0.00/0.09 % 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.U4n9nzfmvF 0.13/0.34 % Computer : n010.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.35 % DateTime : Tue Jul 13 15:35:36 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.53/0.64 % Estimated wc time : 1286 0.53/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.55/0.70 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.56/0.70 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.56/0.76 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.71/10.58 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.77/15.58 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 106.00/15.77 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 139.46/20.62 % Solved by lams/b.sh. 139.46/20.62 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.U4n9nzfmvF/e_input811b6f --cpu-limit=12 --auto -s -p. 139.46/20.62 % done 91 iterations in 4.995s 139.46/20.62 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 139.46/20.62 % SZS output start Refutation 139.46/20.62 tff(conj_2, conjecture, 139.46/20.62 ((![Z:a,S:state]: ((~pa(Z,S)) | termi(body,S) | (S != x))) & 139.46/20.62 (![S:state,T:state]: 139.46/20.62 ((![Z:a]: ((~pa(Z,S)) | (S != x) | qa(Z,T))) | (~exec(S,body,T)))))). 139.46/20.62 tff(zf_stmt_0, negated_conjecture, 139.46/20.62 (~ 139.46/20.62 ((![Z:a,S:state]: ((~pa(Z,S)) | termi(body,S) | (S != x))) & 139.46/20.62 (![S:state,T:state]: 139.46/20.62 ((![Z:a]: ((~pa(Z,S)) | (S != x) | qa(Z,T))) | (~exec(S,body,T))))))). 139.46/20.62 tff('0', plain, 139.46/20.62 ~ ((!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: ((~(pa(Y0, Y1)))|termi(body, Y1)|(Y1 != x)))))))) & 139.46/20.62 (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('cnf', [status(esa)], [zf_stmt_0])). 139.46/20.62 tff('1', plain, 139.46/20.62 (~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: ((~(pa(Y0, Y1)))|termi(body, Y1)|(Y1 != x)))))))) 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['0'])). 139.46/20.62 tff('2', plain, 139.46/20.62 (~ (!!((^[Y0 : state]: ((~(pa('#sk1008', Y0)))|termi(body, Y0)|(Y0 != x))))) 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['1'])). 139.46/20.62 tff('3', plain, 139.46/20.62 (~ ((~(pa('#sk1008', '#sk1009')))|termi(body, '#sk1009')|('#sk1009' != x)) 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['2'])). 139.46/20.62 tff('4', plain, 139.46/20.62 (~ termi(body, '#sk1009') 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['3'])). 139.46/20.62 tff('5', plain, 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 ((!!((^[Y1 : a]: 139.46/20.62 ((~(pa(Y1, '#sk1010')))|('#sk1010' != x)|qa(Y1, Y0))))) | 139.46/20.62 (~(exec('#sk1010', body, Y0))))))) 139.46/20.62 | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['4'])). 139.46/20.62 tff('6', plain, 139.46/20.62 (~ ((!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) | 139.46/20.62 (~(exec('#sk1010', body, '#sk1011')))) 139.46/20.62 | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['5'])). 139.46/20.62 tff('7', plain, 139.46/20.62 (~ (!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) 139.46/20.62 | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['6'])). 139.46/20.62 tff('8', plain, 139.46/20.62 (~ ((~(pa('#sk1012', '#sk1010')))|('#sk1010' != x)| 139.46/20.62 qa('#sk1012', '#sk1011')) 139.46/20.62 | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['7'])). 139.46/20.62 tff('9', plain, (~ qa('#sk1012', '#sk1011') | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['8'])). 139.46/20.62 tff('10', plain, 139.46/20.62 ( exec('#sk1010', body, '#sk1011') | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['6'])). 139.46/20.62 tff('11', plain, 139.46/20.62 ( pa('#sk1008', '#sk1009') 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['3'])). 139.46/20.62 tff('12', plain, 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 ((!!((^[Y1 : a]: 139.46/20.62 ((~(pa(Y1, '#sk1010')))|('#sk1010' != x)|qa(Y1, Y0))))) | 139.46/20.62 (~(exec('#sk1010', body, Y0))))))) 139.46/20.62 | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['11'])). 139.46/20.62 tff('13', plain, 139.46/20.62 (~ ((!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) | 139.46/20.62 (~(exec('#sk1010', body, '#sk1011')))) 139.46/20.62 | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['12'])). 139.46/20.62 tff('14', plain, 139.46/20.62 (~ (!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) 139.46/20.62 | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['13'])). 139.46/20.62 tff('15', plain, 139.46/20.62 (~ ((~(pa('#sk1012', '#sk1010')))|('#sk1010' != x)| 139.46/20.62 qa('#sk1012', '#sk1011')) 139.46/20.62 | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['14'])). 139.46/20.62 tff('16', plain, ( pa('#sk1012', '#sk1010') | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['15'])). 139.46/20.62 tff('17', plain, ( pa('#sk1012', '#sk1010') | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['8'])). 139.46/20.62 tff('18', plain, ('#sk1010' = x | pa('#sk1008', '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['15'])). 139.46/20.62 tff(conj_0, axiom, 139.46/20.62 (![S6:state]: 139.46/20.62 ((((![S:state,T:state]: 139.46/20.62 (exec(S,body,T) => 139.46/20.62 (![Z:a]: 139.46/20.62 ((pa(Z,S) & 139.46/20.62 member1389040324_state(produc64584659_state(S,S6),r)) => 139.46/20.62 qa(Z,T))))) & 139.46/20.62 (![Z:a,S:state]: 139.46/20.62 ((member1389040324_state(produc64584659_state(S,S6),r) & pa(Z,S)) => 139.46/20.62 termi(body,S)))) => 139.46/20.62 ((![S7:state,T4:state]: 139.46/20.62 (exec(S7,body,T4) => 139.46/20.62 (![Z2:a]: (((S7 = S6) & pa(Z2,S7)) => qa(Z2,T4))))) & 139.46/20.62 (![Z2:a,S7:state]: (((S7 = S6) & pa(Z2,S7)) => termi(body,S7))))) & 139.46/20.62 pHoare382919414oare_a(insert2053719859tate_o(produc33908149tate_o( 139.46/20.62 ^[Z4:a,S4:state]: 139.46/20.62 (pa(Z4,S4) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state( 139.46/20.62 S4,S6),r)), 139.46/20.62 produc1948644831tate_o( 139.46/20.62 call,qa)), 139.46/20.62 bot_bo170732493tate_o), 139.46/20.62 ^[Z4:a,S4:state]: ((S4 = S6) & pa(Z4,S4)),body,qa)))). 139.46/20.62 tff('19', plain, 139.46/20.62 (!!((^[Y0 : state]: 139.46/20.62 ((((!!((^[Y1 : state]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 (exec(Y1, body, Y2) => 139.46/20.62 (!!((^[Y3 : a]: 139.46/20.62 ((pa(Y3, Y1) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state(Y1, Y0), r)) => 139.46/20.62 qa(Y3, Y2)))))))))))) & 139.46/20.62 (!!((^[Y1 : a]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y2, Y0), r) & 139.46/20.62 pa(Y1, Y2)) => 139.46/20.62 termi(body, Y2))))))))) => 139.46/20.62 ((!!((^[Y1 : state]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 (exec(Y1, body, Y2) => 139.46/20.62 (!!((^[Y3 : a]: 139.46/20.62 (((Y1 = Y0) & pa(Y3, Y1)) => qa(Y3, Y2)))))))))))) & 139.46/20.62 (!!((^[Y1 : a]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 (((Y2 = Y0) & pa(Y1, Y2)) => termi(body, Y2)))))))))) & 139.46/20.62 pHoare382919414oare_a( 139.46/20.62 insert2053719859tate_o( 139.46/20.62 produc33908149tate_o( 139.46/20.62 (^[Y1 : a,Y2 : state]: 139.46/20.62 (pa(Y1, Y2) & 139.46/20.62 member1389040324_state(produc64584659_state(Y2, Y0), 139.46/20.62 r))), produc1948644831tate_o(call, qa)), 139.46/20.62 bot_bo170732493tate_o), 139.46/20.62 (^[Y1 : a,Y2 : state]: ((Y2 = Y0) & pa(Y1, Y2))), body, qa))))), 139.46/20.62 inference('cnf', [status(esa)], [conj_0])). 139.46/20.62 tff('20', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ((((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 ((pa(Y2, Y0) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state(Y0, X1), r)) => 139.46/20.62 qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))) => 139.46/20.62 ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))) & 139.46/20.62 pHoare382919414oare_a( 139.46/20.62 insert2053719859tate_o( 139.46/20.62 produc33908149tate_o( 139.46/20.62 (^[Y0 : a,Y1 : state]: 139.46/20.62 (pa(Y0, Y1) & 139.46/20.62 member1389040324_state(produc64584659_state(Y1, X1), r))), 139.46/20.62 produc1948644831tate_o(call, qa)), bot_bo170732493tate_o), 139.46/20.62 (^[Y0 : a,Y1 : state]: ((Y1 = X1) & pa(Y0, Y1))), body, qa)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['19'])). 139.46/20.62 tff('21', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 ((pa(Y2, Y0) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state(Y0, X1), r)) => 139.46/20.62 qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))) => 139.46/20.62 ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['20'])). 139.46/20.62 tff('22', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 ((pa(Y2, Y0) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state(Y0, X1), r)) => 139.46/20.62 qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['21'])). 139.46/20.62 tff('23', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 ((pa(Y2, Y0) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state(Y0, X1), r)) => 139.46/20.62 qa(Y2, Y1)))))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['22'])). 139.46/20.62 tff('24', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 (exec('#sk5126'(X1), body, Y0) => 139.46/20.62 (!!((^[Y1 : a]: 139.46/20.62 ((pa(Y1, '#sk5126'(X1)) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state('#sk5126'(X1), X1), r)) => 139.46/20.62 qa(Y1, Y0))))))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['23'])). 139.46/20.62 tff('25', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ (exec('#sk5126'(X1), body, '#sk5127'(X1)) => 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 ((pa(Y0, '#sk5126'(X1)) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state('#sk5126'(X1), X1), r)) => 139.46/20.62 qa(Y0, '#sk5127'(X1))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['24'])). 139.46/20.62 tff('26', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ (!!((^[Y0 : a]: 139.46/20.62 ((pa(Y0, '#sk5126'(X1)) & 139.46/20.62 member1389040324_state( 139.46/20.62 produc64584659_state('#sk5126'(X1), X1), r)) => 139.46/20.62 qa(Y0, '#sk5127'(X1)))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['25'])). 139.46/20.62 tff('27', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))))), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['26'])). 139.46/20.62 tff('28', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['25'])). 139.46/20.62 tff('29', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['28'])). 139.46/20.62 tff('30', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5129'(X1) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('31', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ '#form5129'(X1) 139.46/20.62 | ((!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) & 139.46/20.62 (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1))))))))) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 inference('renaming', [status(thm)], ['27', '30'])). 139.46/20.62 tff('32', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['31'])). 139.46/20.62 tff('33', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( (!!((^[Y0 : state]: (((Y0 = X1) & pa(X2, Y0)) => termi(body, Y0))))) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['32'])). 139.46/20.62 tff('34', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 ( (((X3 = X1) & pa(X2, X3)) => termi(body, X3)) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['33'])). 139.46/20.62 tff('35', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 ( (((X3 = X1) & pa(X2, X3)) => termi(body, X3)) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['33'])). 139.46/20.62 tff('36', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5132'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('37', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (~ '#form5132'(X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | (((X3 = X1) & pa(X2, X3)) => termi(body, X3))), 139.46/20.62 inference('renaming', [status(thm)], ['34', '36'])). 139.46/20.62 tff('38', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (~ ((X3 = X1) & pa(X2, X3)) 139.46/20.62 | termi(body, X3) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['37'])). 139.46/20.62 tff('39', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (X3 != X1 139.46/20.62 | ~ pa(X2, X3) 139.46/20.62 | ~ '#form5132'(X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | termi(body, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['38'])). 139.46/20.62 tff('40', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( termi(body, X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ '#form5132'(X1) 139.46/20.62 | ~ pa(X2, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['39'])). 139.46/20.62 tff('41', plain, ('#sk1010' = x | ~ termi(body, '#sk1009')), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['8'])). 139.46/20.62 tff('42', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1)))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['28'])). 139.46/20.62 tff('43', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5129'(X1) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('44', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (((Y1 = X1) & pa(Y0, Y1)) => termi(body, Y1))))))))), 139.46/20.62 inference('renaming', [status(thm)], ['42', '43'])). 139.46/20.62 tff('45', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( (!!((^[Y0 : state]: (((Y0 = X1) & pa(X2, Y0)) => termi(body, Y0))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['44'])). 139.46/20.62 tff('46', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 ( (((X3 = X1) & pa(X2, X3)) => termi(body, X3)) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1))), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['45'])). 139.46/20.62 tff('47', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (~ ((X3 = X1) & pa(X2, X3)) 139.46/20.62 | termi(body, X3) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['46'])). 139.46/20.62 tff('48', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (X3 != X1 139.46/20.62 | ~ pa(X2, X3) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | termi(body, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['47'])). 139.46/20.62 tff('49', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( termi(body, X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ pa(X2, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['48'])). 139.46/20.62 tff('50', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5132'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('51', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), r)) 139.46/20.62 | '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['50'])). 139.46/20.62 tff('52', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( member1389040324_state(produc64584659_state('#sk5126'(X1), X1), r) 139.46/20.62 | '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['51'])). 139.46/20.62 tff('53', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['31'])). 139.46/20.62 tff('54', plain, 139.46/20.62 ![X1 : state, X2 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (exec(X2, body, Y0) => 139.46/20.62 (!!((^[Y1 : a]: (((X2 = X1) & pa(Y1, X2)) => qa(Y1, Y0))))))))) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['53'])). 139.46/20.62 tff('55', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 ( (exec(X2, body, X3) => 139.46/20.62 (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3)))))) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1))) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['54'])). 139.46/20.62 tff('56', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 (~ exec(X2, body, X3) 139.46/20.62 | (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3))))) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['55'])). 139.46/20.62 tff('57', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5132'(X1) 139.46/20.62 | ~ ((pa('#sk5128'(X1), '#sk5126'(X1)) & 139.46/20.62 member1389040324_state(produc64584659_state('#sk5126'(X1), X1), 139.46/20.62 r)) => 139.46/20.62 qa('#sk5128'(X1), '#sk5127'(X1)))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('58', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 (~ '#form5132'(X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3))))) 139.46/20.62 | ~ exec(X2, body, X3)), 139.46/20.62 inference('renaming', [status(thm)], ['56', '57'])). 139.46/20.62 tff('59', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 ( (((X2 = X1) & pa(X4, X2)) => qa(X4, X3)) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['58'])). 139.46/20.62 tff('60', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (~ ((X2 = X1) & pa(X4, X2)) 139.46/20.62 | qa(X4, X3) 139.46/20.62 | ~ '#form5132'(X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ exec(X2, body, X3)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['59'])). 139.46/20.62 tff('61', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (X2 != X1 139.46/20.62 | ~ pa(X4, X2) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ '#form5132'(X1) 139.46/20.62 | qa(X4, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['60'])). 139.46/20.62 tff('62', plain, 139.46/20.62 ![X1 : state, X3 : state, X4 : a]: 139.46/20.62 ( qa(X4, X3) 139.46/20.62 | ~ '#form5132'(X1) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ exec(X1, body, X3) 139.46/20.62 | ~ pa(X4, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['61'])). 139.46/20.62 tff('63', plain, 139.46/20.62 ![X1 : state]: (~ qa('#sk5128'(X1), '#sk5127'(X1)) | '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['50'])). 139.46/20.62 tff('64', plain, 139.46/20.62 ('#sk1009' = x 139.46/20.62 | ~ (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((!!((^[Y2 : a]: 139.46/20.62 ((~(pa(Y2, Y0)))|(Y0 != x)|qa(Y2, Y1))))) | 139.46/20.62 (~(exec(Y0, body, Y1))))))))))), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['3'])). 139.46/20.62 tff('65', plain, 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 ((!!((^[Y1 : a]: 139.46/20.62 ((~(pa(Y1, '#sk1010')))|('#sk1010' != x)|qa(Y1, Y0))))) | 139.46/20.62 (~(exec('#sk1010', body, Y0))))))) 139.46/20.62 | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['64'])). 139.46/20.62 tff('66', plain, 139.46/20.62 (~ ((!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) | 139.46/20.62 (~(exec('#sk1010', body, '#sk1011')))) 139.46/20.62 | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['65'])). 139.46/20.62 tff('67', plain, ( exec('#sk1010', body, '#sk1011') | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['66'])). 139.46/20.62 tff('68', plain, 139.46/20.62 (~ (!!((^[Y0 : a]: 139.46/20.62 ((~(pa(Y0, '#sk1010')))|('#sk1010' != x)|qa(Y0, '#sk1011'))))) 139.46/20.62 | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['66'])). 139.46/20.62 tff('69', plain, 139.46/20.62 (~ ((~(pa('#sk1012', '#sk1010')))|('#sk1010' != x)| 139.46/20.62 qa('#sk1012', '#sk1011')) 139.46/20.62 | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['68'])). 139.46/20.62 tff('70', plain, (~ qa('#sk1012', '#sk1011') | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['69'])). 139.46/20.62 tff('71', plain, ( pa('#sk1012', '#sk1010') | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['69'])). 139.46/20.62 tff('72', plain, 139.46/20.62 ![X1 : state]: ( pa('#sk5128'(X1), '#sk5126'(X1)) | '#form5132'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['51'])). 139.46/20.62 tff(conj_1, axiom, 139.46/20.62 (![Y4:state]: 139.46/20.62 (member1389040324_state(produc64584659_state(Y4,x),r) => 139.46/20.62 ((![Z2:a,S7:state]: ((pa(Z2,S7) & (S7 = Y4)) => termi(body,S7))) & 139.46/20.62 (![S7:state,T4:state]: 139.46/20.62 (exec(S7,body,T4) => 139.46/20.62 (![Z2:a]: (((S7 = Y4) & pa(Z2,S7)) => qa(Z2,T4))))))))). 139.46/20.62 tff('73', plain, 139.46/20.62 (!!((^[Y0 : state]: 139.46/20.62 (member1389040324_state(produc64584659_state(Y0, x), r) => 139.46/20.62 ((!!((^[Y1 : a]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 ((pa(Y1, Y2) & (Y2 = Y0)) => termi(body, Y2)))))))) & 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (!!((^[Y2 : state]: 139.46/20.62 (exec(Y1, body, Y2) => 139.46/20.62 (!!((^[Y3 : a]: 139.46/20.62 (((Y1 = Y0) & pa(Y3, Y1)) => qa(Y3, Y2))))))))))))))))), 139.46/20.62 inference('cnf', [status(esa)], [conj_1])). 139.46/20.62 tff('74', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (member1389040324_state(produc64584659_state(X1, x), r) => 139.46/20.62 ((!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((pa(Y0, Y1) & (Y1 = X1)) => termi(body, Y1)))))))) & 139.46/20.62 (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))))), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['73'])). 139.46/20.62 tff('75', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | ((!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((pa(Y0, Y1) & (Y1 = X1)) => termi(body, Y1)))))))) & 139.46/20.62 (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))))), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['74'])). 139.46/20.62 tff('76', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['75'])). 139.46/20.62 tff('77', plain, 139.46/20.62 ![X1 : state, X2 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (exec(X2, body, Y0) => 139.46/20.62 (!!((^[Y1 : a]: (((X2 = X1) & pa(Y1, X2)) => qa(Y1, Y0))))))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['76'])). 139.46/20.62 tff('78', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 ( (exec(X2, body, X3) => 139.46/20.62 (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3)))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['77'])). 139.46/20.62 tff('79', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 (~ exec(X2, body, X3) 139.46/20.62 | (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['78'])). 139.46/20.62 tff('80', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 ( (((X2 = X1) & pa(X4, X2)) => qa(X4, X3)) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | ~ exec(X2, body, X3)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['79'])). 139.46/20.62 tff('81', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (~ ((X2 = X1) & pa(X4, X2)) 139.46/20.62 | qa(X4, X3) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['80'])). 139.46/20.62 tff('82', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (X2 != X1 139.46/20.62 | ~ pa(X4, X2) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | qa(X4, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['81'])). 139.46/20.62 tff('83', plain, 139.46/20.62 ![X1 : state, X3 : state, X4 : a]: 139.46/20.62 ( qa(X4, X3) 139.46/20.62 | ~ exec(X1, body, X3) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | ~ pa(X4, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['82'])). 139.46/20.62 tff('84', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1)))))))))))) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1)))))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1))), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['28'])). 139.46/20.62 tff('85', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5129'(X1) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('86', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | (!!((^[Y0 : state]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 (exec(Y0, body, Y1) => 139.46/20.62 (!!((^[Y2 : a]: 139.46/20.62 (((Y0 = X1) & pa(Y2, Y0)) => qa(Y2, Y1))))))))))))), 139.46/20.62 inference('renaming', [status(thm)], ['84', '85'])). 139.46/20.62 tff('87', plain, 139.46/20.62 ![X1 : state, X2 : state]: 139.46/20.62 ( (!!((^[Y0 : state]: 139.46/20.62 (exec(X2, body, Y0) => 139.46/20.62 (!!((^[Y1 : a]: (((X2 = X1) & pa(Y1, X2)) => qa(Y1, Y0))))))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['86'])). 139.46/20.62 tff('88', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 ( (exec(X2, body, X3) => 139.46/20.62 (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3)))))) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1))), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['87'])). 139.46/20.62 tff('89', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state]: 139.46/20.62 (~ exec(X2, body, X3) 139.46/20.62 | (!!((^[Y0 : a]: (((X2 = X1) & pa(Y0, X2)) => qa(Y0, X3))))) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['88'])). 139.46/20.62 tff('90', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 ( (((X2 = X1) & pa(X4, X2)) => qa(X4, X3)) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ exec(X2, body, X3)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['89'])). 139.46/20.62 tff('91', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (~ ((X2 = X1) & pa(X4, X2)) 139.46/20.62 | qa(X4, X3) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['90'])). 139.46/20.62 tff('92', plain, 139.46/20.62 ![X1 : state, X2 : state, X3 : state, X4 : a]: 139.46/20.62 (X2 != X1 139.46/20.62 | ~ pa(X4, X2) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ exec(X2, body, X3) 139.46/20.62 | qa(X4, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['91'])). 139.46/20.62 tff('93', plain, 139.46/20.62 ![X1 : state, X3 : state, X4 : a]: 139.46/20.62 ( qa(X4, X3) 139.46/20.62 | ~ exec(X1, body, X3) 139.46/20.62 | exec('#sk5126'(X1), body, '#sk5127'(X1)) 139.46/20.62 | ~ '#form5129'(X1) 139.46/20.62 | ~ pa(X4, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['92'])). 139.46/20.62 tff('94', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( '#form5129'(X1) 139.46/20.62 | ~ (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((member1389040324_state( 139.46/20.62 produc64584659_state(Y1, X1), r) & 139.46/20.62 pa(Y0, Y1)) => 139.46/20.62 termi(body, Y1))))))))), 139.46/20.62 define([status(thm)])). 139.46/20.62 tff('95', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ (!!((^[Y0 : state]: 139.46/20.62 ((member1389040324_state(produc64584659_state(Y0, X1), r) & 139.46/20.62 pa('#sk5130'(X1), Y0)) => 139.46/20.62 termi(body, Y0))))) 139.46/20.62 | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['94'])). 139.46/20.62 tff('96', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 (~ ((member1389040324_state(produc64584659_state('#sk5131'(X1), X1), r) & 139.46/20.62 pa('#sk5130'(X1), '#sk5131'(X1))) => 139.46/20.62 termi(body, '#sk5131'(X1))) 139.46/20.62 | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_exists', [status(thm)], ['95'])). 139.46/20.62 tff('97', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (member1389040324_state(produc64584659_state('#sk5131'(X1), X1), r) & 139.46/20.62 pa('#sk5130'(X1), '#sk5131'(X1))) 139.46/20.62 | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['96'])). 139.46/20.62 tff('98', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( member1389040324_state(produc64584659_state('#sk5131'(X1), X1), r) 139.46/20.62 | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['97'])). 139.46/20.62 tff('99', plain, ('#sk1010' = x | '#sk1009' = x), 139.46/20.62 inference('lazy_cnf_or', [status(thm)], ['69'])). 139.46/20.62 tff('100', plain, 139.46/20.62 ![X1 : state]: (~ termi(body, '#sk5131'(X1)) | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['96'])). 139.46/20.62 tff('101', plain, 139.46/20.62 ![X1 : state]: ( pa('#sk5130'(X1), '#sk5131'(X1)) | '#form5129'(X1)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['97'])). 139.46/20.62 tff('102', plain, 139.46/20.62 ![X1 : state]: 139.46/20.62 ( (!!((^[Y0 : a]: 139.46/20.62 (!!((^[Y1 : state]: 139.46/20.62 ((pa(Y0, Y1) & (Y1 = X1)) => termi(body, Y1)))))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['75'])). 139.46/20.62 tff('103', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( (!!((^[Y0 : state]: ((pa(X2, Y0) & (Y0 = X1)) => termi(body, Y0))))) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['102'])). 139.46/20.62 tff('104', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 ( ((pa(X2, X3) & (X3 = X1)) => termi(body, X3)) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_forall', [status(thm)], ['103'])). 139.46/20.62 tff('105', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (~ (pa(X2, X3) & (X3 = X1)) 139.46/20.62 | termi(body, X3) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r)), 139.46/20.62 inference('lazy_cnf_imply', [status(thm)], ['104'])). 139.46/20.62 tff('106', plain, 139.46/20.62 ![X1 : state, X2 : a, X3 : state]: 139.46/20.62 (~ pa(X2, X3) 139.46/20.62 | X3 != X1 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | termi(body, X3)), 139.46/20.62 inference('lazy_cnf_and', [status(thm)], ['105'])). 139.46/20.62 tff('107', plain, 139.46/20.62 ![X1 : state, X2 : a]: 139.46/20.62 ( termi(body, X1) 139.46/20.62 | ~ member1389040324_state(produc64584659_state(X1, x), r) 139.46/20.62 | ~ pa(X2, X1)), 139.46/20.62 inference('simplify', [status(thm)], ['106'])). 139.46/20.62 tff('108', plain, $false, 139.46/20.62 inference('eprover', [status(thm)], 139.46/20.62 ['9', '10', '16', '17', '18', '40', '41', '49', '52', '62', 139.46/20.62 '63', '67', '70', '71', '72', '83', '93', '98', '99', '100', 139.46/20.62 '101', '107'])). 139.46/20.62 139.46/20.62 % SZS output end Refutation 139.46/20.62 139.46/20.62 139.46/20.62 % Terminating... 139.46/20.70 % Runner terminated. 139.46/20.71 % Zipperpin 1.5 exiting 139.46/20.72 EOF