459) | cC32(iV16459))) | cC30(iV16459) | cC32(iV16459)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(299,plain,
% 0.21/0.51 (~(cC30(iV16459) | cC32(iV16459))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[298, 297, 294])).
% 0.21/0.51 tff(300,plain,
% 0.21/0.51 ((~(cC34(iV16459) <=> (~(cC30(iV16459) | cC32(iV16459))))) | cC34(iV16459) | (cC30(iV16459) | cC32(iV16459))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(301,plain,
% 0.21/0.51 ((~(cC34(iV16459) <=> (~(cC30(iV16459) | cC32(iV16459))))) | cC34(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[300, 299])).
% 0.21/0.51 tff(302,plain,
% 0.21/0.51 (cC34(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[301, 291])).
% 0.21/0.51 tff(303,plain,
% 0.21/0.51 (^[X: $i] : refl((cC50(X) <=> (~(cC46(X) | cC48(X)))) <=> (cC50(X) <=> (~(cC46(X) | cC48(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(304,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X)))) <=> ![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[303])).
% 0.21/0.51 tff(305,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC50(X) <=> ((~cC46(X)) & (~cC48(X)))) <=> (cC50(X) <=> (~(cC46(X) | cC48(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(306,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X)))) <=> ![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[305])).
% 0.21/0.51 tff(307,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X)))) <=> ![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(308,axiom,(![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_33')).
% 0.21/0.51 tff(309,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.21/0.51 tff(310,plain,(
% 0.21/0.51 ![X: $i] : (cC50(X) <=> ((~cC46(X)) & (~cC48(X))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[309])).
% 0.21/0.51 tff(311,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[310, 306])).
% 0.21/0.51 tff(312,plain,
% 0.21/0.51 (![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[311, 304])).
% 0.21/0.51 tff(313,plain,
% 0.21/0.51 ((~![X: $i] : (cC50(X) <=> (~(cC46(X) | cC48(X))))) | (cC50(iV16459) <=> (~(cC46(iV16459) | cC48(iV16459))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(314,plain,
% 0.21/0.51 (cC50(iV16459) <=> (~(cC46(iV16459) | cC48(iV16459)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[313, 312])).
% 0.21/0.51 tff(315,plain,
% 0.21/0.51 ((~cC46(iV16459)) <=> (~cC46(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(316,axiom,(~cC46(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_124')).
% 0.21/0.51 tff(317,plain,
% 0.21/0.51 (~cC46(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.21/0.51 tff(318,plain,
% 0.21/0.51 ((~cC48(iV16459)) <=> (~cC48(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(319,axiom,(~cC48(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_120')).
% 0.21/0.51 tff(320,plain,
% 0.21/0.51 (~cC48(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.21/0.51 tff(321,plain,
% 0.21/0.51 ((~(cC46(iV16459) | cC48(iV16459))) | cC46(iV16459) | cC48(iV16459)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(322,plain,
% 0.21/0.51 (~(cC46(iV16459) | cC48(iV16459))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[321, 320, 317])).
% 0.21/0.51 tff(323,plain,
% 0.21/0.51 ((~(cC50(iV16459) <=> (~(cC46(iV16459) | cC48(iV16459))))) | cC50(iV16459) | (cC46(iV16459) | cC48(iV16459))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(324,plain,
% 0.21/0.51 ((~(cC50(iV16459) <=> (~(cC46(iV16459) | cC48(iV16459))))) | cC50(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[323, 322])).
% 0.21/0.51 tff(325,plain,
% 0.21/0.51 (cC50(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[324, 314])).
% 0.21/0.51 tff(326,plain,
% 0.21/0.51 (^[X: $i] : refl((cC88(X) <=> (~(cC84(X) | cC86(X)))) <=> (cC88(X) <=> (~(cC84(X) | cC86(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(327,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X)))) <=> ![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[326])).
% 0.21/0.51 tff(328,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC88(X) <=> ((~cC84(X)) & (~cC86(X)))) <=> (cC88(X) <=> (~(cC84(X) | cC86(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(329,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X)))) <=> ![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[328])).
% 0.21/0.51 tff(330,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X)))) <=> ![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(331,axiom,(![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_53')).
% 0.21/0.51 tff(332,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.21/0.51 tff(333,plain,(
% 0.21/0.51 ![X: $i] : (cC88(X) <=> ((~cC84(X)) & (~cC86(X))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[332])).
% 0.21/0.51 tff(334,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[333, 329])).
% 0.21/0.51 tff(335,plain,
% 0.21/0.51 (![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[334, 327])).
% 0.21/0.51 tff(336,plain,
% 0.21/0.51 ((~![X: $i] : (cC88(X) <=> (~(cC84(X) | cC86(X))))) | (cC88(iV16459) <=> (~(cC84(iV16459) | cC86(iV16459))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(337,plain,
% 0.21/0.51 (cC88(iV16459) <=> (~(cC84(iV16459) | cC86(iV16459)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[336, 335])).
% 0.21/0.51 tff(338,plain,
% 0.21/0.51 ((~cC84(iV16459)) <=> (~cC84(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(339,axiom,(~cC84(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_132')).
% 0.21/0.51 tff(340,plain,
% 0.21/0.51 (~cC84(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.21/0.51 tff(341,plain,
% 0.21/0.51 ((~cC86(iV16459)) <=> (~cC86(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(342,axiom,(~cC86(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_123')).
% 0.21/0.51 tff(343,plain,
% 0.21/0.51 (~cC86(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.21/0.51 tff(344,plain,
% 0.21/0.51 ((~(cC84(iV16459) | cC86(iV16459))) | cC84(iV16459) | cC86(iV16459)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(345,plain,
% 0.21/0.51 (~(cC84(iV16459) | cC86(iV16459))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[344, 343, 340])).
% 0.21/0.51 tff(346,plain,
% 0.21/0.51 ((~(cC88(iV16459) <=> (~(cC84(iV16459) | cC86(iV16459))))) | cC88(iV16459) | (cC84(iV16459) | cC86(iV16459))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(347,plain,
% 0.21/0.51 ((~(cC88(iV16459) <=> (~(cC84(iV16459) | cC86(iV16459))))) | cC88(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[346, 345])).
% 0.21/0.51 tff(348,plain,
% 0.21/0.51 (cC88(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[347, 337])).
% 0.21/0.51 tff(349,plain,
% 0.21/0.51 (^[X: $i] : refl((cC68(X) <=> (~(cC64(X) | cC66(X)))) <=> (cC68(X) <=> (~(cC64(X) | cC66(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(350,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X)))) <=> ![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[349])).
% 0.21/0.51 tff(351,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC68(X) <=> ((~cC64(X)) & (~cC66(X)))) <=> (cC68(X) <=> (~(cC64(X) | cC66(X)))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(352,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X)))) <=> ![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[351])).
% 0.21/0.51 tff(353,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X)))) <=> ![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(354,axiom,(![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_43')).
% 0.21/0.51 tff(355,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.21/0.51 tff(356,plain,(
% 0.21/0.51 ![X: $i] : (cC68(X) <=> ((~cC64(X)) & (~cC66(X))))),
% 0.21/0.51 inference(skolemize,[status(sab)],[355])).
% 0.21/0.51 tff(357,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.21/0.51 tff(358,plain,
% 0.21/0.51 (![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[357, 350])).
% 0.21/0.51 tff(359,plain,
% 0.21/0.51 ((~![X: $i] : (cC68(X) <=> (~(cC64(X) | cC66(X))))) | (cC68(iV16459) <=> (~(cC64(iV16459) | cC66(iV16459))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(360,plain,
% 0.21/0.51 (cC68(iV16459) <=> (~(cC64(iV16459) | cC66(iV16459)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[359, 358])).
% 0.21/0.51 tff(361,plain,
% 0.21/0.51 ((~cC64(iV16459)) <=> (~cC64(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(362,axiom,(~cC64(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_133')).
% 0.21/0.51 tff(363,plain,
% 0.21/0.51 (~cC64(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.21/0.51 tff(364,plain,
% 0.21/0.51 ((~cC66(iV16459)) <=> (~cC66(iV16459))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(365,axiom,(~cC66(iV16459)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_127')).
% 0.21/0.51 tff(366,plain,
% 0.21/0.51 (~cC66(iV16459)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.21/0.51 tff(367,plain,
% 0.21/0.51 ((~(cC64(iV16459) | cC66(iV16459))) | cC64(iV16459) | cC66(iV16459)),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(368,plain,
% 0.21/0.51 (~(cC64(iV16459) | cC66(iV16459))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[367, 366, 363])).
% 0.21/0.51 tff(369,plain,
% 0.21/0.51 ((~(cC68(iV16459) <=> (~(cC64(iV16459) | cC66(iV16459))))) | cC68(iV16459) | (cC64(iV16459) | cC66(iV16459))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(370,plain,
% 0.21/0.51 ((~(cC68(iV16459) <=> (~(cC64(iV16459) | cC66(iV16459))))) | cC68(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.21/0.51 tff(371,plain,
% 0.21/0.51 (cC68(iV16459)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[370, 360])).
% 0.21/0.51 tff(372,plain,
% 0.21/0.51 (^[X: $i] : refl((cC38(X) <=> (~(cC36(X) | (~cTOP(X))))) <=> (cC38(X) <=> (~(cC36(X) | (~cTOP(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(373,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X))))) <=> ![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[372])).
% 0.21/0.51 tff(374,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC38(X) <=> ((~cC36(X)) & cTOP(X))) <=> (cC38(X) <=> (~(cC36(X) | (~cTOP(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(375,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X))) <=> ![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[374])).
% 0.21/0.51 tff(376,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X))) <=> ![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(377,axiom,(![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_27')).
% 0.21/0.51 tff(378,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.21/0.51 tff(379,plain,(
% 0.21/0.51 ![X: $i] : (cC38(X) <=> ((~cC36(X)) & cTOP(X)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[378])).
% 0.21/0.51 tff(380,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[379, 375])).
% 0.21/0.51 tff(381,plain,
% 0.21/0.51 (![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[380, 373])).
% 0.21/0.51 tff(382,plain,
% 0.21/0.51 ((~![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))) | (cC38(iV16457) <=> (~(cC36(iV16457) | (~cTOP(iV16457)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(383,plain,
% 0.21/0.51 (cC38(iV16457) <=> (~(cC36(iV16457) | (~cTOP(iV16457))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[382, 381])).
% 0.21/0.51 tff(384,plain,
% 0.21/0.51 (cTOP(iV16457) <=> cTOP(iV16457)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(385,axiom,(cTOP(iV16457)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_113')).
% 0.21/0.51 tff(386,plain,
% 0.21/0.51 (cTOP(iV16457)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.21/0.51 tff(387,plain,
% 0.21/0.51 ((~cC36(iV16457)) <=> (~cC36(iV16457))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(388,axiom,(~cC36(iV16457)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_108')).
% 0.21/0.51 tff(389,plain,
% 0.21/0.51 (~cC36(iV16457)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[388, 387])).
% 0.21/0.51 tff(390,plain,
% 0.21/0.51 ((~(cC36(iV16457) | (~cTOP(iV16457)))) | cC36(iV16457) | (~cTOP(iV16457))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(391,plain,
% 0.21/0.51 (~(cC36(iV16457) | (~cTOP(iV16457)))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[390, 389, 386])).
% 0.21/0.51 tff(392,plain,
% 0.21/0.51 ((~(cC38(iV16457) <=> (~(cC36(iV16457) | (~cTOP(iV16457)))))) | cC38(iV16457) | (cC36(iV16457) | (~cTOP(iV16457)))),
% 0.21/0.51 inference(tautology,[status(thm)],[])).
% 0.21/0.51 tff(393,plain,
% 0.21/0.51 ((~(cC38(iV16457) <=> (~(cC36(iV16457) | (~cTOP(iV16457)))))) | cC38(iV16457)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[392, 391])).
% 0.21/0.51 tff(394,plain,
% 0.21/0.51 (cC38(iV16457)),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[393, 383])).
% 0.21/0.51 tff(395,plain,
% 0.21/0.51 (^[X: $i] : refl((cC106(X) <=> (~(cC100(X) | (~cC104(X))))) <=> (cC106(X) <=> (~(cC100(X) | (~cC104(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(396,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X))))) <=> ![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[395])).
% 0.21/0.51 tff(397,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC106(X) <=> ((~cC100(X)) & cC104(X))) <=> (cC106(X) <=> (~(cC100(X) | (~cC104(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(398,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X))) <=> ![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[397])).
% 0.21/0.51 tff(399,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X))) <=> ![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(400,axiom,(![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_5')).
% 0.21/0.51 tff(401,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.21/0.51 tff(402,plain,(
% 0.21/0.51 ![X: $i] : (cC106(X) <=> ((~cC100(X)) & cC104(X)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[401])).
% 0.21/0.51 tff(403,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[402, 398])).
% 0.21/0.51 tff(404,plain,
% 0.21/0.51 (![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[403, 396])).
% 0.21/0.51 tff(405,plain,
% 0.21/0.51 ((~![X: $i] : (cC106(X) <=> (~(cC100(X) | (~cC104(X)))))) | (cC106(iV16439) <=> (~(cC100(iV16439) | (~cC104(iV16439)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(406,plain,
% 0.21/0.51 (cC106(iV16439) <=> (~(cC100(iV16439) | (~cC104(iV16439))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[405, 404])).
% 0.21/0.51 tff(407,plain,
% 0.21/0.51 (^[X: $i] : refl((cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))) <=> (cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(408,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))) <=> ![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[407])).
% 0.21/0.51 tff(409,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cC108(X) <=> (cC28(X) & cC106(X))) <=> (cC108(X) <=> (~((~cC28(X)) | (~cC106(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(410,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X))) <=> ![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[409])).
% 0.21/0.51 tff(411,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X))) <=> ![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(412,axiom,(![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_6')).
% 0.21/0.51 tff(413,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.21/0.51 tff(414,plain,(
% 0.21/0.51 ![X: $i] : (cC108(X) <=> (cC28(X) & cC106(X)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[413])).
% 0.21/0.51 tff(415,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[414, 410])).
% 0.21/0.51 tff(416,plain,
% 0.21/0.51 (![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[415, 408])).
% 0.21/0.51 tff(417,plain,
% 0.21/0.51 (((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))) <=> ((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(418,plain,
% 0.21/0.51 ((cC108(iV16439) <=> (~((~cC28(iV16439)) | (~cC106(iV16439))))) <=> (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(419,plain,
% 0.21/0.51 (((~![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))))))),
% 0.21/0.51 inference(monotonicity,[status(thm)],[418])).
% 0.21/0.51 tff(420,plain,
% 0.21/0.51 (((~![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))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[419, 417])).
% 0.21/0.51 tff(421,plain,
% 0.21/0.51 ((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC28(iV16439)) | (~cC106(iV16439)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(422,plain,
% 0.21/0.51 ((~![X: $i] : (cC108(X) <=> (~((~cC28(X)) | (~cC106(X)))))) | (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.21/0.51 tff(423,plain,
% 0.21/0.51 (cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[422, 416])).
% 0.21/0.51 tff(424,plain,
% 0.21/0.51 (^[X: $i] : refl((cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))) <=> (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(425,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))) <=> ![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[424])).
% 0.21/0.51 tff(426,plain,
% 0.21/0.51 (^[X: $i] : rewrite((cTEST(X) <=> (cC108(X) & cC130(X))) <=> (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X))))))),
% 0.21/0.51 inference(bind,[status(th)],[])).
% 0.21/0.51 tff(427,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X))) <=> ![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.21/0.51 inference(quant_intro,[status(thm)],[426])).
% 0.21/0.51 tff(428,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X))) <=> ![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(429,axiom,(![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_59')).
% 0.21/0.51 tff(430,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.21/0.51 tff(431,plain,(
% 0.21/0.51 ![X: $i] : (cTEST(X) <=> (cC108(X) & cC130(X)))),
% 0.21/0.51 inference(skolemize,[status(sab)],[430])).
% 0.21/0.51 tff(432,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[431, 427])).
% 0.21/0.51 tff(433,plain,
% 0.21/0.51 (![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[432, 425])).
% 0.21/0.51 tff(434,plain,
% 0.21/0.51 ((~![X: $i] : (cTEST(X) <=> (~((~cC108(X)) | (~cC130(X)))))) | (cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439)))))),
% 0.21/0.51 inference(quant_inst,[status(thm)],[])).
% 0.21/0.51 tff(435,plain,
% 0.21/0.51 (cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.21/0.51 inference(unit_resolution,[status(thm)],[434, 433])).
% 0.21/0.51 tff(436,plain,
% 0.21/0.51 (cTEST(iV16439) <=> cTEST(iV16439)),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(437,axiom,(cTEST(iV16439)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_61')).
% 0.21/0.51 tff(438,plain,
% 0.21/0.51 (cTEST(iV16439)),
% 0.21/0.51 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.21/0.51 tff(439,plain,
% 0.21/0.51 ((~(cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439)))))) | (~cTEST(iV16439)) | (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(440,plain,
% 0.21/0.52 ((~(cTEST(iV16439) <=> (~((~cC108(iV16439)) | (~cC130(iV16439)))))) | (~((~cC108(iV16439)) | (~cC130(iV16439))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[439, 438])).
% 0.21/0.52 tff(441,plain,
% 0.21/0.52 (~((~cC108(iV16439)) | (~cC130(iV16439)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[440, 435])).
% 0.21/0.52 tff(442,plain,
% 0.21/0.52 (((~cC108(iV16439)) | (~cC130(iV16439))) | cC108(iV16439)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(443,plain,
% 0.21/0.52 (cC108(iV16439)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[442, 441])).
% 0.21/0.52 tff(444,plain,
% 0.21/0.52 ((~(cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))) | (~cC108(iV16439)) | (~((~cC106(iV16439)) | (~cC28(iV16439))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(445,plain,
% 0.21/0.52 ((~(cC108(iV16439) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)))))) | (~((~cC106(iV16439)) | (~cC28(iV16439))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[444, 443])).
% 0.21/0.52 tff(446,plain,
% 0.21/0.52 (~((~cC106(iV16439)) | (~cC28(iV16439)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[445, 423])).
% 0.21/0.52 tff(447,plain,
% 0.21/0.52 (((~cC106(iV16439)) | (~cC28(iV16439))) | cC106(iV16439)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(448,plain,
% 0.21/0.52 (cC106(iV16439)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[447, 446])).
% 0.21/0.52 tff(449,plain,
% 0.21/0.52 ((~(cC106(iV16439) <=> (~(cC100(iV16439) | (~cC104(iV16439)))))) | (~cC106(iV16439)) | (~(cC100(iV16439) | (~cC104(iV16439))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(450,plain,
% 0.21/0.52 (~(cC100(iV16439) | (~cC104(iV16439)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[449, 448, 406])).
% 0.21/0.52 tff(451,plain,
% 0.21/0.52 ((cC100(iV16439) | (~cC104(iV16439))) | cC104(iV16439)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(452,plain,
% 0.21/0.52 (cC104(iV16439)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[451, 450])).
% 0.21/0.52 tff(453,plain,
% 0.21/0.52 (((~cC106(iV16439)) | (~cC28(iV16439))) | cC28(iV16439)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(454,plain,
% 0.21/0.52 (cC28(iV16439)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[453, 446])).
% 0.21/0.52 tff(455,plain,
% 0.21/0.52 ((~![X: $i] : (cC38(X) <=> (~(cC36(X) | (~cTOP(X)))))) | (cC38(iV16448) <=> (~(cC36(iV16448) | (~cTOP(iV16448)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(456,plain,
% 0.21/0.52 (cC38(iV16448) <=> (~(cC36(iV16448) | (~cTOP(iV16448))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[455, 381])).
% 0.21/0.52 tff(457,plain,
% 0.21/0.52 (cTOP(iV16448) <=> cTOP(iV16448)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(458,axiom,(cTOP(iV16448)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_79')).
% 0.21/0.52 tff(459,plain,
% 0.21/0.52 (cTOP(iV16448)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.21/0.52 tff(460,plain,
% 0.21/0.52 ((~cC36(iV16448)) <=> (~cC36(iV16448))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(461,axiom,(~cC36(iV16448)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_76')).
% 0.21/0.52 tff(462,plain,
% 0.21/0.52 (~cC36(iV16448)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.21/0.52 tff(463,plain,
% 0.21/0.52 ((~(cC36(iV16448) | (~cTOP(iV16448)))) | cC36(iV16448) | (~cTOP(iV16448))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(464,plain,
% 0.21/0.52 (~(cC36(iV16448) | (~cTOP(iV16448)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[463, 462, 459])).
% 0.21/0.52 tff(465,plain,
% 0.21/0.52 ((~(cC38(iV16448) <=> (~(cC36(iV16448) | (~cTOP(iV16448)))))) | cC38(iV16448) | (cC36(iV16448) | (~cTOP(iV16448)))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(466,plain,
% 0.21/0.52 ((~(cC38(iV16448) <=> (~(cC36(iV16448) | (~cTOP(iV16448)))))) | cC38(iV16448)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[465, 464])).
% 0.21/0.52 tff(467,plain,
% 0.21/0.52 (cC38(iV16448)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[466, 456])).
% 0.21/0.52 tff(468,plain,
% 0.21/0.52 (rR1(iV16439, iV16440) <=> rR1(iV16439, iV16440)),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(469,axiom,(rR1(iV16439, iV16440)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_64')).
% 0.21/0.52 tff(470,plain,
% 0.21/0.52 (rR1(iV16439, iV16440)),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[469, 468])).
% 0.21/0.52 tff(471,plain,
% 0.21/0.52 (^[X: $i] : refl((cC98(X) | (~rR1(iV16439, X))) <=> (cC98(X) | (~rR1(iV16439, X))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(472,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) | (~rR1(iV16439, X))) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[471])).
% 0.21/0.52 tff(473,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) | (~rR1(iV16439, X))) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(474,plain,
% 0.21/0.52 (^[X: $i] : rewrite((rR1(iV16439, X) => cC98(X)) <=> (cC98(X) | (~rR1(iV16439, X))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(475,plain,
% 0.21/0.52 (![X: $i] : (rR1(iV16439, X) => cC98(X)) <=> ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[474])).
% 0.21/0.52 tff(476,axiom,(![X: $i] : (rR1(iV16439, X) => cC98(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_60')).
% 0.21/0.52 tff(477,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.21/0.52 tff(478,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[477, 473])).
% 0.21/0.52 tff(479,plain,(
% 0.21/0.52 ![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[478])).
% 0.21/0.52 tff(480,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) | (~rR1(iV16439, X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[479, 472])).
% 0.21/0.52 tff(481,plain,
% 0.21/0.52 (((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | (cC98(iV16440) | (~rR1(iV16439, iV16440)))) <=> ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | cC98(iV16440) | (~rR1(iV16439, iV16440)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(482,plain,
% 0.21/0.52 ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | (cC98(iV16440) | (~rR1(iV16439, iV16440)))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(483,plain,
% 0.21/0.52 ((~![X: $i] : (cC98(X) | (~rR1(iV16439, X)))) | cC98(iV16440) | (~rR1(iV16439, iV16440))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.21/0.52 tff(484,plain,
% 0.21/0.52 (cC98(iV16440)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[483, 480, 470])).
% 0.21/0.52 tff(485,plain,
% 0.21/0.52 (^[X: $i] : refl((cC98(X) <=> (~(cC96(X) | (~cC82(X))))) <=> (cC98(X) <=> (~(cC96(X) | (~cC82(X))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(486,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X))))) <=> ![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[485])).
% 0.21/0.52 tff(487,plain,
% 0.21/0.52 (^[X: $i] : rewrite((cC98(X) <=> ((~cC96(X)) & cC82(X))) <=> (cC98(X) <=> (~(cC96(X) | (~cC82(X))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(488,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X))) <=> ![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[487])).
% 0.21/0.52 tff(489,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X))) <=> ![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(490,axiom,(![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_58')).
% 0.21/0.52 tff(491,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.21/0.52 tff(492,plain,(
% 0.21/0.52 ![X: $i] : (cC98(X) <=> ((~cC96(X)) & cC82(X)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[491])).
% 0.21/0.52 tff(493,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.21/0.52 tff(494,plain,
% 0.21/0.52 (![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[493, 486])).
% 0.21/0.52 tff(495,plain,
% 0.21/0.52 ((~![X: $i] : (cC98(X) <=> (~(cC96(X) | (~cC82(X)))))) | (cC98(iV16440) <=> (~(cC96(iV16440) | (~cC82(iV16440)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(496,plain,
% 0.21/0.52 (cC98(iV16440) <=> (~(cC96(iV16440) | (~cC82(iV16440))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[495, 494])).
% 0.21/0.52 tff(497,plain,
% 0.21/0.52 ((~(cC98(iV16440) <=> (~(cC96(iV16440) | (~cC82(iV16440)))))) | (~cC98(iV16440)) | (~(cC96(iV16440) | (~cC82(iV16440))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(498,plain,
% 0.21/0.52 (~(cC96(iV16440) | (~cC82(iV16440)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[497, 484, 496])).
% 0.21/0.52 tff(499,plain,
% 0.21/0.52 ((cC96(iV16440) | (~cC82(iV16440))) | cC82(iV16440)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(500,plain,
% 0.21/0.52 (cC82(iV16440)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[499, 498])).
% 0.21/0.52 tff(501,plain,
% 0.21/0.52 (^[X: $i] : refl((cC82(X) <=> (~(cC78(X) | (~cC80(X))))) <=> (cC82(X) <=> (~(cC78(X) | (~cC80(X))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(502,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X))))) <=> ![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[501])).
% 0.21/0.52 tff(503,plain,
% 0.21/0.52 (^[X: $i] : rewrite((cC82(X) <=> ((~cC78(X)) & cC80(X))) <=> (cC82(X) <=> (~(cC78(X) | (~cC80(X))))))),
% 0.21/0.52 inference(bind,[status(th)],[])).
% 0.21/0.52 tff(504,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X))) <=> ![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X)))))),
% 0.21/0.52 inference(quant_intro,[status(thm)],[503])).
% 0.21/0.52 tff(505,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X))) <=> ![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(506,axiom,(![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom_50')).
% 0.21/0.52 tff(507,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X)))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.21/0.52 tff(508,plain,(
% 0.21/0.52 ![X: $i] : (cC82(X) <=> ((~cC78(X)) & cC80(X)))),
% 0.21/0.52 inference(skolemize,[status(sab)],[507])).
% 0.21/0.52 tff(509,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[508, 504])).
% 0.21/0.52 tff(510,plain,
% 0.21/0.52 (![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X)))))),
% 0.21/0.52 inference(modus_ponens,[status(thm)],[509, 502])).
% 0.21/0.52 tff(511,plain,
% 0.21/0.52 ((~![X: $i] : (cC82(X) <=> (~(cC78(X) | (~cC80(X)))))) | (cC82(iV16440) <=> (~(cC78(iV16440) | (~cC80(iV16440)))))),
% 0.21/0.52 inference(quant_inst,[status(thm)],[])).
% 0.21/0.52 tff(512,plain,
% 0.21/0.52 (cC82(iV16440) <=> (~(cC78(iV16440) | (~cC80(iV16440))))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[511, 510])).
% 0.21/0.52 tff(513,plain,
% 0.21/0.52 ((~(cC82(iV16440) <=> (~(cC78(iV16440) | (~cC80(iV16440)))))) | (~cC82(iV16440)) | (~(cC78(iV16440) | (~cC80(iV16440))))),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(514,plain,
% 0.21/0.52 (~(cC78(iV16440) | (~cC80(iV16440)))),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[513, 500, 512])).
% 0.21/0.52 tff(515,plain,
% 0.21/0.52 ((cC78(iV16440) | (~cC80(iV16440))) | cC80(iV16440)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(516,plain,
% 0.21/0.52 (cC80(iV16440)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[515, 514])).
% 0.21/0.52 tff(517,plain,
% 0.21/0.52 (((~cC108(iV16439)) | (~cC130(iV16439))) | cC130(iV16439)),
% 0.21/0.52 inference(tautology,[status(thm)],[])).
% 0.21/0.52 tff(518,plain,
% 0.21/0.52 (cC130(iV16439)),
% 0.21/0.52 inference(unit_resolution,[status(thm)],[517, 441])).
% 0.21/0.52 tff(519,plain,
% 0.21/0.52 ((~(~((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465))))) <=> ((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(520,plain,
% 0.21/0.52 ((cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465)) <=> (~((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(521,plain,
% 0.21/0.52 ((~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465))) <=> (~(~((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465)))))),
% 0.21/0.52 inference(monotonicity,[status(thm)],[520])).
% 0.21/0.52 tff(522,plain,
% 0.21/0.52 ((~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465))) <=> ((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465)))),
% 0.21/0.52 inference(transitivity,[status(thm)],[521, 519])).
% 0.21/0.52 tff(523,plain,
% 0.21/0.52 ((~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465))) <=> (~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(524,plain,
% 0.21/0.52 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465))) <=> (~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465)))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(525,plain,
% 0.21/0.52 ((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465)) <=> (![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(526,plain,
% 0.21/0.52 ((~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465)))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[525])).
% 0.21/0.53 tff(527,plain,
% 0.21/0.53 ((~((((((((((((((((((((((((((((((((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC106(iV16439)) & cC28(iV16439)) & cC130(iV16439)) & cowlThing(iV16439)) & cC108(iV16439)) & cC104(iV16439)) & cC80(iV16440)) & cowlThing(iV16440)) & cC82(iV16440)) & cC98(iV16440)) & cowlThing(iV16448)) & cC38(iV16448)) & cC62(iV16453)) & cowlThing(iV16453)) & cC76(iV16453)) & cC60(iV16453)) & cC44(iV16455)) & cowlThing(iV16455)) & cC56(iV16455)) & cC42(iV16455)) & cowlThing(iV16457)) & cC38(iV16457)) & cC68(iV16459)) & cowlThing(iV16459)) & cC88(iV16459)) & cC50(iV16459)) & cC34(iV16459)) & cowlThing(iV16460)) & cC38(iV16460)) & cC44(iV16461)) & cowlThing(iV16461)) & cC56(iV16461)) & cC42(iV16461)) & cowlThing(iV16462)) & cC38(iV16462)) & cC62(iV16463)) & cowlThing(iV16463)) & cC76(iV16463)) & cC60(iV16463)) & cC44(iV16464)) & cowlThing(iV16464)) & cC56(iV16464)) & cC42(iV16464)) & cowlThing(iV16465)) & cC38(iV16465))) <=> (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465)))),
% 0.21/0.53 inference(rewrite,[status(thm)],[])).
% 0.21/0.53 tff(528,axiom,(~((((((((((((((((((((((((((((((((((((((((((((((![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X)))) & cC106(iV16439)) & cC28(iV16439)) & cC130(iV16439)) & cowlThing(iV16439)) & cC108(iV16439)) & cC104(iV16439)) & cC80(iV16440)) & cowlThing(iV16440)) & cC82(iV16440)) & cC98(iV16440)) & cowlThing(iV16448)) & cC38(iV16448)) & cC62(iV16453)) & cowlThing(iV16453)) & cC76(iV16453)) & cC60(iV16453)) & cC44(iV16455)) & cowlThing(iV16455)) & cC56(iV16455)) & cC42(iV16455)) & cowlThing(iV16457)) & cC38(iV16457)) & cC68(iV16459)) & cowlThing(iV16459)) & cC88(iV16459)) & cC50(iV16459)) & cC34(iV16459)) & cowlThing(iV16460)) & cC38(iV16460)) & cC44(iV16461)) & cowlThing(iV16461)) & cC56(iV16461)) & cC42(iV16461)) & cowlThing(iV16462)) & cC38(iV16462)) & cC62(iV16463)) & cowlThing(iV16463)) & cC76(iV16463)) & cC60(iV16463)) & cC44(iV16464)) & cowlThing(iV16464)) & cC56(iV16464)) & cC42(iV16464)) & cowlThing(iV16465)) & cC38(iV16465))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','the_axiom')).
% 0.43/0.53 tff(529,plain,
% 0.43/0.53 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[528, 527])).
% 0.43/0.53 tff(530,plain,
% 0.43/0.53 (~(![X: $i] : (cowlThing(X) & (~cowlNothing(X))) & ![X: $i] : (xsd_string(X) <=> (~xsd_integer(X))) & cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cowlThing(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cowlThing(iV16440) & cC82(iV16440) & cC98(iV16440) & cowlThing(iV16448) & cC38(iV16448) & cC62(iV16453) & cowlThing(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cowlThing(iV16455) & cC56(iV16455) & cC42(iV16455) & cowlThing(iV16457) & cC38(iV16457) & cC68(iV16459) & cowlThing(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cowlThing(iV16460) & cC38(iV16460) & cC44(iV16461) & cowlThing(iV16461) & cC56(iV16461) & cC42(iV16461) & cowlThing(iV16462) & cC38(iV16462) & cC62(iV16463) & cowlThing(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cowlThing(iV16464) & cC56(iV16464) & cC42(iV16464) & cowlThing(iV16465) & cC38(iV16465))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[529, 526])).
% 0.43/0.53 tff(531,plain,
% 0.43/0.53 (~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[530, 524])).
% 0.43/0.53 tff(532,plain,
% 0.43/0.53 (~(cC106(iV16439) & cC28(iV16439) & cC130(iV16439) & cC108(iV16439) & cC104(iV16439) & cC80(iV16440) & cC82(iV16440) & cC98(iV16440) & cC38(iV16448) & cC62(iV16453) & cC76(iV16453) & cC60(iV16453) & cC44(iV16455) & cC56(iV16455) & cC42(iV16455) & cC38(iV16457) & cC68(iV16459) & cC88(iV16459) & cC50(iV16459) & cC34(iV16459) & cC38(iV16460) & cC44(iV16461) & cC56(iV16461) & cC42(iV16461) & cC38(iV16462) & cC62(iV16463) & cC76(iV16463) & cC60(iV16463) & cC44(iV16464) & cC56(iV16464) & cC42(iV16464) & cC38(iV16465))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[531, 523])).
% 0.43/0.53 tff(533,plain,
% 0.43/0.53 ((~cC106(iV16439)) | (~cC28(iV16439)) | (~cC130(iV16439)) | (~cC108(iV16439)) | (~cC104(iV16439)) | (~cC80(iV16440)) | (~cC82(iV16440)) | (~cC98(iV16440)) | (~cC38(iV16448)) | (~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455)) | (~cC38(iV16457)) | (~cC68(iV16459)) | (~cC88(iV16459)) | (~cC50(iV16459)) | (~cC34(iV16459)) | (~cC38(iV16460)) | (~cC44(iV16461)) | (~cC56(iV16461)) | (~cC42(iV16461)) | (~cC38(iV16462)) | (~cC62(iV16463)) | (~cC76(iV16463)) | (~cC60(iV16463)) | (~cC44(iV16464)) | (~cC56(iV16464)) | (~cC42(iV16464)) | (~cC38(iV16465))),
% 0.43/0.53 inference(modus_ponens,[status(thm)],[532, 522])).
% 0.43/0.53 tff(534,plain,
% 0.43/0.53 ((~cC62(iV16453)) | (~cC76(iV16453)) | (~cC60(iV16453)) | (~cC44(iV16455)) | (~cC56(iV16455)) | (~cC42(iV16455))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[533, 518, 443, 448, 516, 500, 484, 467, 454, 452, 394, 371, 348, 325, 302, 279, 261, 257, 265, 239, 218, 214, 222, 179, 175, 183, 154])).
% 0.43/0.53 tff(535,plain,
% 0.43/0.53 (~cC76(iV16453)),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[534, 55, 34, 116, 137, 95])).
% 0.43/0.53 tff(536,plain,
% 0.43/0.53 ((~![X: $i] : (cC76(X) <=> (~(cC74(X) | (~cC62(X)))))) | (cC76(iV16453) <=> (~(cC74(iV16453) | (~cC62(iV16453)))))),
% 0.43/0.53 inference(quant_inst,[status(thm)],[])).
% 0.43/0.53 tff(537,plain,
% 0.43/0.53 (cC76(iV16453) <=> (~(cC74(iV16453) | (~cC62(iV16453))))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[536, 195])).
% 0.43/0.53 tff(538,plain,
% 0.43/0.53 ((~(cC76(iV16453) <=> (~(cC74(iV16453) | (~cC62(iV16453)))))) | cC76(iV16453) | (cC74(iV16453) | (~cC62(iV16453)))),
% 0.43/0.53 inference(tautology,[status(thm)],[])).
% 0.43/0.53 tff(539,plain,
% 0.43/0.53 (cC76(iV16453) | (cC74(iV16453) | (~cC62(iV16453)))),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[538, 537])).
% 0.43/0.53 tff(540,plain,
% 0.43/0.53 ($false),
% 0.43/0.53 inference(unit_resolution,[status(thm)],[539, 535, 61])).
% 0.43/0.53 % SZS output end Proof
%------------------------------------------------------------------------------