0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.9ACn7W8WfU 0.14/0.34 % Computer : n024.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 : 180 0.14/0.34 % DateTime : Thu Aug 29 09:36:05 EDT 2019 0.14/0.34 % CPUTime : 103.03/103.59 % Running portfolio for 180 s 103.03/103.59 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 103.03/103.59 % TempDir : /export/starexec/sandbox2/tmp/tmp.9ACn7W8WfU 103.03/103.59 % Recognized as monomorphic HO. 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/competitive.sh for 18 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/competitive.2.sh for 13 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/competitive.3.sh for 3 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.sh for 28 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.1.sh for 12 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.rudimentary.2.sh for 7 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.sh for 3 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.1.sh for 15 103.03/103.59 % Running /export/starexec/sandbox2/solver/bin/pragmatic.shallow.2.sh for 12 103.03/103.59 % Solved by: pragmatic.shallow.2.sh 103.03/103.59 % done 397 iterations in 4.604s 103.03/103.59 % hashcons stats for terms: size 4096, num 3064, sum length 24091, buckets: small 0, median 7, big 13 103.03/103.59 % proof state stats: {active 58, passive 905, simpl 0} 103.03/103.59 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 103.03/103.59 % SZS output start Refutation 103.03/103.59 tff(cTHM120I_pme, conjecture, 103.03/103.59 (?[R:(($i > $o * $i > $o) > $o)]: 103.03/103.59 ((![Xx:($i > $o),Xy:($i > $o),Xz:($i > $o)]: 103.03/103.59 ((R(Xx,Xy) & R(Xy,Xz)) => R(Xx,Xz))) & 103.03/103.59 (![X:($i > $o),Y:($i > $o)]: 103.03/103.59 ((R(X,Y) & R(Y,X)) => (![Xx]: (Y(Xx) <=> X(Xx))))) & 103.03/103.59 (![Xx:($i > $o)]: R(Xx,Xx))))). 103.03/103.59 tff(zf_stmt_0, negated_conjecture, 103.03/103.59 (~ 103.03/103.59 (?[R:(($i > $o * $i > $o) > $o)]: 103.03/103.59 ((![Xx:($i > $o),Xy:($i > $o),Xz:($i > $o)]: 103.03/103.59 ((R(Xx,Xy) & R(Xy,Xz)) => R(Xx,Xz))) & 103.03/103.59 (![X:($i > $o),Y:($i > $o)]: 103.03/103.59 ((R(X,Y) & R(Y,X)) => (![Xx]: (Y(Xx) <=> X(Xx))))) & 103.03/103.59 (![Xx:($i > $o)]: R(Xx,Xx)))))). 103.03/103.59 tff('0', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xy_(X0), sk_Xz_(X0)) 103.03/103.59 | sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('1', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['0'])). 103.03/103.59 tff('2', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['1'])). 103.03/103.59 tff('3', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['2'])). 103.03/103.59 tff('4', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['3'])). 103.03/103.59 tff('5', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (~ X0(sk_Xx_(X0), sk_Xz_(X0)) 103.03/103.59 | sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('6', plain, 103.03/103.59 (~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['5'])). 103.03/103.59 tff('7', plain, 103.03/103.59 (~ (= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['6'])). 103.03/103.59 tff('8', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['7'])). 103.03/103.59 tff('9', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['8'])). 103.03/103.59 tff('10', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xx_(X0), sk_Xy_(X0)) 103.03/103.59 | sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('11', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['10'])). 103.03/103.59 tff('12', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['11'])). 103.03/103.59 tff('13', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['12'])). 103.03/103.59 tff('14', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['13'])). 103.03/103.59 tff('15', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xx_(X0), sk_Xy_(X0)) 103.03/103.59 | X0(sk_X_(X0), sk_Y_(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('16', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['15'])). 103.03/103.59 tff('17', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (= (> $o, $i), 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['16'])). 103.03/103.59 tff('18', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['17'])). 103.03/103.59 tff('19', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['18'])). 103.03/103.59 tff('20', plain, 103.03/103.59 ![X1]: 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('ho_complete_eq', [status(thm)], ['19'])). 103.03/103.59 tff('21', plain, 103.03/103.59 ![X0]: 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0)), 103.03/103.59 inference('cnf_otf', [status(thm)], ['20'])). 103.03/103.59 tff('22', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('clc', [status(thm)], ['14', '21'])). 103.03/103.59 tff('23', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xx_(X0), sk_Xy_(X0)) 103.03/103.59 | ~ sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('24', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['23'])). 103.03/103.59 tff('25', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['24'])). 103.03/103.59 tff('26', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['25'])). 103.03/103.59 tff('27', plain, 103.03/103.59 (~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['26'])). 103.03/103.59 tff('28', plain, 103.03/103.59 ![X0]: 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0)), 103.03/103.59 inference('cnf_otf', [status(thm)], ['20'])). 103.03/103.59 tff('29', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('clc', [status(thm)], ['27', '28'])). 103.03/103.59 tff('30', plain, 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 inference('clc', [status(thm)], ['22', '29'])). 103.03/103.59 tff('31', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('demod', [status(thm)], ['9', '30'])). 103.03/103.59 tff('32', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (~ X0(sk_Xx_(X0), sk_Xz_(X0)) 103.03/103.59 | X0(sk_X_(X0), sk_Y_(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('33', plain, 103.03/103.59 (~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['32'])). 103.03/103.59 tff('34', plain, 103.03/103.59 (~ (= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (= (> $o, $i), 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['33'])). 103.03/103.59 tff('35', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['34'])). 103.03/103.59 tff('36', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['35'])). 103.03/103.59 tff('37', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('demod', [status(thm)], ['36', '30'])). 103.03/103.59 tff('38', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xy_(X0), sk_Xz_(X0)) 103.03/103.59 | X0(sk_X_(X0), sk_Y_(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('39', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['38'])). 103.03/103.59 tff('40', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | (= (> $o, $i), 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['39'])). 103.03/103.59 tff('41', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['40'])). 103.03/103.59 tff('42', plain, 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['41'])). 103.03/103.59 tff('43', plain, 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 inference('clc', [status(thm)], ['37', '42'])). 103.03/103.59 tff('44', plain, 103.03/103.59 ![X1]: 103.03/103.59 sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1), 103.03/103.59 inference('ho_complete_eq', [status(thm)], ['43'])). 103.03/103.59 tff('45', plain, 103.03/103.59 ![X0]: 103.03/103.59 (sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0)), 103.03/103.59 inference('cnf_otf', [status(thm)], ['44'])). 103.03/103.59 tff('46', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('clc', [status(thm)], ['31', '45'])). 103.03/103.59 tff('47', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (~ X0(sk_Xx_(X0), sk_Xz_(X0)) 103.03/103.59 | ~ sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('48', plain, 103.03/103.59 (~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['47'])). 103.03/103.59 tff('49', plain, 103.03/103.59 (~ (= (> $o, $i), 103.03/103.59 sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['48'])). 103.03/103.59 tff('50', plain, 103.03/103.59 (sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['49'])). 103.03/103.59 tff('51', plain, 103.03/103.59 (~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['50'])). 103.03/103.59 tff('52', plain, 103.03/103.59 (~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('demod', [status(thm)], ['51', '30'])). 103.03/103.59 tff('53', plain, 103.03/103.59 ![X1]: 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1)), 103.03/103.59 inference('cnf_otf', [status(thm)], ['44'])). 103.03/103.59 tff('54', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('clc', [status(thm)], ['52', '53'])). 103.03/103.59 tff('55', plain, 103.03/103.59 ![X0 : ($i > $o * $i > $o) > $o]: 103.03/103.59 (X0(sk_Xy_(X0), sk_Xz_(X0)) 103.03/103.59 | ~ sk_Y_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ sk_X_(X0, sk_Xx_1(X0)) 103.03/103.59 | ~ X0(sk_Xx_2(X0), sk_Xx_2(X0))), 103.03/103.59 inference('cnf', [status(esa)], [zf_stmt_0])). 103.03/103.59 tff('56', plain, 103.03/103.59 ((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))( 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('ho.refine', [status(thm)], ['55'])). 103.03/103.59 tff('57', plain, 103.03/103.59 ((= (> $o, $i), 103.03/103.59 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ (= (> $o, $i), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.59 sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('lambda-normalize', [status(thm)], ['56'])). 103.03/103.59 tff('58', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 != sk_Xx_2((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify nested equalities', [status(thm)], ['57'])). 103.03/103.59 tff('59', plain, 103.03/103.59 (~ sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('simplify', [status(thm)], ['58'])). 103.03/103.59 tff('60', plain, 103.03/103.59 ![X1]: 103.03/103.59 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 = sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X1) 103.03/103.59 | sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.59 inference('ho_complete_eq', [status(thm)], ['42'])). 103.03/103.59 tff('61', plain, 103.03/103.59 ![X0]: 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), X0)), 103.03/103.59 inference('cnf_otf', [status(thm)], ['60'])). 103.03/103.59 tff('62', plain, 103.03/103.59 (sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 = sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.59 | ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.59 inference('clc', [status(thm)], ['59', '61'])). 103.03/103.59 tff('63', plain, 103.03/103.59 ~ sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.59 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.60 inference('clc', [status(thm)], ['54', '62'])). 103.03/103.60 tff('64', plain, 103.03/103.60 sk_Xy_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))) 103.03/103.60 != sk_Xz_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))), 103.03/103.60 inference('clc', [status(thm)], ['46', '63'])). 103.03/103.60 tff('65', plain, 103.03/103.60 (sk_X_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.60 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))) 103.03/103.60 | sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.60 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1))))), 103.03/103.60 inference('simplify_reflect-', [status(thm)], ['4', '64'])). 103.03/103.60 tff('66', plain, 103.03/103.60 sk_Y_((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)), 103.03/103.60 sk_Xx_1((^[Y0 : $i > $o,Y1 : $i > $o]: (= (> $o, $i), Y0, Y1)))), 103.03/103.60 inference('clc', [status(thm)], ['65', '45'])). 103.03/103.60 tff('67', plain, $false, inference('sup-', [status(thm)], ['66', '63'])). 103.03/103.60 103.03/103.60 % SZS output end Refutation 103.03/103.60 % Zipperpin 1.5 exiting 103.03/103.60 EOF