0.06/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.11 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.qQBSEzxFha 0.10/0.32 % Computer : n021.cluster.edu 0.10/0.32 % Model : x86_64 x86_64 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.32 % Memory : 8042.1875MB 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.32 % CPULimit : 1200 0.10/0.32 % DateTime : Tue Jul 13 15:52:56 EDT 2021 0.10/0.32 % CPUTime : 0.10/0.32 % Running portfolio for 120 s 0.10/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.10/0.32 % Number of cores: 8 0.10/0.32 % Python version: Python 3.6.8 0.10/0.32 % Running in HO mode 0.44/0.57 % Estimated wc time : 1286 0.44/0.57 % Estimated cpu time (7 cpus) : 183.71428571428572 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.46/0.66 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.46/0.67 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.46/0.67 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 0.47/1.00 % Solved by lams/s6.ds.sh. 0.47/1.00 % done 135 iterations in 0.300s 0.47/1.00 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.47/1.00 % SZS output start Refutation 0.47/1.00 tff(conj_thm_2Einteger_2EINT__DIVIDES__RSUB, conjecture, 0.47/1.00 (![V0p:tp__ty_2Einteger_2Eint,V1q:tp__ty_2Einteger_2Eint, 0.47/1.00 V2r:tp__ty_2Einteger_2Eint]: 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))) => 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V2r))) <=> 0.47/1.00 p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V2r)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q)))))))). 0.47/1.00 tff(zf_stmt_0, negated_conjecture, 0.47/1.00 (~ 0.47/1.00 (![V0p:tp__ty_2Einteger_2Eint,V1q:tp__ty_2Einteger_2Eint, 0.47/1.00 V2r:tp__ty_2Einteger_2Eint]: 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))) => 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V2r))) <=> 0.47/1.00 p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(V2r)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))))))))). 0.47/1.00 tff('0', plain, 0.47/1.00 ~ (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y2))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__sub, 0.47/1.00 inj__ty_2Einteger_2Eint(Y2)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))))))))), 0.47/1.00 inference('cnf', [status(esa)], [zf_stmt_0])). 0.47/1.00 tff('1', plain, 0.47/1.00 ~ (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__sub, 0.47/1.00 inj__ty_2Einteger_2Eint(Y1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))))))))))), 0.47/1.00 inference('lazy_cnf_exists', [status(thm)], ['0'])). 0.47/1.00 tff('2', plain, 0.47/1.00 ~ (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3'))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3'))))))))), 0.47/1.00 inference('lazy_cnf_exists', [status(thm)], ['1'])). 0.47/1.00 tff('3', plain, 0.47/1.00 ~ (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3'))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint('#sk4')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3')))))), 0.47/1.00 inference('lazy_cnf_exists', [status(thm)], ['2'])). 0.47/1.00 tff('4', plain, 0.47/1.00 ~ (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))) <=> 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint('#sk4')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3'))))), 0.47/1.00 inference('lazy_cnf_imply', [status(thm)], ['3'])). 0.47/1.00 tff('5', plain, 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))) 0.47/1.00 != p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint('#sk4')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3')))), 0.47/1.00 inference('simplify nested equalities', [status(thm)], ['4'])). 0.47/1.00 tff(stp_eq_fo_c_2Einteger_2Eint__sub, axiom, 0.47/1.00 (![X0:tp__ty_2Einteger_2Eint,X1:tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X0,X1)) = 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub,inj__ty_2Einteger_2Eint(X0)), 0.47/1.00 inj__ty_2Einteger_2Eint(X1))))). 0.47/1.00 tff('6', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint( 0.47/1.00 fo__c_2Einteger_2Eint__sub(Y0, Y1)) = 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))), 0.47/1.00 inference('cnf', [status(esa)], [stp_eq_fo_c_2Einteger_2Eint__sub])). 0.47/1.00 tff('7', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X1, Y0)) = 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['6'])). 0.47/1.00 tff('8', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X1, X2)) 0.47/1.00 = ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['7'])). 0.47/1.00 tff('9', plain, 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))) 0.47/1.00 != p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint( 0.47/1.00 fo__c_2Einteger_2Eint__sub('#sk4', '#sk3')))), 0.47/1.00 inference('demod', [status(thm)], ['5', '8'])). 0.47/1.00 tff('10', plain, 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk3'))), 0.47/1.00 inference('lazy_cnf_imply', [status(thm)], ['3'])). 0.47/1.00 tff(conj_thm_2Einteger_2EINT__DIVIDES__NEG, axiom, 0.47/1.00 (![V0p:tp__ty_2Einteger_2Eint,V1q:tp__ty_2Einteger_2Eint]: 0.47/1.00 ((p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))) <=> 0.47/1.00 p(ap(ap(c_2Einteger_2Eint__divides, 0.47/1.00 ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V0p))), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q)))) & 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(V1q)))) <=> 0.47/1.00 p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))))))). 0.47/1.00 tff('11', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 ((p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 ap(c_2Einteger_2Eint__neg, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1)))) & 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, 0.47/1.00 inj__ty_2Einteger_2Eint(Y1)))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))))), 0.47/1.00 inference('cnf', [status(esa)], [conj_thm_2Einteger_2EINT__DIVIDES__NEG])). 0.47/1.00 tff('12', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 ((p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X1))), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))) & 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(Y0)))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['11'])). 0.47/1.00 tff('13', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 ((p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X1))), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))) & 0.47/1.00 (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X2)))) <=> 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['12'])). 0.47/1.00 tff('14', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X2)))) <=> 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))), 0.47/1.00 inference('lazy_cnf_and', [status(thm)], ['13'])). 0.47/1.00 tff('15', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X2)))) 0.47/1.00 = p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))), 0.47/1.00 inference('simplify nested equalities', [status(thm)], ['14'])). 0.47/1.00 tff(stp_eq_fo_c_2Einteger_2Eint__neg, axiom, 0.47/1.00 (![X0:tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X0)) = 0.47/1.00 ap(c_2Einteger_2Eint__neg,inj__ty_2Einteger_2Eint(X0))))). 0.47/1.00 tff('16', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(Y0)) = 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(Y0)))))), 0.47/1.00 inference('cnf', [status(esa)], [stp_eq_fo_c_2Einteger_2Eint__neg])). 0.47/1.00 tff('17', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X1)) 0.47/1.00 = ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['16'])). 0.47/1.00 tff('18', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X2)))) 0.47/1.00 = p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))), 0.47/1.00 inference('demod', [status(thm)], ['15', '17'])). 0.47/1.00 tff(conj_thm_2Einteger_2EINT__DIVIDES__RADD, axiom, 0.47/1.00 (![V0p:tp__ty_2Einteger_2Eint,V1q:tp__ty_2Einteger_2Eint, 0.47/1.00 V2r:tp__ty_2Einteger_2Eint]: 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q))) => 0.47/1.00 (p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(V2r)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1q)))) <=> 0.47/1.00 p(ap(ap(c_2Einteger_2Eint__divides,inj__ty_2Einteger_2Eint(V0p)), 0.47/1.00 inj__ty_2Einteger_2Eint(V2r))))))). 0.47/1.00 tff('19', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__add, 0.47/1.00 inj__ty_2Einteger_2Eint(Y2)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1)))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y2)))))))))))))), 0.47/1.00 inference('cnf', [status(esa)], [conj_thm_2Einteger_2EINT__DIVIDES__RADD])). 0.47/1.00 tff('20', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__add, 0.47/1.00 inj__ty_2Einteger_2Eint(Y1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['19'])). 0.47/1.00 tff('21', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) => 0.47/1.00 (p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))) <=> 0.47/1.00 p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, 0.47/1.00 inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['20'])). 0.47/1.00 tff('22', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint, 0.47/1.00 X3 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) => 0.47/1.00 (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X3)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))) <=> 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X3))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['21'])). 0.47/1.00 tff('23', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint, 0.47/1.00 X3 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (~ p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) 0.47/1.00 | (p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X3)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))) <=> 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X3))))), 0.47/1.00 inference('lazy_cnf_imply', [status(thm)], ['22'])). 0.47/1.00 tff('24', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint, 0.47/1.00 X3 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (~ p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) 0.47/1.00 | p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X3)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))) 0.47/1.00 = p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X3)))), 0.47/1.00 inference('simplify nested equalities', [status(thm)], ['23'])). 0.47/1.00 tff(stp_eq_fo_c_2Einteger_2Eint__add, axiom, 0.47/1.00 (![X0:tp__ty_2Einteger_2Eint,X1:tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X0,X1)) = 0.47/1.00 ap(ap(c_2Einteger_2Eint__add,inj__ty_2Einteger_2Eint(X0)), 0.47/1.00 inj__ty_2Einteger_2Eint(X1))))). 0.47/1.00 tff('25', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint( 0.47/1.00 fo__c_2Einteger_2Eint__add(Y0, Y1)) = 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))), 0.47/1.00 inference('cnf', [status(esa)], [stp_eq_fo_c_2Einteger_2Eint__add])). 0.47/1.00 tff('26', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X1, Y0)) = 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['25'])). 0.47/1.00 tff('27', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X1, X2)) 0.47/1.00 = ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['26'])). 0.47/1.00 tff('28', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint, 0.47/1.00 X3 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (~ p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) 0.47/1.00 | p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X3, X2)))) 0.47/1.00 = p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X3)))), 0.47/1.00 inference('demod', [status(thm)], ['24', '27'])). 0.47/1.00 tff('29', plain, 0.47/1.00 ![X0 : tp__ty_2Einteger_2Eint, X1 : tp__ty_2Einteger_2Eint, 0.47/1.00 X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (~ p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X0))) 0.47/1.00 | p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint( 0.47/1.00 fo__c_2Einteger_2Eint__add(X2, fo__c_2Einteger_2Eint__neg(X0))))) 0.47/1.00 = p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))), 0.47/1.00 inference('sup-', [status(thm)], ['18', '28'])). 0.47/1.00 tff(ax_thm_2Einteger_2Eint__sub, axiom, 0.47/1.00 (![V0x:tp__ty_2Einteger_2Eint,V1y:tp__ty_2Einteger_2Eint]: 0.47/1.00 (surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__sub, 0.47/1.00 inj__ty_2Einteger_2Eint(V0x)), 0.47/1.00 inj__ty_2Einteger_2Eint(V1y))) = 0.47/1.00 surj__ty_2Einteger_2Eint(ap(ap(c_2Einteger_2Eint__add, 0.47/1.00 inj__ty_2Einteger_2Eint(V0x)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, 0.47/1.00 inj__ty_2Einteger_2Eint(V1y))))))). 0.47/1.00 tff('30', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (surj__ty_2Einteger_2Eint( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__sub, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))) = 0.47/1.00 surj__ty_2Einteger_2Eint( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__add, 0.47/1.00 inj__ty_2Einteger_2Eint(Y0)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, 0.47/1.00 inj__ty_2Einteger_2Eint(Y1))))))))))), 0.47/1.00 inference('cnf', [status(esa)], [ax_thm_2Einteger_2Eint__sub])). 0.47/1.00 tff('31', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (surj__ty_2Einteger_2Eint( 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(Y0))) = 0.47/1.00 surj__ty_2Einteger_2Eint( 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(Y0)))))))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['30'])). 0.47/1.00 tff('32', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 surj__ty_2Einteger_2Eint( 0.47/1.00 ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2))) 0.47/1.00 = surj__ty_2Einteger_2Eint( 0.47/1.00 ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X2)))), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['31'])). 0.47/1.00 tff('33', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X1, X2)) 0.47/1.00 = ap(ap(c_2Einteger_2Eint__sub, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['7'])). 0.47/1.00 tff(stp_inj_surj_ty_2Einteger_2Eint, axiom, 0.47/1.00 (![X:tp__ty_2Einteger_2Eint]: 0.47/1.00 (surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X)) = X))). 0.47/1.00 tff('34', plain, 0.47/1.00 (!!((^[Y0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(Y0)) = Y0)))), 0.47/1.00 inference('cnf', [status(esa)], [stp_inj_surj_ty_2Einteger_2Eint])). 0.47/1.00 tff('35', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X1)) = X1, 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['34'])). 0.47/1.00 tff('36', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__neg(X1)) 0.47/1.00 = ap(c_2Einteger_2Eint__neg, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['16'])). 0.47/1.00 tff('37', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__add(X1, X2)) 0.47/1.00 = ap(ap(c_2Einteger_2Eint__add, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)), 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['26'])). 0.47/1.00 tff('38', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint]: 0.47/1.00 surj__ty_2Einteger_2Eint(inj__ty_2Einteger_2Eint(X1)) = X1, 0.47/1.00 inference('lazy_cnf_forall', [status(thm)], ['34'])). 0.47/1.00 tff('39', plain, 0.47/1.00 ![X1 : tp__ty_2Einteger_2Eint, X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 fo__c_2Einteger_2Eint__sub(X1, X2) 0.47/1.00 = fo__c_2Einteger_2Eint__add(X1, fo__c_2Einteger_2Eint__neg(X2)), 0.47/1.00 inference('demod', [status(thm)], ['32', '33', '35', '36', '37', '38'])). 0.47/1.00 tff('40', plain, 0.47/1.00 ![X0 : tp__ty_2Einteger_2Eint, X1 : tp__ty_2Einteger_2Eint, 0.47/1.00 X2 : tp__ty_2Einteger_2Eint]: 0.47/1.00 (~ p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X0))) 0.47/1.00 | p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X2, X0)))) 0.47/1.00 = p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint(X1)), 0.47/1.00 inj__ty_2Einteger_2Eint(X2)))), 0.47/1.00 inference('demod', [status(thm)], ['29', '39'])). 0.47/1.00 tff('41', plain, 0.47/1.00 ![X0 : tp__ty_2Einteger_2Eint]: 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint(fo__c_2Einteger_2Eint__sub(X0, '#sk3')))) 0.47/1.00 = p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint(X0))), 0.47/1.00 inference('sup-', [status(thm)], ['10', '40'])). 0.47/1.00 tff('42', plain, 0.47/1.00 p( 0.47/1.00 ap(ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))) 0.47/1.00 != p( 0.47/1.00 ap( 0.47/1.00 ap(c_2Einteger_2Eint__divides, inj__ty_2Einteger_2Eint('#sk2')), 0.47/1.00 inj__ty_2Einteger_2Eint('#sk4'))), 0.47/1.00 inference('demod', [status(thm)], ['9', '41'])). 0.47/1.00 tff('43', plain, $false, inference('simplify', [status(thm)], ['42'])). 0.47/1.00 0.47/1.00 % SZS output end Refutation 0.47/1.00 0.47/1.00 0.47/1.00 % Terminating... 1.66/1.10 % Runner terminated. 1.66/1.10 % Zipperpin 1.5 exiting 1.66/1.12 EOF