%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU683^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:52:43 AM UTC 2026 % Result : Theorem 0.62s 0.81s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU683^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n014.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:47:13 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.62/0.81 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.81 % SZS status Theorem % 0.62/0.81 % SZS output start Proof % 0.62/0.81 ( % 0.62/0.81 (declare-sort $$unsorted 0) % 0.62/0.81 (declare-const tptp.emptyset $$unsorted) % 0.62/0.81 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.62/0.81 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.62/0.81 (declare-const tptp.uniqinunit Bool) % 0.62/0.81 (declare-const tptp.dsetconstrI Bool) % 0.62/0.81 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.62/0.81 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.62/0.81 (define @t1 () (@var "Xy" $$unsorted)) % 0.62/0.81 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.62/0.81 (define @t3 () (_ @t2 @t1)) % 0.62/0.81 (define @t4 () (@list @t1)) % 0.62/0.81 (define @t5 () (lambda @t4 @t3)) % 0.62/0.81 (define @t6 () (@var "A" $$unsorted)) % 0.62/0.81 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.62/0.81 (define @t8 () (_ @t7 @t5)) % 0.62/0.81 (define @t9 () (@var "Xx" $$unsorted)) % 0.62/0.81 (define @t10 () (_ tptp.in @t9)) % 0.62/0.81 (define @t11 () (_ @t10 @t8)) % 0.62/0.81 (define @t12 () (_ @t2 @t9)) % 0.62/0.81 (define @t13 () (=> @t12 @t11)) % 0.62/0.81 (define @t14 () (_ @t10 @t6)) % 0.62/0.81 (define @t15 () (@list @t6 @t2 @t9)) % 0.62/0.81 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.62/0.81 (define @t17 () (= tptp.dsetconstrI @t16)) % 0.62/0.81 (define @t18 () (= @t9 @t1)) % 0.62/0.81 (define @t19 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.62/0.81 (define @t20 () (_ @t10 @t19)) % 0.62/0.81 (define @t21 () (@list @t9 @t1)) % 0.62/0.81 (define @t22 () (forall @t21 (=> @t20 @t18))) % 0.62/0.81 (define @t23 () (= tptp.uniqinunit @t22)) % 0.62/0.81 (define @t24 () (=> @t3 @t18)) % 0.62/0.81 (define @t25 () (=> @t12 @t24)) % 0.62/0.81 (define @t26 () (_ (_ tptp.in @t1) @t6)) % 0.62/0.81 (define @t27 () (forall @t4 (=> @t26 @t25))) % 0.62/0.81 (define @t28 () (=> @t14 @t27)) % 0.62/0.81 (define @t29 () (@list @t9)) % 0.62/0.81 (define @t30 () (forall @t29 @t28)) % 0.62/0.81 (define @t31 () (lambda @t29 @t12)) % 0.62/0.81 (define @t32 () (=> (_ (_ tptp.ex1 @t6) @t31) @t30)) % 0.62/0.81 (define @t33 () (@list @t6 @t2)) % 0.62/0.81 (define @t34 () (forall @t33 @t32)) % 0.62/0.81 (define @t35 () (=> tptp.uniqinunit @t34)) % 0.62/0.81 (define @t36 () (=> tptp.dsetconstrI @t35)) % 0.62/0.81 (define @t37 () (not @t36)) % 0.62/0.81 (define @t38 () (_ (_ tptp.setadjoin @t9) tptp.emptyset)) % 0.62/0.81 (define @t39 () (= @t6 @t38)) % 0.62/0.81 (define @t40 () (and @t14 @t39)) % 0.62/0.81 (define @t41 () (exists @t29 @t40)) % 0.62/0.81 (define @t42 () (@list @t6)) % 0.62/0.81 (define @t43 () (lambda @t42 @t41)) % 0.62/0.81 (define @t44 () (_ @t7 @t31)) % 0.62/0.81 (define @t45 () (lambda @t33 (_ tptp.singleton @t44))) % 0.62/0.81 (define @t46 () (@var "BOUND_VARIABLE_7673" $$unsorted)) % 0.62/0.81 (define @t47 () (@var "BOUND_VARIABLE_7671" $$unsorted)) % 0.62/0.81 (define @t48 () (= @t47 @t46)) % 0.62/0.81 (define @t49 () (not (_ @t2 @t46))) % 0.62/0.81 (define @t50 () (not (tptp.in @t46 @t6))) % 0.62/0.81 (define @t51 () (not (_ @t2 @t47))) % 0.62/0.81 (define @t52 () (not (tptp.in @t47 @t6))) % 0.62/0.81 (define @t53 () (@var "BOUND_VARIABLE_7663" $$unsorted)) % 0.62/0.81 (define @t54 () (tptp.setadjoin @t53 tptp.emptyset)) % 0.62/0.81 (define @t55 () (tptp.dsetconstr @t6 @t2)) % 0.62/0.81 (define @t56 () (not (tptp.in @t53 @t55))) % 0.62/0.81 (define @t57 () (@list @t6 @t2 @t53 @t47 @t46)) % 0.62/0.81 (define @t58 () (forall @t57 (or @t56 (not (= @t55 @t54)) @t52 @t51 @t50 @t49 @t48))) % 0.62/0.81 (define @t59 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.62/0.81 (define @t60 () (tptp.in @t9 @t59)) % 0.62/0.81 (define @t61 () (not @t20)) % 0.62/0.81 (define @t62 () (or @t61 @t18)) % 0.62/0.81 (define @t63 () (=> tptp.uniqinunit @t58)) % 0.62/0.81 (define @t64 () (_ @t2 @t1)) % 0.62/0.81 (define @t65 () (lambda @t4 @t64)) % 0.62/0.81 (define @t66 () (tptp.dsetconstr @t6 @t65)) % 0.62/0.81 (define @t67 () (tptp.in @t9 @t66)) % 0.62/0.81 (define @t68 () (_ @t2 @t9)) % 0.62/0.81 (define @t69 () (not @t68)) % 0.62/0.81 (define @t70 () (tptp.in @t9 @t6)) % 0.62/0.81 (define @t71 () (not @t70)) % 0.62/0.81 (define @t72 () (or @t71 @t69 @t67)) % 0.62/0.81 (define @t73 () (not @t12)) % 0.62/0.81 (define @t74 () (not @t14)) % 0.62/0.81 (define @t75 () (or @t74 @t73 @t11)) % 0.62/0.81 (define @t76 () (=> tptp.dsetconstrI @t63)) % 0.62/0.81 (define @t77 () (not (= @t54 @t55))) % 0.62/0.81 (define @t78 () (or @t56 @t77 @t52 @t51 @t50 @t49 @t48)) % 0.62/0.81 (define @t79 () (or @t52 @t51 @t50 @t49 @t48)) % 0.62/0.81 (define @t80 () (or @t56 @t77)) % 0.62/0.81 (define @t81 () (or @t80 @t79)) % 0.62/0.81 (define @t82 () (forall @t57 @t81)) % 0.62/0.81 (define @t83 () (forall (@list @t53 @t47 @t46) @t81)) % 0.62/0.81 (define @t84 () (forall (@list @t47 @t46) @t79)) % 0.62/0.81 (define @t85 () (@var "BOUND_VARIABLE_7646" $$unsorted)) % 0.62/0.81 (define @t86 () (forall (@list @t53) @t80)) % 0.62/0.81 (define @t87 () (@list @t9)) % 0.62/0.81 (define @t88 () (or @t86 @t84)) % 0.62/0.81 (define @t89 () (= @t9 @t85)) % 0.62/0.81 (define @t90 () (not (_ @t2 @t85))) % 0.62/0.81 (define @t91 () (not (tptp.in @t85 @t6))) % 0.62/0.81 (define @t92 () (or @t71 @t69 @t91 @t90 @t89)) % 0.62/0.81 (define @t93 () (@list @t9 @t85)) % 0.62/0.81 (define @t94 () (forall @t93 @t92)) % 0.62/0.81 (define @t95 () (tptp.setadjoin @t9 tptp.emptyset)) % 0.62/0.81 (define @t96 () (forall @t29 (or (not (tptp.in @t9 @t55)) (not (= @t95 @t55))))) % 0.62/0.81 (define @t97 () (not @t96)) % 0.62/0.81 (define @t98 () (or @t91 @t90 @t89)) % 0.62/0.81 (define @t99 () (or @t71 @t69 @t98)) % 0.62/0.81 (define @t100 () (forall @t93 @t99)) % 0.62/0.81 (define @t101 () (@list @t85)) % 0.62/0.81 (define @t102 () (forall @t101 @t99)) % 0.62/0.81 (define @t103 () (forall @t101 @t98)) % 0.62/0.81 (define @t104 () (or @t71 @t69 @t103)) % 0.62/0.81 (define @t105 () (tptp.in @t1 @t6)) % 0.62/0.81 (define @t106 () (forall @t4 (or (not @t105) (not @t64) @t18))) % 0.62/0.81 (define @t107 () (or @t74 @t73 @t106)) % 0.62/0.81 (define @t108 () (or @t73 @t106)) % 0.62/0.81 (define @t109 () (not @t3)) % 0.62/0.81 (define @t110 () (not @t26)) % 0.62/0.81 (define @t111 () (or @t110 @t109 @t18)) % 0.62/0.81 (define @t112 () (forall @t4 @t111)) % 0.62/0.81 (define @t113 () (or @t73 @t112)) % 0.62/0.81 (define @t114 () (or @t73 @t111)) % 0.62/0.81 (define @t115 () (or @t110 @t73 @t109 @t18)) % 0.62/0.81 (define @t116 () (or @t73 @t109 @t18)) % 0.62/0.81 (define @t117 () (@var "BOUND_VARIABLE_7604" $$unsorted)) % 0.62/0.81 (define @t118 () (_ @t2 @t117)) % 0.62/0.81 (define @t119 () (@list @t117)) % 0.62/0.81 (define @t120 () (lambda @t119 @t118)) % 0.62/0.81 (define @t121 () (tptp.dsetconstr @t6 @t120)) % 0.62/0.81 (define @t122 () (= @t95 @t121)) % 0.62/0.81 (define @t123 () (not @t122)) % 0.62/0.81 (define @t124 () (tptp.in @t9 @t121)) % 0.62/0.81 (define @t125 () (not @t124)) % 0.62/0.81 (define @t126 () (or @t125 @t123)) % 0.62/0.81 (define @t127 () (_ @t2 @t117)) % 0.62/0.81 (define @t128 () (lambda @t119 @t127)) % 0.62/0.81 (define @t129 () (tptp.dsetconstr @t6 @t128)) % 0.62/0.81 (define @t130 () (= @t95 @t129)) % 0.62/0.81 (define @t131 () (not @t130)) % 0.62/0.81 (define @t132 () (tptp.in @t9 @t129)) % 0.62/0.81 (define @t133 () (not @t132)) % 0.62/0.81 (define @t134 () (or @t133 @t131)) % 0.62/0.81 (define @t135 () (tptp.dsetconstr @t6 @t31)) % 0.62/0.81 (define @t136 () (= @t95 @t135)) % 0.62/0.81 (define @t137 () (not @t136)) % 0.62/0.81 (define @t138 () (tptp.in @t9 @t135)) % 0.62/0.81 (define @t139 () (not @t138)) % 0.62/0.81 (define @t140 () (or @t139 @t137)) % 0.62/0.81 (define @t141 () (forall @t29 @t140)) % 0.62/0.81 (define @t142 () (not @t141)) % 0.62/0.81 (define @t143 () (lambda (@list @t2) @t97)) % 0.62/0.81 (define @t144 () (_ (lambda @t33 @t97) @t6)) % 0.62/0.81 (define @t145 () (=> (_ @t144 @t31) @t30)) % 0.62/0.81 (define @t146 () (forall @t33 @t145)) % 0.62/0.81 (define @t147 () (=> tptp.uniqinunit @t146)) % 0.62/0.81 (define @t148 () (=> tptp.dsetconstrI @t147)) % 0.62/0.81 (define @t149 () (@var "BOUND_VARIABLE_7496" $$unsorted)) % 0.62/0.81 (define @t150 () (_ @t2 @t149)) % 0.62/0.81 (define @t151 () (@list @t149)) % 0.62/0.81 (define @t152 () (lambda @t151 @t150)) % 0.62/0.81 (define @t153 () (tptp.dsetconstr @t6 @t152)) % 0.62/0.81 (define @t154 () (= @t95 @t153)) % 0.62/0.81 (define @t155 () (not @t154)) % 0.62/0.81 (define @t156 () (tptp.in @t9 @t153)) % 0.62/0.81 (define @t157 () (not @t156)) % 0.62/0.81 (define @t158 () (or @t157 @t155)) % 0.62/0.81 (define @t159 () (_ @t2 @t149)) % 0.62/0.81 (define @t160 () (lambda @t151 @t159)) % 0.62/0.81 (define @t161 () (_ @t7 @t160)) % 0.62/0.81 (define @t162 () (= @t95 @t161)) % 0.62/0.81 (define @t163 () (not @t162)) % 0.62/0.81 (define @t164 () (tptp.in @t9 @t161)) % 0.62/0.81 (define @t165 () (not @t164)) % 0.62/0.81 (define @t166 () (or @t165 @t163)) % 0.62/0.81 (define @t167 () (= @t95 @t44)) % 0.62/0.81 (define @t168 () (not @t167)) % 0.62/0.81 (define @t169 () (tptp.in @t9 @t44)) % 0.62/0.81 (define @t170 () (not @t169)) % 0.62/0.81 (define @t171 () (or @t170 @t168)) % 0.62/0.81 (define @t172 () (not (= @t44 @t95))) % 0.62/0.81 (define @t173 () (or @t170 @t172)) % 0.62/0.81 (define @t174 () (forall @t29 @t173)) % 0.62/0.81 (define @t175 () (not @t174)) % 0.62/0.81 (define @t176 () (not @t39)) % 0.62/0.81 (define @t177 () (or @t74 @t176)) % 0.62/0.81 (define @t178 () (forall @t29 (not @t40))) % 0.62/0.81 (define @t179 () (not @t178)) % 0.62/0.81 (define @t180 () (@quantifiers_skolemize @t58 4)) % 0.62/0.81 (define @t181 () (@quantifiers_skolemize @t58 1)) % 0.62/0.81 (define @t182 () (@quantifiers_skolemize @t58 0)) % 0.62/0.81 (define @t183 () (_ @t181 @t180)) % 0.62/0.81 (define @t184 () (@quantifiers_skolemize @t58 3)) % 0.62/0.81 (define @t185 () (= @t184 @t180)) % 0.62/0.81 (define @t186 () (not @t183)) % 0.62/0.81 (define @t187 () (tptp.in @t180 @t182)) % 0.62/0.81 (define @t188 () (not @t187)) % 0.62/0.81 (define @t189 () (_ @t181 @t184)) % 0.62/0.81 (define @t190 () (not @t189)) % 0.62/0.81 (define @t191 () (tptp.in @t184 @t182)) % 0.62/0.81 (define @t192 () (not @t191)) % 0.62/0.81 (define @t193 () (@quantifiers_skolemize @t58 2)) % 0.62/0.81 (define @t194 () (tptp.setadjoin @t193 tptp.emptyset)) % 0.62/0.81 (define @t195 () (tptp.dsetconstr @t182 @t181)) % 0.62/0.81 (define @t196 () (= @t195 @t194)) % 0.62/0.81 (define @t197 () (not @t196)) % 0.62/0.81 (define @t198 () (or (not (tptp.in @t193 @t195)) @t197 @t192 @t190 @t188 @t186 @t185)) % 0.62/0.81 (define @t199 () (@list true)) % 0.62/0.81 (define @t200 () (@list @t198)) % 0.62/0.81 (define @t201 () (tptp.in @t180 @t195)) % 0.62/0.81 (define @t202 () (or @t188 @t186 @t201)) % 0.62/0.81 (define @t203 () (@list false false false)) % 0.62/0.81 (define @t204 () (tptp.in @t180 @t194)) % 0.62/0.81 (define @t205 () (not @t204)) % 0.62/0.81 (define @t206 () (or @t205 (= @t180 @t193))) % 0.62/0.81 (define @t207 () (forall @t21 (or (not @t60) @t18))) % 0.62/0.81 (define @t208 () (= @t193 @t180)) % 0.62/0.81 (define @t209 () (or @t205 @t208)) % 0.62/0.81 (define @t210 () (@list false)) % 0.62/0.81 (define @t211 () (@list @t207)) % 0.62/0.81 (define @t212 () (tptp.in @t184 @t194)) % 0.62/0.81 (define @t213 () (not @t212)) % 0.62/0.81 (define @t214 () (or @t213 (= @t184 @t193))) % 0.62/0.81 (define @t215 () (= @t193 @t184)) % 0.62/0.81 (define @t216 () (or @t213 @t215)) % 0.62/0.81 (define @t217 () (tptp.in @t184 @t195)) % 0.62/0.81 (define @t218 () (or @t192 @t190 @t217)) % 0.62/0.81 (assume @p1 @t17) % 0.62/0.81 (assume @p2 @t23) % 0.62/0.81 (assume @p3 @t37) % 0.62/0.81 (assume @p4 true) % 0.62/0.81 (step @p5 (= tptp.singleton @t43) :rule refl :args (@t43)) % 0.62/0.81 (step @p6 (= tptp.ex1 @t45) :rule refl :args (@t45)) % 0.62/0.81 (step @p7 :rule evaluate :args ((= false true))) % 0.62/0.81 (step @p8 :rule refl :args (@t58)) % 0.62/0.81 (step @p9 :rule refl :args (@t18)) % 0.62/0.81 (step @p10 :rule refl :args ((tptp.in @t9 @t19))) % 0.62/0.81 (step @p11 :rule refl :args (@t59)) % 0.62/0.81 (step @p12 :rule refl :args (@t9)) % 0.62/0.81 (step @p13 :rule cong :premises (@p12 @p11) :args (@t60)) % 0.62/0.81 (step @p14 :rule trans :premises (@p13 @p10)) % 0.62/0.81 (step @p15 :rule refl :args (@t10)) % 0.62/0.81 (step @p16 :rule ho_cong :premises (@p15 @p11)) % 0.62/0.81 (step @p17 :rule cong :premises (@p16 @p14) :args ((= (_ @t10 @t59) @t60))) % 0.62/0.81 (step @p18 :rule symm :premises (@p17)) % 0.62/0.81 (step @p19 :rule refl :args (@t20)) % 0.62/0.81 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 0.62/0.81 (step @p21 :rule refl :args (@t19)) % 0.62/0.81 (step @p22 :rule cong :premises (@p21 @p11) :args ((= @t19 @t59))) % 0.62/0.81 (step @p23 :rule symm :premises (@p22)) % 0.62/0.81 (step @p24 :rule eq_resolve :premises (@p21 @p23)) % 0.62/0.81 (step @p25 :rule ho_cong :premises (@p15 @p24)) % 0.62/0.81 (step @p26 :rule trans :premises (@p25 @p20)) % 0.62/0.81 (step @p27 :rule cong :premises (@p26) :args (@t61)) % 0.62/0.81 (step @p28 :rule nary_cong :premises (@p27 @p9) :args (@t62)) % 0.62/0.81 (step @p29 :rule cong :premises (@p28) :args ((forall @t21 @t62))) % 0.62/0.81 (step @p30 :rule bool-impl-elim :args (@t20 @t18)) % 0.62/0.81 (step @p31 :rule cong :premises (@p30) :args (@t22)) % 0.62/0.81 (step @p32 :rule trans :premises (@p31 @p29)) % 0.62/0.81 (step @p33 :rule refl :args (tptp.uniqinunit)) % 0.62/0.81 (step @p34 :rule cong :premises (@p33 @p32) :args (@t23)) % 0.62/0.81 (step @p35 :rule eq_resolve :premises (@p2 @p34)) % 0.62/0.81 (step @p36 :rule cong :premises (@p35 @p8) :args (@t63)) % 0.62/0.81 (step @p37 :rule lambda-elim :args ((= @t65 @t2))) % 0.62/0.81 (step @p38 :rule refl :args (@t6)) % 0.62/0.81 (step @p39 :rule cong :premises (@p38 @p37) :args (@t66)) % 0.62/0.81 (step @p40 :rule refl :args (@t9)) % 0.62/0.81 (step @p41 :rule cong :premises (@p40 @p39) :args (@t67)) % 0.62/0.81 (step @p42 :rule refl :args (@t69)) % 0.62/0.81 (step @p43 :rule refl :args (@t71)) % 0.62/0.81 (step @p44 :rule nary_cong :premises (@p43 @p42 @p41) :args (@t72)) % 0.62/0.81 (step @p45 :rule cong :premises (@p44) :args ((forall @t15 @t72))) % 0.62/0.81 (step @p46 :rule refl :args ((tptp.in @t9 @t8))) % 0.62/0.81 (step @p47 :rule refl :args ((tptp.dsetconstr @t6 @t5))) % 0.62/0.81 (step @p48 :rule refl :args (@t64)) % 0.62/0.81 (step @p49 :rule cong :premises (@p48) :args (@t65)) % 0.62/0.81 (step @p50 :rule refl :args (@t6)) % 0.62/0.81 (step @p51 :rule cong :premises (@p50 @p49) :args (@t66)) % 0.62/0.81 (step @p52 :rule trans :premises (@p51 @p47)) % 0.62/0.81 (step @p53 :rule cong :premises (@p12 @p52) :args (@t67)) % 0.62/0.81 (step @p54 :rule trans :premises (@p53 @p46)) % 0.62/0.81 (step @p55 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:rule nary_cong :premises (@p86 @p294) :args (@t177)) % 0.62/0.81 (step @p296 :rule cong :premises (@p295) :args ((forall @t29 @t177))) % 0.62/0.81 (step @p297 :rule bool-and-de-morgan :args (@t14 @t39 true)) % 0.62/0.81 (step @p298 :rule cong :premises (@p297) :args (@t178)) % 0.62/0.81 (step @p299 :rule trans :premises (@p298 @p296)) % 0.62/0.81 (step @p300 :rule cong :premises (@p299) :args (@t179)) % 0.62/0.81 (step @p301 :rule exists-elim :args ((= @t41 @t179))) % 0.62/0.81 (step @p302 :rule trans :premises (@p301 @p300)) % 0.62/0.81 (step @p303 :rule cong :premises (@p302) :args (@t43)) % 0.62/0.81 (step @p304 :rule trans :premises (@p5 @p303)) % 0.62/0.81 (step @p305 :rule ho_cong :premises (@p304 @p287)) % 0.62/0.81 (step @p306 :rule trans :premises (@p305 @p286)) % 0.62/0.81 (step @p307 :rule cong :premises (@p306) :args (@t45)) % 0.62/0.81 (step @p308 :rule trans :premises (@p6 @p307)) % 0.62/0.81 (step @p309 :rule ho_cong :premises (@p308 @p38)) % 0.62/0.81 (step @p310 :rule ho_cong :premises (@p309 @p226)) % 0.62/0.81 (step @p311 :rule cong :premises (@p310 @p236) :args (@t32)) % 0.62/0.81 (step @p312 :rule cong :premises (@p311) :args (@t34)) % 0.62/0.81 (step @p313 :rule cong :premises (@p33 @p312) :args (@t35)) % 0.62/0.81 (step @p314 :rule cong :premises (@p99 @p313) :args (@t36)) % 0.62/0.81 (step @p315 :rule cong :premises (@p314) :args (@t37)) % 0.62/0.81 (step @p316 :rule trans :premises (@p315 @p235)) % 0.62/0.81 (step @p317 :rule trans :premises (@p316 @p103)) % 0.62/0.81 (step @p318 :rule eq_resolve :premises (@p3 @p317)) % 0.62/0.81 (step @p319 :rule not_implies_elim1 :premises (@p318)) % 0.62/0.81 (step @p320 :rule instantiate :premises (@p319) :args ((@list @t182 @t181 @t180))) % 0.62/0.81 (step @p321 :rule not_implies_elim2 :premises (@p318)) % 0.62/0.81 (step @p322 :rule not_implies_elim2 :premises (@p321)) % 0.62/0.81 (step @p323 :rule skolemize :premises (@p322)) % 0.62/0.81 (step @p324 :rule bool-double-not-elim :args (@t183)) % 0.62/0.81 (step @p325 :rule refl :args (@t198)) % 0.62/0.81 (step @p326 :rule nary_cong :premises (@p325 @p324) :args ((or @t198 (not @t186)))) % 0.62/0.81 (step @p327 :rule cnf_or_neg :args (@t198 5)) % 0.62/0.81 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 0.62/0.81 (step @p329 :rule reordering :premises (@p328) :args ((or @t183 @t198))) % 0.62/0.81 (step @p330 :rule chain_m_resolution :premises (@p329 @p323) :args (@t183 @t199 @t200)) % 0.62/0.81 (step @p331 :rule bool-double-not-elim :args (@t187)) % 0.62/0.81 (step @p332 :rule nary_cong :premises (@p325 @p331) :args ((or @t198 (not @t188)))) % 0.62/0.81 (step @p333 :rule cnf_or_neg :args (@t198 4)) % 0.62/0.81 (step @p334 :rule eq_resolve :premises (@p333 @p332)) % 0.62/0.81 (step @p335 :rule reordering :premises (@p334) :args ((or @t187 @t198))) % 0.62/0.81 (step @p336 :rule chain_m_resolution :premises (@p335 @p323) :args (@t187 @t199 @t200)) % 0.62/0.81 (step @p337 :rule cnf_or_pos :args (@t202)) % 0.62/0.81 (step @p338 :rule reordering :premises (@p337) :args ((or @t188 @t186 @t201 (not @t202)))) % 0.62/0.81 (step @p339 :rule chain_m_resolution :premises (@p338 @p336 @p330 @p320) :args (@t201 @t203 (@list @t187 @t183 @t202))) % 0.62/0.81 (step @p340 :rule true_intro :premises (@p339)) % 0.62/0.81 (step @p341 :rule bool-double-not-elim :args (@t196)) % 0.62/0.81 (step @p342 :rule nary_cong :premises (@p325 @p341) :args ((or @t198 (not @t197)))) % 0.62/0.81 (step @p343 :rule cnf_or_neg :args (@t198 1)) % 0.62/0.81 (step @p344 :rule eq_resolve :premises (@p343 @p342)) % 0.62/0.81 (step @p345 :rule reordering :premises (@p344) :args ((or @t196 @t198))) % 0.62/0.81 (step @p346 :rule chain_m_resolution :premises (@p345 @p323) :args (@t196 @t199 @t200)) % 0.62/0.81 (step @p347 :rule symm :premises (@p346)) % 0.62/0.81 (step @p348 :rule refl :args (@t180)) % 0.62/0.81 (step @p349 :rule cong :premises (@p348 @p347) :args (@t204)) % 0.62/0.81 (step @p350 :rule not_implies_elim1 :premises (@p321)) % 0.62/0.81 (step @p351 :rule eq-symm :args (@t180 @t193)) % 0.62/0.81 (step @p352 :rule refl :args (@t205)) % 0.62/0.81 (step @p353 :rule nary_cong :premises (@p352 @p351) :args (@t206)) % 0.62/0.81 (step @p354 :rule refl :args (@t207)) % 0.62/0.81 (step @p355 :rule cong :premises (@p354 @p353) :args ((=> @t207 @t206))) % 0.62/0.81 (assume-push @p411 @t207) % 0.62/0.81 (step @p357 :rule instantiate :premises (@p350) :args ((@list @t180 @t193))) % 0.62/0.81 (step-pop @p412 :rule scope :premises (@p357)) % 0.62/0.81 (step @p358 :rule process_scope :premises (@p412) :args (@t206)) % 0.62/0.81 (step @p360 :rule eq_resolve :premises (@p358 @p355)) % 0.62/0.81 (step @p361 :rule implies_elim :premises (@p360)) % 0.62/0.81 (step @p362 :rule chain_m_resolution :premises (@p361 @p350) :args (@t209 @t210 @t211)) % 0.62/0.81 (step @p363 :rule cnf_or_neg :args (@t198 6)) % 0.62/0.81 (step @p364 :rule chain_m_resolution :premises (@p363 @p323) :args ((not @t185) @t199 @t200)) % 0.62/0.81 (step @p365 :rule false_intro :premises (@p364)) % 0.62/0.81 (step @p366 :rule eq-symm :args (@t184 @t193)) % 0.62/0.81 (step @p367 :rule refl :args (@t213)) % 0.62/0.81 (step @p368 :rule nary_cong :premises (@p367 @p366) :args (@t214)) % 0.62/0.81 (step @p369 :rule cong :premises (@p354 @p368) :args ((=> @t207 @t214))) % 0.62/0.81 (assume-push @p413 @t207) % 0.62/0.81 (step @p371 :rule instantiate :premises (@p350) :args ((@list @t184 @t193))) % 0.62/0.81 (step-pop @p414 :rule scope :premises (@p371)) % 0.62/0.81 (step @p372 :rule process_scope :premises (@p414) :args (@t214)) % 0.62/0.81 (step @p374 :rule eq_resolve :premises (@p372 @p369)) % 0.62/0.81 (step @p375 :rule implies_elim :premises (@p374)) % 0.62/0.81 (step @p376 :rule chain_m_resolution :premises (@p375 @p350) :args (@t216 @t210 @t211)) % 0.62/0.81 (step @p377 :rule instantiate :premises (@p319) :args ((@list @t182 @t181 @t184))) % 0.62/0.81 (step @p378 :rule bool-double-not-elim :args (@t189)) % 0.62/0.81 (step @p379 :rule nary_cong :premises (@p325 @p378) :args ((or @t198 (not @t190)))) % 0.62/0.81 (step @p380 :rule cnf_or_neg :args (@t198 3)) % 0.62/0.81 (step @p381 :rule eq_resolve :premises (@p380 @p379)) % 0.62/0.81 (step @p382 :rule reordering :premises (@p381) :args ((or @t189 @t198))) % 0.62/0.81 (step @p383 :rule chain_m_resolution :premises (@p382 @p323) :args (@t189 @t199 @t200)) % 0.62/0.81 (step @p384 :rule bool-double-not-elim :args (@t191)) % 0.62/0.81 (step @p385 :rule nary_cong :premises (@p325 @p384) :args ((or @t198 (not @t192)))) % 0.62/0.81 (step @p386 :rule cnf_or_neg :args (@t198 2)) % 0.62/0.81 (step @p387 :rule eq_resolve :premises (@p386 @p385)) % 0.62/0.81 (step @p388 :rule reordering :premises (@p387) :args ((or @t191 @t198))) % 0.62/0.81 (step @p389 :rule chain_m_resolution :premises (@p388 @p323) :args (@t191 @t199 @t200)) % 0.62/0.81 (step @p390 :rule cnf_or_pos :args (@t218)) % 0.62/0.81 (step @p391 :rule reordering :premises (@p390) :args ((or @t192 @t190 @t217 (not @t218)))) % 0.62/0.81 (step @p392 :rule chain_m_resolution :premises (@p391 @p389 @p383 @p377) :args (@t217 @t203 (@list @t191 @t189 @t218))) % 0.62/0.81 (step @p393 :rule true_intro :premises (@p392)) % 0.62/0.81 (step @p394 :rule refl :args (@t184)) % 0.62/0.81 (step @p395 :rule cong :premises (@p394 @p347) :args (@t212)) % 0.62/0.81 (step @p396 :rule trans :premises (@p395 @p393)) % 0.62/0.81 (step @p397 :rule true_elim :premises (@p396)) % 0.62/0.81 (step @p398 :rule cnf_or_pos :args (@t216)) % 0.62/0.81 (step @p399 :rule reordering :premises (@p398) :args ((or @t213 @t215 (not @t216)))) % 0.62/0.81 (step @p400 :rule chain_m_resolution :premises (@p399 @p397 @p376) :args (@t215 (@list false false) (@list @t212 @t216))) % 0.62/0.81 (step @p401 :rule cong :premises (@p400 @p348) :args (@t208)) % 0.62/0.81 (step @p402 :rule trans :premises (@p401 @p365)) % 0.62/0.81 (step @p403 :rule false_elim :premises (@p402)) % 0.62/0.81 (step @p404 :rule cnf_or_pos :args (@t209)) % 0.62/0.81 (step @p405 :rule reordering :premises (@p404) :args ((or @t205 @t208 (not @t209)))) % 0.62/0.81 (step @p406 :rule chain_m_resolution :premises (@p405 @p403 @p362) :args (@t205 (@list true false) (@list @t208 @t209))) % 0.62/0.81 (step @p407 :rule false_intro :premises (@p406)) % 0.62/0.81 (step @p408 :rule symm :premises (@p407)) % 0.62/0.81 (step @p409 :rule trans :premises (@p408 @p349 @p340)) % 0.62/0.81 (step @p410 false :rule eq_resolve :premises (@p409 @p7)) % 0.62/0.81 ) % 0.62/0.81 % SZS output end Proof % 0.62/0.81 % cvc5 exiting %------------------------------------------------------------------------------