0.12/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.biG4OpuE2x 0.14/0.36 % Computer : n026.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 960 0.14/0.36 % DateTime : Thu Jul 2 07:26:10 EDT 2020 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.37 % Running in HO mode 0.55/0.64 % Estimated wc time : 1286 0.55/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.56/0.75 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.57/0.76 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 0.57/0.85 % Solved by lams/s6.ds.sh. 0.57/0.85 % done 142 iterations in 0.053s 0.57/0.85 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 0.57/0.85 % SZS output start Refutation 0.57/0.85 tff(meuclidean, axiom, meuclidean() = 0.57/0.85 ^[R:(($i * $i) > $o)]: (![S,T,U]: ((R(S,T) & R(S,U)) => R(T,U)))). 0.57/0.85 tff('0', plain, 0.57/0.85 meuclidean = 0.57/0.85 (^[R:(($i * $i) > $o)]: (![S,T,U]: ((R(S,T) & R(S,U)) => R(T,U)))), 0.57/0.85 inference('simplify_rw_rule', [status(thm)], [meuclidean])). 0.57/0.85 tff('1', plain, 0.57/0.85 meuclidean = 0.57/0.85 (^[V_1:(($i * $i) > $o)]: 0.57/0.85 (![X4,X6,X8]: ((V_1(X4,X6) & V_1(X4,X8)) => V_1(X6,X8)))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff(mtransitive, axiom, mtransitive() = 0.57/0.85 ^[R:(($i * $i) > $o)]: (![S,T,U]: ((R(S,T) & R(T,U)) => R(S,U)))). 0.57/0.85 tff('2', plain, 0.57/0.85 mtransitive = 0.57/0.85 (^[R:(($i * $i) > $o)]: (![S,T,U]: ((R(S,T) & R(T,U)) => R(S,U)))), 0.57/0.85 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 0.57/0.85 tff('3', plain, 0.57/0.85 mtransitive = 0.57/0.85 (^[V_1:(($i * $i) > $o)]: 0.57/0.85 (![X4,X6,X8]: ((V_1(X4,X6) & V_1(X6,X8)) => V_1(X4,X8)))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff(mserial, axiom, mserial() = 0.57/0.85 ^[R:(($i * $i) > $o)]: (![S]: (?[T]: R(S,T)))). 0.57/0.85 tff('4', plain, mserial = (^[R:(($i * $i) > $o)]: (![S]: (?[T]: R(S,T)))), 0.57/0.85 inference('simplify_rw_rule', [status(thm)], [mserial])). 0.57/0.85 tff('5', plain, 0.57/0.85 mserial = (^[V_1:(($i * $i) > $o)]: (![X4]: (?[X6]: V_1(X4,X6)))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff(msymmetric, axiom, msymmetric() = 0.57/0.85 ^[R:(($i * $i) > $o)]: (![S,T]: (R(S,T) => R(T,S)))). 0.57/0.85 tff('6', plain, 0.57/0.85 msymmetric = (^[R:(($i * $i) > $o)]: (![S,T]: (R(S,T) => R(T,S)))), 0.57/0.85 inference('simplify_rw_rule', [status(thm)], [msymmetric])). 0.57/0.85 tff('7', plain, 0.57/0.85 msymmetric = 0.57/0.85 (^[V_1:(($i * $i) > $o)]: (![X4,X6]: (V_1(X4,X6) => V_1(X6,X4)))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff(mreflexive, axiom, mreflexive() = ^[R:(($i * $i) > $o)]: (![S]: R(S,S))). 0.57/0.85 tff('8', plain, mreflexive = (^[R:(($i * $i) > $o)]: (![S]: R(S,S))), 0.57/0.85 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 0.57/0.85 tff('9', plain, mreflexive = (^[V_1:(($i * $i) > $o)]: (![X4]: V_1(X4,X4))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff(conj, conjecture, 0.57/0.85 (![R:(($i * $i) > $o)]: 0.57/0.85 ((mserial(R) & mtransitive(R) & msymmetric(R)) <=> 0.57/0.85 (mreflexive(R) & meuclidean(R))))). 0.57/0.85 tff(zf_stmt_0, conjecture, 0.57/0.85 (![X4:(($i * $i) > $o)]: 0.57/0.85 (((![X16,X18]: (X4(X16,X18) => X4(X18,X16))) & 0.57/0.85 (![X10,X12,X14]: ((X4(X12,X14) & X4(X10,X12)) => X4(X10,X14))) & 0.57/0.85 (![X6]: (?[X8]: X4(X6,X8)))) <=> 0.57/0.85 ((![X22,X24,X26]: ((X4(X22,X26) & X4(X22,X24)) => X4(X24,X26))) & 0.57/0.85 (![X20]: X4(X20,X20)))))). 0.57/0.85 tff(zf_stmt_1, negated_conjecture, 0.57/0.85 (~ 0.57/0.85 (![X4:(($i * $i) > $o)]: 0.57/0.85 (((![X16,X18]: (X4(X16,X18) => X4(X18,X16))) & 0.57/0.85 (![X10,X12,X14]: ((X4(X12,X14) & X4(X10,X12)) => X4(X10,X14))) & 0.57/0.85 (![X6]: (?[X8]: X4(X6,X8)))) <=> 0.57/0.85 ((![X22,X24,X26]: ((X4(X22,X26) & X4(X22,X24)) => X4(X24,X26))) & 0.57/0.85 (![X20]: X4(X20,X20))))))). 0.57/0.85 tff('10', plain, 0.57/0.85 ~ (!!((^[Y0 : ($i * $i) > $o]: 0.57/0.85 (((!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: (Y0(Y1, Y2) => Y0(Y2, Y1))))))))& 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (!!((^[Y3 : $i]: 0.57/0.85 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))& 0.57/0.85 (!!((^[Y1 : $i]: (??((^[Y2 : $i]: Y0(Y1, Y2)))))))) <=> 0.57/0.85 ((!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (!!((^[Y3 : $i]: 0.57/0.85 ((Y0(Y1, Y3) & Y0(Y1, Y2)) => Y0(Y2, Y3))))))))))) & 0.57/0.85 (!!((^[Y1 : $i]: Y0(Y1, Y1))))))))), 0.57/0.85 inference('cnf', [status(esa)], [zf_stmt_1])). 0.57/0.85 tff('11', plain, 0.57/0.85 ~ (!!((^[Y0 : ($i * $i) > $o]: 0.57/0.85 (((!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: (Y0(Y1, Y2) => Y0(Y2, Y1))))))))& 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (!!((^[Y3 : $i]: 0.57/0.85 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))& 0.57/0.85 (!!((^[Y1 : $i]: (??(Y0(Y1))))))) <=> 0.57/0.85 ((!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (!!((^[Y3 : $i]: 0.57/0.85 ((Y0(Y1, Y3) & Y0(Y1, Y2)) => Y0(Y2, Y3))))))))))) & 0.57/0.85 (!!((^[Y1 : $i]: Y0(Y1, Y1))))))))), 0.57/0.85 inference('ho_norm', [status(thm)], ['10'])). 0.57/0.85 tff('12', plain, 0.57/0.85 ~ (((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) <=> 0.57/0.85 ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['11'])). 0.57/0.85 tff('13', plain, 0.57/0.85 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) 0.57/0.85 != ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('simplify nested equalities', [status(thm)], ['12'])). 0.57/0.85 tff('14', plain, 0.57/0.85 ( ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('eq_elim', [status(thm)], ['13'])). 0.57/0.85 tff('15', plain, 0.57/0.85 ( (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['14'])). 0.57/0.85 tff('16', plain, 0.57/0.85 ![X1]: 0.57/0.85 ( (??('#sk1'(X1))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['15'])). 0.57/0.85 tff('17', plain, 0.57/0.85 ![X1]: 0.57/0.85 ( (??('#sk1'(X1))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['15'])). 0.57/0.85 tff('18', plain, 0.57/0.85 (~ '#form2' 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('19', plain, ![X1]: ( '#form2' | (??('#sk1'(X1)))), 0.57/0.85 inference('renaming', [status(thm)], ['16', '18'])). 0.57/0.85 tff('20', plain, ![X1]: ( '#sk1'(X1, '#sk3'(X1)) | '#form2'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['19'])). 0.57/0.85 tff('21', plain, ![X1]: ( '#sk1'(X1, '#sk3'(X1)) | '#form2'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['19'])). 0.57/0.85 tff('22', plain, 0.57/0.85 ( (!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0)))))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['14'])). 0.57/0.85 tff('23', plain, 0.57/0.85 ![X1]: 0.57/0.85 ( (!!((^[Y0 : $i]: ('#sk1'(X1, Y0) => '#sk1'(Y0, X1))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['22'])). 0.57/0.85 tff('24', plain, 0.57/0.85 ![X1, X2]: 0.57/0.85 ( ('#sk1'(X1, X2) => '#sk1'(X2, X1)) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['23'])). 0.57/0.85 tff('25', plain, 0.57/0.85 (~ '#form2' 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('26', plain, 0.57/0.85 ![X1, X2]: ( '#form2' | ('#sk1'(X1, X2) => '#sk1'(X2, X1))), 0.57/0.85 inference('renaming', [status(thm)], ['24', '25'])). 0.57/0.85 tff('27', plain, ![X1, X2]: (~ '#sk1'(X1, X2) | '#sk1'(X2, X1) | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['26'])). 0.57/0.85 tff('28', plain, ![X0]: ( '#form2' | '#form2' | '#sk1'('#sk3'(X0), X0)), 0.57/0.85 inference('sup-', [status(thm)], ['21', '27'])). 0.57/0.85 tff('29', plain, ![X0]: ( '#sk1'('#sk3'(X0), X0) | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['28'])). 0.57/0.85 tff('30', plain, 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['14'])). 0.57/0.85 tff('31', plain, 0.57/0.85 ![X1]: 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (('#sk1'(Y0, Y1) & '#sk1'(X1, Y0)) => '#sk1'(X1, Y1)))))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['30'])). 0.57/0.85 tff('32', plain, 0.57/0.85 ![X1, X2]: 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (('#sk1'(X2, Y0) & '#sk1'(X1, X2)) => '#sk1'(X1, Y0))))) 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['31'])). 0.57/0.85 tff('33', plain, 0.57/0.85 (~ '#form2' 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('34', plain, 0.57/0.85 ![X1, X2]: 0.57/0.85 ( '#form2' 0.57/0.85 | (!!((^[Y0 : $i]: 0.57/0.85 (('#sk1'(X2, Y0) & '#sk1'(X1, X2)) => '#sk1'(X1, Y0)))))), 0.57/0.85 inference('renaming', [status(thm)], ['32', '33'])). 0.57/0.85 tff('35', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 ( (('#sk1'(X2, X3) & '#sk1'(X1, X2)) => '#sk1'(X1, X3)) | '#form2'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['34'])). 0.57/0.85 tff('36', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 (~ ('#sk1'(X2, X3) & '#sk1'(X1, X2)) | '#sk1'(X1, X3) | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['35'])). 0.57/0.85 tff('37', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 (~ '#sk1'(X2, X3) | ~ '#sk1'(X1, X2) | '#form2' | '#sk1'(X1, X3)), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['36'])). 0.57/0.85 tff('38', plain, 0.57/0.85 ![X0, X1]: 0.57/0.85 ( '#form2' | '#sk1'(X1, X0) | '#form2' | ~ '#sk1'(X1, '#sk3'(X0))), 0.57/0.85 inference('sup-', [status(thm)], ['29', '37'])). 0.57/0.85 tff('39', plain, 0.57/0.85 ![X0, X1]: (~ '#sk1'(X1, '#sk3'(X0)) | '#sk1'(X1, X0) | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['38'])). 0.57/0.85 tff('40', plain, ![X0]: ( '#form2' | '#form2' | '#sk1'(X0, X0)), 0.57/0.85 inference('sup-', [status(thm)], ['20', '39'])). 0.57/0.85 tff('41', plain, ![X0]: ( '#sk1'(X0, X0) | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['40'])). 0.57/0.85 tff('42', plain, 0.57/0.85 (~ '#form2' 0.57/0.85 | ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('43', plain, ( (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['42'])). 0.57/0.85 tff('44', plain, ![X1]: ( '#sk1'(X1, X1) | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['43'])). 0.57/0.85 tff('45', plain, ![X0]: '#sk1'(X0, X0), 0.57/0.85 inference('clc', [status(thm)], ['41', '44'])). 0.57/0.85 tff('46', plain, 0.57/0.85 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) 0.57/0.85 != ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('simplify nested equalities', [status(thm)], ['12'])). 0.57/0.85 tff('47', plain, 0.57/0.85 (~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) 0.57/0.85 | ~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('eq_elim', [status(thm)], ['46'])). 0.57/0.85 tff('48', plain, 0.57/0.85 (~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0))))))) 0.57/0.85 | ~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 inference('eq_elim', [status(thm)], ['46'])). 0.57/0.85 tff('49', plain, 0.57/0.85 ( '#form2' 0.57/0.85 | ~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('50', plain, 0.57/0.85 (~ '#form2' 0.57/0.85 | ~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))& 0.57/0.85 (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))& 0.57/0.85 (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))))), 0.57/0.85 inference('renaming', [status(thm)], ['47', '49'])). 0.57/0.85 tff('51', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0)))))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['50'])). 0.57/0.85 tff('52', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: ('#sk1'('#sk4', Y0) => '#sk1'(Y0, '#sk4'))))) 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['51'])). 0.57/0.85 tff('53', plain, 0.57/0.85 (~ ('#sk1'('#sk4', '#sk6') => '#sk1'('#sk6', '#sk4')) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['52'])). 0.57/0.85 tff('54', plain, 0.57/0.85 (~ '#sk1'('#sk6', '#sk4') 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['53'])). 0.57/0.85 tff('55', plain, 0.57/0.85 (~ (??('#sk1'('#sk9'))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ '#sk1'('#sk6', '#sk4')), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['54'])). 0.57/0.85 tff('56', plain, 0.57/0.85 ( '#sk1'('#sk4', '#sk6') 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: (??('#sk1'(Y0)))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['53'])). 0.57/0.85 tff('57', plain, 0.57/0.85 (~ (??('#sk1'('#sk9'))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ~ '#form2' 0.57/0.85 | '#sk1'('#sk4', '#sk6')), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['56'])). 0.57/0.85 tff('58', plain, 0.57/0.85 ( '#form10' 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('59', plain, 0.57/0.85 (~ '#form10' 0.57/0.85 | ~ '#sk1'('#sk6', '#sk4') 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ (??('#sk1'('#sk9')))), 0.57/0.85 inference('renaming', [status(thm)], ['55', '58'])). 0.57/0.85 tff('60', plain, 0.57/0.85 ![X1]: 0.57/0.85 (~ '#sk1'('#sk9', X1) 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ '#sk1'('#sk6', '#sk4') 0.57/0.85 | ~ '#form10'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['59'])). 0.57/0.85 tff('61', plain, (~ '#form10' | ~ '#sk1'('#sk6', '#sk4') | ~ '#form2'), 0.57/0.85 inference('sup-', [status(thm)], ['45', '60'])). 0.57/0.85 tff('62', plain, 0.57/0.85 ( '#form2' 0.57/0.85 | ~ ((!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) & 0.57/0.85 (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('63', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) 0.57/0.85 | '#form2'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['62'])). 0.57/0.85 tff('64', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (('#sk1'('#sk5', Y1) & '#sk1'('#sk5', Y0)) => 0.57/0.85 '#sk1'(Y0, Y1)))))))) 0.57/0.85 | '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['63'])). 0.57/0.85 tff('65', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (('#sk1'('#sk5', Y0) & '#sk1'('#sk5', '#sk7')) => 0.57/0.85 '#sk1'('#sk7', Y0))))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) 0.57/0.85 | '#form2'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['64'])). 0.57/0.85 tff('66', plain, 0.57/0.85 (~ (('#sk1'('#sk5', '#sk8') & '#sk1'('#sk5', '#sk7')) => 0.57/0.85 '#sk1'('#sk7', '#sk8')) 0.57/0.85 | '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['65'])). 0.57/0.85 tff('67', plain, 0.57/0.85 ( ('#sk1'('#sk5', '#sk8') & '#sk1'('#sk5', '#sk7')) 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) 0.57/0.85 | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['66'])). 0.57/0.85 tff('68', plain, 0.57/0.85 ( '#sk1'('#sk5', '#sk7') 0.57/0.85 | '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['67'])). 0.57/0.85 tff('69', plain, 0.57/0.85 (~ '#sk1'('#sk7', '#sk8') 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) 0.57/0.85 | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['66'])). 0.57/0.85 tff('70', plain, ( '#form11' | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('71', plain, (~ '#form11' | '#form2' | '#sk1'('#sk5', '#sk7')), 0.57/0.85 inference('renaming', [status(thm)], ['68', '70'])). 0.57/0.85 tff('72', plain, ( '#form11' | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('73', plain, (~ '#sk1'('#sk13', '#sk13') | '#form11'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['72'])). 0.57/0.85 tff('74', plain, ![X0]: '#sk1'(X0, X0), 0.57/0.85 inference('clc', [status(thm)], ['41', '44'])). 0.57/0.85 tff('75', plain, '#form11', inference('demod', [status(thm)], ['73', '74'])). 0.57/0.85 tff('76', plain, ( '#form2' | '#sk1'('#sk5', '#sk7')), 0.57/0.85 inference('demod', [status(thm)], ['71', '75'])). 0.57/0.85 tff('77', plain, ![X1, X2]: (~ '#sk1'(X1, X2) | '#sk1'(X2, X1) | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['26'])). 0.57/0.85 tff('78', plain, ( '#form2' | '#form2' | '#sk1'('#sk7', '#sk5')), 0.57/0.85 inference('sup-', [status(thm)], ['76', '77'])). 0.57/0.85 tff('79', plain, ( '#sk1'('#sk7', '#sk5') | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['78'])). 0.57/0.85 tff('80', plain, 0.57/0.85 ( '#sk1'('#sk5', '#sk8') 0.57/0.85 | '#form2' 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['67'])). 0.57/0.85 tff('81', plain, ( '#form11' | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('82', plain, (~ '#form11' | '#form2' | '#sk1'('#sk5', '#sk8')), 0.57/0.85 inference('renaming', [status(thm)], ['80', '81'])). 0.57/0.85 tff('83', plain, '#form11', inference('demod', [status(thm)], ['73', '74'])). 0.57/0.85 tff('84', plain, ( '#form2' | '#sk1'('#sk5', '#sk8')), 0.57/0.85 inference('demod', [status(thm)], ['82', '83'])). 0.57/0.85 tff('85', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 (~ '#sk1'(X2, X3) | ~ '#sk1'(X1, X2) | '#form2' | '#sk1'(X1, X3)), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['36'])). 0.57/0.85 tff('86', plain, 0.57/0.85 ![X0]: 0.57/0.85 ( '#form2' | '#sk1'(X0, '#sk8') | '#form2' | ~ '#sk1'(X0, '#sk5')), 0.57/0.85 inference('sup-', [status(thm)], ['84', '85'])). 0.57/0.85 tff('87', plain, 0.57/0.85 ![X0]: (~ '#sk1'(X0, '#sk5') | '#sk1'(X0, '#sk8') | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['86'])). 0.57/0.85 tff('88', plain, ( '#form2' | '#form2' | '#sk1'('#sk7', '#sk8')), 0.57/0.85 inference('sup-', [status(thm)], ['79', '87'])). 0.57/0.85 tff('89', plain, ( '#sk1'('#sk7', '#sk8') | '#form2'), 0.57/0.85 inference('simplify', [status(thm)], ['88'])). 0.57/0.85 tff('90', plain, 0.57/0.85 (~ '#sk1'('#sk7', '#sk8') 0.57/0.85 | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0)))) 0.57/0.85 | '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['66'])). 0.57/0.85 tff('91', plain, ( '#form11' | ~ (!!((^[Y0 : $i]: '#sk1'(Y0, Y0))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('92', plain, (~ '#form11' | '#form2' | ~ '#sk1'('#sk7', '#sk8')), 0.57/0.85 inference('renaming', [status(thm)], ['90', '91'])). 0.57/0.85 tff('93', plain, '#form11', inference('demod', [status(thm)], ['73', '74'])). 0.57/0.85 tff('94', plain, ( '#form2' | ~ '#sk1'('#sk7', '#sk8')), 0.57/0.85 inference('demod', [status(thm)], ['92', '93'])). 0.57/0.85 tff('95', plain, '#form2', inference('clc', [status(thm)], ['89', '94'])). 0.57/0.85 tff('96', plain, (~ '#form10' | ~ '#sk1'('#sk6', '#sk4')), 0.57/0.85 inference('demod', [status(thm)], ['61', '95'])). 0.57/0.85 tff('97', plain, 0.57/0.85 ( '#form10' 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('98', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (('#sk1'(Y0, Y1) & '#sk1'('#sk12', Y0)) => 0.57/0.85 '#sk1'('#sk12', Y1)))))))) 0.57/0.85 | '#form10'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['97'])). 0.57/0.85 tff('99', plain, 0.57/0.85 (~ (!!((^[Y0 : $i]: 0.57/0.85 (('#sk1'('#sk14', Y0) & '#sk1'('#sk12', '#sk14')) => 0.57/0.85 '#sk1'('#sk12', Y0))))) 0.57/0.85 | '#form10'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['98'])). 0.57/0.85 tff('100', plain, 0.57/0.85 (~ (('#sk1'('#sk14', '#sk15') & '#sk1'('#sk12', '#sk14')) => 0.57/0.85 '#sk1'('#sk12', '#sk15')) 0.57/0.85 | '#form10'), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['99'])). 0.57/0.85 tff('101', plain, 0.57/0.85 ( ('#sk1'('#sk14', '#sk15') & '#sk1'('#sk12', '#sk14')) | '#form10'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['100'])). 0.57/0.85 tff('102', plain, ( '#sk1'('#sk12', '#sk14') | '#form10'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['101'])). 0.57/0.85 tff('103', plain, ![X0]: '#sk1'(X0, X0), 0.57/0.85 inference('clc', [status(thm)], ['41', '44'])). 0.57/0.85 tff('104', plain, 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y0, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y1, Y2))))))))))) 0.57/0.85 | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['42'])). 0.57/0.85 tff('105', plain, 0.57/0.85 ![X1]: 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (('#sk1'(X1, Y1) & '#sk1'(X1, Y0)) => '#sk1'(Y0, Y1)))))))) 0.57/0.85 | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['104'])). 0.57/0.85 tff('106', plain, 0.57/0.85 ![X1, X2]: 0.57/0.85 ( (!!((^[Y0 : $i]: 0.57/0.85 (('#sk1'(X1, Y0) & '#sk1'(X1, X2)) => '#sk1'(X2, Y0))))) 0.57/0.85 | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['105'])). 0.57/0.85 tff('107', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 ( (('#sk1'(X1, X3) & '#sk1'(X1, X2)) => '#sk1'(X2, X3)) | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['106'])). 0.57/0.85 tff('108', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 (~ ('#sk1'(X1, X3) & '#sk1'(X1, X2)) | '#sk1'(X2, X3) | ~ '#form2'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['107'])). 0.57/0.85 tff('109', plain, 0.57/0.85 ![X1, X2, X3]: 0.57/0.85 (~ '#sk1'(X1, X3) | ~ '#sk1'(X1, X2) | ~ '#form2' | '#sk1'(X2, X3)), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['108'])). 0.57/0.85 tff('110', plain, '#form2', inference('clc', [status(thm)], ['89', '94'])). 0.57/0.85 tff('111', plain, 0.57/0.85 ![X1, X2, X3]: (~ '#sk1'(X1, X3) | ~ '#sk1'(X1, X2) | '#sk1'(X2, X3)), 0.57/0.85 inference('demod', [status(thm)], ['109', '110'])). 0.57/0.85 tff('112', plain, ![X0, X1]: ( '#sk1'(X1, X0) | ~ '#sk1'(X0, X1)), 0.57/0.85 inference('sup-', [status(thm)], ['103', '111'])). 0.57/0.85 tff('113', plain, ( '#form10' | '#sk1'('#sk14', '#sk12')), 0.57/0.85 inference('sup-', [status(thm)], ['102', '112'])). 0.57/0.85 tff('114', plain, ( '#sk1'('#sk14', '#sk15') | '#form10'), 0.57/0.85 inference('lazy_cnf_and', [status(thm)], ['101'])). 0.57/0.85 tff('115', plain, 0.57/0.85 ![X1, X2, X3]: (~ '#sk1'(X1, X3) | ~ '#sk1'(X1, X2) | '#sk1'(X2, X3)), 0.57/0.85 inference('demod', [status(thm)], ['109', '110'])). 0.57/0.85 tff('116', plain, 0.57/0.85 ![X0]: ( '#form10' | '#sk1'(X0, '#sk15') | ~ '#sk1'('#sk14', X0)), 0.57/0.85 inference('sup-', [status(thm)], ['114', '115'])). 0.57/0.85 tff('117', plain, ( '#form10' | '#sk1'('#sk12', '#sk15') | '#form10'), 0.57/0.85 inference('sup-', [status(thm)], ['113', '116'])). 0.57/0.85 tff('118', plain, ( '#sk1'('#sk12', '#sk15') | '#form10'), 0.57/0.85 inference('simplify', [status(thm)], ['117'])). 0.57/0.85 tff('119', plain, (~ '#sk1'('#sk12', '#sk15') | '#form10'), 0.57/0.85 inference('lazy_cnf_imply', [status(thm)], ['100'])). 0.57/0.85 tff('120', plain, '#form10', inference('clc', [status(thm)], ['118', '119'])). 0.57/0.85 tff('121', plain, ~ '#sk1'('#sk6', '#sk4'), 0.57/0.85 inference('demod', [status(thm)], ['96', '120'])). 0.57/0.85 tff('122', plain, ![X0]: '#sk1'(X0, X0), 0.57/0.85 inference('clc', [status(thm)], ['41', '44'])). 0.57/0.85 tff('123', plain, 0.57/0.85 (~ (??('#sk1'('#sk9'))) 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2))))))))))) 0.57/0.85 | ~ '#form2' 0.57/0.85 | '#sk1'('#sk4', '#sk6')), 0.57/0.85 inference('lazy_cnf_exists', [status(thm)], ['56'])). 0.57/0.85 tff('124', plain, 0.57/0.85 ( '#form10' 0.57/0.85 | ~ (!!((^[Y0 : $i]: 0.57/0.85 (!!((^[Y1 : $i]: 0.57/0.85 (!!((^[Y2 : $i]: 0.57/0.85 (('#sk1'(Y1, Y2) & '#sk1'(Y0, Y1)) => 0.57/0.85 '#sk1'(Y0, Y2)))))))))))), 0.57/0.85 define([status(thm)])). 0.57/0.85 tff('125', plain, 0.57/0.85 (~ '#form10' 0.57/0.85 | '#sk1'('#sk4', '#sk6') 0.57/0.85 | ~ '#form2' 0.57/0.85 | ~ (??('#sk1'('#sk9')))), 0.57/0.85 inference('renaming', [status(thm)], ['123', '124'])). 0.57/0.85 tff('126', plain, 0.57/0.85 ![X1]: 0.57/0.85 (~ '#sk1'('#sk9', X1) 0.57/0.85 | ~ '#form2' 0.57/0.85 | '#sk1'('#sk4', '#sk6') 0.57/0.85 | ~ '#form10'), 0.57/0.85 inference('lazy_cnf_forall', [status(thm)], ['125'])). 0.57/0.85 tff('127', plain, (~ '#form10' | '#sk1'('#sk4', '#sk6') | ~ '#form2'), 0.57/0.85 inference('sup-', [status(thm)], ['122', '126'])). 0.57/0.85 tff('128', plain, '#form2', inference('clc', [status(thm)], ['89', '94'])). 0.57/0.85 tff('129', plain, (~ '#form10' | '#sk1'('#sk4', '#sk6')), 0.57/0.85 inference('demod', [status(thm)], ['127', '128'])). 0.57/0.85 tff('130', plain, '#form10', inference('clc', [status(thm)], ['118', '119'])). 0.57/0.85 tff('131', plain, '#sk1'('#sk4', '#sk6'), 0.57/0.85 inference('demod', [status(thm)], ['129', '130'])). 0.57/0.85 tff('132', plain, ![X0, X1]: ( '#sk1'(X1, X0) | ~ '#sk1'(X0, X1)), 0.57/0.85 inference('sup-', [status(thm)], ['103', '111'])). 0.57/0.85 tff('133', plain, '#sk1'('#sk6', '#sk4'), 0.57/0.85 inference('sup-', [status(thm)], ['131', '132'])). 0.57/0.85 tff('134', plain, $false, inference('demod', [status(thm)], ['121', '133'])). 0.57/0.85 0.57/0.85 % SZS output end Refutation 0.57/0.85 0.57/0.85 0.57/0.85 % Terminating... 0.66/0.96 % Runner terminated. 0.66/0.98 % Zipperpin 1.5 exiting 0.66/0.98 EOF