%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU668^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:52:39 AM UTC 2026 % Result : Theorem 0.36s 0.61s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU668^2 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:46:17 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.36/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.61 % SZS status Theorem % 0.36/0.61 % SZS output start Proof % 0.36/0.61 ( % 0.36/0.61 (declare-sort $$unsorted 0) % 0.36/0.61 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.61 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.61 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.36/0.61 (declare-const tptp.setukpairinjR Bool) % 0.36/0.61 (declare-const tptp.setukpairinjL Bool) % 0.36/0.61 (declare-const tptp.dsetconstrER Bool) % 0.36/0.61 (define tptp.dpsetconstr () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xu" $$unsorted))) (let ((_let_4 (@var "Xphi" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "B" $$unsorted))) (let ((_let_6 (@var "A" $$unsorted))) (lambda (@list _let_6 _let_5 _let_4) (_ (_ tptp.dsetconstr (_ (_ tptp.cartprod _let_6) _let_5)) (lambda (@list _let_3) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_6) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_5) (_ (_ _let_4 _let_2) _let_1) (= _let_3 (_ (_ tptp.kpair _let_2) _let_1)))))))))))))))) % 0.36/0.61 (define @t1 () (@var "Xx" $$unsorted)) % 0.36/0.61 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.36/0.61 (define @t3 () (_ @t2 @t1)) % 0.36/0.61 (define @t4 () (@var "Xy" $$unsorted)) % 0.36/0.61 (define @t5 () (_ @t2 @t4)) % 0.36/0.61 (define @t6 () (@list @t4)) % 0.36/0.61 (define @t7 () (lambda @t6 @t5)) % 0.36/0.61 (define @t8 () (@var "A" $$unsorted)) % 0.36/0.61 (define @t9 () (_ tptp.dsetconstr @t8)) % 0.36/0.61 (define @t10 () (_ @t9 @t7)) % 0.36/0.61 (define @t11 () (_ tptp.in @t1)) % 0.36/0.61 (define @t12 () (_ @t11 @t10)) % 0.36/0.61 (define @t13 () (@list @t8 @t2 @t1)) % 0.36/0.61 (define @t14 () (forall @t13 (=> @t12 @t3))) % 0.36/0.61 (define @t15 () (= tptp.dsetconstrER @t14)) % 0.36/0.61 (define @t16 () (@var "Xz" $$unsorted)) % 0.36/0.61 (define @t17 () (= @t1 @t16)) % 0.36/0.61 (define @t18 () (@var "Xu" $$unsorted)) % 0.36/0.61 (define @t19 () (_ (_ tptp.kpair @t16) @t18)) % 0.36/0.61 (define @t20 () (_ tptp.kpair @t1)) % 0.36/0.61 (define @t21 () (_ @t20 @t4)) % 0.36/0.61 (define @t22 () (= @t21 @t19)) % 0.36/0.61 (define @t23 () (@list @t1 @t4 @t16 @t18)) % 0.36/0.61 (define @t24 () (forall @t23 (=> @t22 @t17))) % 0.36/0.61 (define @t25 () (= tptp.setukpairinjL @t24)) % 0.36/0.61 (define @t26 () (= @t4 @t18)) % 0.36/0.61 (define @t27 () (forall @t23 (=> @t22 @t26))) % 0.36/0.61 (define @t28 () (= tptp.setukpairinjR @t27)) % 0.36/0.61 (define @t29 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t30 () (_ @t29 @t1)) % 0.36/0.61 (define @t31 () (_ @t30 @t4)) % 0.36/0.61 (define @t32 () (lambda (@list @t16 @t18) (_ (_ @t29 @t16) @t18))) % 0.36/0.61 (define @t33 () (@var "B" $$unsorted)) % 0.36/0.61 (define @t34 () (_ tptp.in @t21)) % 0.36/0.61 (define @t35 () (=> (_ @t34 (_ (_ (_ tptp.dpsetconstr @t8) @t33) @t32)) @t31)) % 0.36/0.61 (define @t36 () (_ (_ tptp.in @t4) @t33)) % 0.36/0.61 (define @t37 () (=> @t36 @t35)) % 0.36/0.61 (define @t38 () (forall @t6 @t37)) % 0.36/0.61 (define @t39 () (_ @t11 @t8)) % 0.36/0.61 (define @t40 () (=> @t39 @t38)) % 0.36/0.61 (define @t41 () (@list @t8 @t33 @t29 @t1)) % 0.36/0.61 (define @t42 () (forall @t41 @t40)) % 0.36/0.61 (define @t43 () (=> tptp.setukpairinjR @t42)) % 0.36/0.61 (define @t44 () (=> tptp.setukpairinjL @t43)) % 0.36/0.61 (define @t45 () (=> tptp.dsetconstrER @t44)) % 0.36/0.61 (define @t46 () (not @t45)) % 0.36/0.61 (define @t47 () (= @t18 @t21)) % 0.36/0.61 (define @t48 () (and @t36 @t31 @t47)) % 0.36/0.61 (define @t49 () (exists @t6 @t48)) % 0.36/0.61 (define @t50 () (and @t39 @t49)) % 0.36/0.61 (define @t51 () (@list @t1)) % 0.36/0.61 (define @t52 () (exists @t51 @t50)) % 0.36/0.61 (define @t53 () (@list @t18)) % 0.36/0.61 (define @t54 () (lambda @t53 @t52)) % 0.36/0.61 (define @t55 () (_ (_ tptp.cartprod @t8) @t33)) % 0.36/0.61 (define @t56 () (_ tptp.dsetconstr @t55)) % 0.36/0.61 (define @t57 () (@list @t8 @t33 @t29)) % 0.36/0.61 (define @t58 () (lambda @t57 (_ @t56 @t54))) % 0.36/0.61 (define @t59 () (@var "BOUND_VARIABLE_7666" $$unsorted)) % 0.36/0.61 (define @t60 () (_ @t29 @t1 @t59)) % 0.36/0.61 (define @t61 () (@var "BOUND_VARIABLE_7504" $$unsorted)) % 0.36/0.61 (define @t62 () (@var "BOUND_VARIABLE_7641" $$unsorted)) % 0.36/0.61 (define @t63 () (tptp.kpair @t62 @t61)) % 0.36/0.61 (define @t64 () (not (= @t18 @t63))) % 0.36/0.61 (define @t65 () (tptp.in @t61 @t33)) % 0.36/0.61 (define @t66 () (not @t65)) % 0.36/0.61 (define @t67 () (@list @t62 @t61)) % 0.36/0.61 (define @t68 () (tptp.cartprod @t8 @t33)) % 0.36/0.61 (define @t69 () (tptp.dsetconstr @t68 (lambda @t53 (not (forall @t67 (or (not (tptp.in @t62 @t8)) @t66 (not (_ @t29 @t62 @t61)) @t64)))))) % 0.36/0.61 (define @t70 () (not (tptp.in (tptp.kpair @t1 @t59) @t69))) % 0.36/0.61 (define @t71 () (not (tptp.in @t59 @t33))) % 0.36/0.61 (define @t72 () (tptp.in @t1 @t8)) % 0.36/0.61 (define @t73 () (not @t72)) % 0.36/0.61 (define @t74 () (or @t73 @t71 @t70 @t60)) % 0.36/0.61 (define @t75 () (@list @t8 @t33 @t29 @t1 @t59)) % 0.36/0.61 (define @t76 () (forall @t75 @t74)) % 0.36/0.61 (define @t77 () (tptp.kpair @t16 @t18)) % 0.36/0.61 (define @t78 () (tptp.kpair @t1 @t4)) % 0.36/0.61 (define @t79 () (not @t22)) % 0.36/0.61 (define @t80 () (or @t79 @t26)) % 0.36/0.61 (define @t81 () (=> tptp.setukpairinjR @t76)) % 0.36/0.61 (define @t82 () (or @t79 @t17)) % 0.36/0.61 (define @t83 () (=> tptp.setukpairinjL @t81)) % 0.36/0.61 (define @t84 () (_ @t2 @t1)) % 0.36/0.61 (define @t85 () (_ @t2 @t4)) % 0.36/0.61 (define @t86 () (lambda @t6 @t85)) % 0.36/0.61 (define @t87 () (tptp.dsetconstr @t8 @t86)) % 0.36/0.61 (define @t88 () (tptp.in @t1 @t87)) % 0.36/0.61 (define @t89 () (not @t88)) % 0.36/0.61 (define @t90 () (or @t89 @t84)) % 0.36/0.61 (define @t91 () (not @t12)) % 0.36/0.61 (define @t92 () (or @t91 @t3)) % 0.36/0.61 (define @t93 () (=> tptp.dsetconstrER @t83)) % 0.36/0.61 (define @t94 () (or @t71 @t70 @t60)) % 0.36/0.61 (define @t95 () (or @t73 @t94)) % 0.36/0.61 (define @t96 () (forall @t75 @t95)) % 0.36/0.61 (define @t97 () (@list @t59)) % 0.36/0.61 (define @t98 () (forall @t97 @t95)) % 0.36/0.61 (define @t99 () (forall @t97 @t94)) % 0.36/0.61 (define @t100 () (@list @t4)) % 0.36/0.61 (define @t101 () (or @t73 @t99)) % 0.36/0.61 (define @t102 () (_ @t29 @t1 @t4)) % 0.36/0.61 (define @t103 () (tptp.in @t4 @t33)) % 0.36/0.61 (define @t104 () (not @t103)) % 0.36/0.61 (define @t105 () (forall @t6 (or @t104 (not (tptp.in @t78 @t69)) @t102))) % 0.36/0.61 (define @t106 () (not @t39)) % 0.36/0.61 (define @t107 () (or @t106 @t105)) % 0.36/0.61 (define @t108 () (tptp.kpair @t1 @t61)) % 0.36/0.61 (define @t109 () (= @t18 @t108)) % 0.36/0.61 (define @t110 () (not @t109)) % 0.36/0.61 (define @t111 () (_ @t29 @t1 @t61)) % 0.36/0.61 (define @t112 () (not @t111)) % 0.36/0.61 (define @t113 () (or @t73 @t66 @t112 @t110)) % 0.36/0.61 (define @t114 () (@list @t1 @t61)) % 0.36/0.61 (define @t115 () (forall @t114 @t113)) % 0.36/0.61 (define @t116 () (not @t115)) % 0.36/0.61 (define @t117 () (lambda @t53 @t116)) % 0.36/0.61 (define @t118 () (tptp.dsetconstr @t68 @t117)) % 0.36/0.61 (define @t119 () (tptp.in @t78 @t118)) % 0.36/0.61 (define @t120 () (not @t119)) % 0.36/0.61 (define @t121 () (or @t104 @t120 @t102)) % 0.36/0.61 (define @t122 () (forall @t6 @t121)) % 0.36/0.61 (define @t123 () (=> @t39 @t122)) % 0.36/0.61 (define @t124 () (_ @t30 @t61)) % 0.36/0.61 (define @t125 () (not @t124)) % 0.36/0.61 (define @t126 () (lambda @t53 (not (forall @t114 (or @t106 (not (_ (_ tptp.in @t61) @t33)) @t125 (not (= @t18 (_ @t20 @t61)))))))) % 0.36/0.61 (define @t127 () (_ @t56 @t126)) % 0.36/0.61 (define @t128 () (_ @t56 @t117)) % 0.36/0.61 (define @t129 () (_ @t34 @t128)) % 0.36/0.61 (define @t130 () (not @t129)) % 0.36/0.61 (define @t131 () (not @t36)) % 0.36/0.61 (define @t132 () (or @t131 @t130 @t31)) % 0.36/0.61 (define @t133 () (=> @t129 @t31)) % 0.36/0.61 (define @t134 () (or @t73 @t66 @t125 @t110)) % 0.36/0.61 (define @t135 () (_ @t32 @t1 @t61)) % 0.36/0.61 (define @t136 () (not @t135)) % 0.36/0.61 (define @t137 () (or @t73 @t66 @t136 @t110)) % 0.36/0.61 (define @t138 () (forall @t114 @t137)) % 0.36/0.61 (define @t139 () (not @t138)) % 0.36/0.61 (define @t140 () (lambda @t53 @t139)) % 0.36/0.61 (define @t141 () (lambda (@list @t29) @t128)) % 0.36/0.61 (define @t142 () (lambda (@list @t33 @t29) @t128)) % 0.36/0.61 (define @t143 () (_ (lambda @t57 @t128) @t8)) % 0.36/0.61 (define @t144 () (=> (_ @t34 (_ (_ @t143 @t33) @t32)) @t31)) % 0.36/0.61 (define @t145 () (=> @t36 @t144)) % 0.36/0.61 (define @t146 () (forall @t6 @t145)) % 0.36/0.61 (define @t147 () (=> @t39 @t146)) % 0.36/0.61 (define @t148 () (forall @t41 @t147)) % 0.36/0.61 (define @t149 () (=> tptp.setukpairinjR @t148)) % 0.36/0.61 (define @t150 () (=> tptp.setukpairinjL @t149)) % 0.36/0.61 (define @t151 () (=> tptp.dsetconstrER @t150)) % 0.36/0.61 (define @t152 () (or @t66 @t112 @t110)) % 0.36/0.61 (define @t153 () (or @t73 @t152)) % 0.36/0.61 (define @t154 () (forall @t114 @t153)) % 0.36/0.61 (define @t155 () (@list @t61)) % 0.36/0.61 (define @t156 () (forall @t155 @t153)) % 0.36/0.61 (define @t157 () (forall @t155 @t152)) % 0.36/0.61 (define @t158 () (or @t73 @t157)) % 0.36/0.61 (define @t159 () (forall @t6 (or @t104 (not @t102) (not (= @t18 @t78))))) % 0.36/0.61 (define @t160 () (or @t106 @t159)) % 0.36/0.61 (define @t161 () (not @t159)) % 0.36/0.61 (define @t162 () (and @t39 @t161)) % 0.36/0.61 (define @t163 () (forall @t51 (not @t162))) % 0.36/0.61 (define @t164 () (not @t163)) % 0.36/0.61 (define @t165 () (not @t47)) % 0.36/0.61 (define @t166 () (not @t31)) % 0.36/0.61 (define @t167 () (or @t131 @t166 @t165)) % 0.36/0.61 (define @t168 () (forall @t6 (not @t48))) % 0.36/0.61 (define @t169 () (not @t168)) % 0.36/0.61 (define @t170 () (@quantifiers_skolemize @t76 4)) % 0.36/0.61 (define @t171 () (@quantifiers_skolemize @t76 3)) % 0.36/0.61 (define @t172 () (@quantifiers_skolemize @t76 2)) % 0.36/0.61 (define @t173 () (_ @t172 @t171 @t170)) % 0.36/0.61 (define @t174 () (not (_ @t172 @t62 @t61))) % 0.36/0.61 (define @t175 () (@quantifiers_skolemize @t76 1)) % 0.36/0.61 (define @t176 () (not (tptp.in @t61 @t175))) % 0.36/0.61 (define @t177 () (@quantifiers_skolemize @t76 0)) % 0.36/0.61 (define @t178 () (not (tptp.in @t62 @t177))) % 0.36/0.61 (define @t179 () (not (forall @t67 (or @t178 @t176 @t174 @t64)))) % 0.36/0.61 (define @t180 () (lambda @t53 @t179)) % 0.36/0.61 (define @t181 () (@purify @t180)) % 0.36/0.61 (define @t182 () (tptp.cartprod @t177 @t175)) % 0.36/0.61 (define @t183 () (tptp.kpair @t171 @t170)) % 0.36/0.61 (define @t184 () (tptp.in @t183 (tptp.dsetconstr @t182 @t181))) % 0.36/0.61 (define @t185 () (not @t184)) % 0.36/0.61 (define @t186 () (not (tptp.in @t170 @t175))) % 0.36/0.61 (define @t187 () (not (tptp.in @t171 @t177))) % 0.36/0.61 (define @t188 () (or @t187 @t186 @t185 @t173)) % 0.36/0.61 (define @t189 () (not @t188)) % 0.36/0.61 (define @t190 () (not @t76)) % 0.36/0.61 (define @t191 () (tptp.dsetconstr @t182 @t180)) % 0.36/0.61 (define @t192 () (tptp.in @t183 @t191)) % 0.36/0.61 (define @t193 () (not @t192)) % 0.36/0.61 (define @t194 () (or @t187 @t186 @t193 @t173)) % 0.36/0.61 (define @t195 () (not @t194)) % 0.36/0.61 (define @t196 () (@list true)) % 0.36/0.61 (define @t197 () (@list @t188)) % 0.36/0.61 (define @t198 () (forall @t67 (or @t178 @t176 @t174 (not (= @t63 @t183))))) % 0.36/0.61 (define @t199 () (@quantifiers_skolemize @t198 1)) % 0.36/0.61 (define @t200 () (@quantifiers_skolemize @t198 0)) % 0.36/0.61 (define @t201 () (@list @t171 @t170 @t200 @t199)) % 0.36/0.61 (define @t202 () (_ @t181 @t18)) % 0.36/0.61 (define @t203 () (_ @t180 @t18)) % 0.36/0.61 (define @t204 () (= @t202 @t203)) % 0.36/0.61 (define @t205 () (forall @t53 @t204)) % 0.36/0.61 (define @t206 () (not (= @t183 @t63))) % 0.36/0.61 (define @t207 () (or @t178 @t176 @t174 @t206)) % 0.36/0.61 (define @t208 () (forall @t67 @t207)) % 0.36/0.61 (define @t209 () (not @t208)) % 0.36/0.61 (define @t210 () (_ @t181 @t183)) % 0.36/0.61 (define @t211 () (forall @t53 (= @t179 @t202))) % 0.36/0.61 (define @t212 () (= @t209 @t210)) % 0.36/0.61 (define @t213 () (not @t198)) % 0.36/0.61 (define @t214 () (= @t210 @t213)) % 0.36/0.61 (define @t215 () (or @t185 @t210)) % 0.36/0.61 (define @t216 () (@list false false)) % 0.36/0.61 (define @t217 () (tptp.kpair @t200 @t199)) % 0.36/0.61 (define @t218 () (= @t183 @t217)) % 0.36/0.61 (define @t219 () (not @t218)) % 0.36/0.61 (define @t220 () (_ @t172 @t200 @t199)) % 0.36/0.61 (define @t221 () (not @t220)) % 0.36/0.61 (define @t222 () (not (tptp.in @t199 @t175))) % 0.36/0.61 (define @t223 () (not (tptp.in @t200 @t177))) % 0.36/0.61 (define @t224 () (or @t223 @t222 @t221 @t219)) % 0.36/0.61 (define @t225 () (not @t224)) % 0.36/0.61 (define @t226 () (not (= @t217 @t183))) % 0.36/0.61 (define @t227 () (or @t223 @t222 @t221 @t226)) % 0.36/0.61 (define @t228 () (not @t227)) % 0.36/0.61 (define @t229 () (@list @t224)) % 0.36/0.61 (define @t230 () (= @t170 @t199)) % 0.36/0.61 (define @t231 () (or @t219 @t230)) % 0.36/0.61 (define @t232 () (= @t171 @t200)) % 0.36/0.61 (define @t233 () (or @t219 @t232)) % 0.36/0.61 (assume @p1 @t15) % 0.36/0.61 (assume @p2 @t25) % 0.36/0.61 (assume @p3 @t28) % 0.36/0.61 (assume @p4 @t46) % 0.36/0.61 (assume @p5 true) % 0.36/0.61 (step @p6 (= tptp.dpsetconstr @t58) :rule refl :args (@t58)) % 0.36/0.61 (step @p7 :rule evaluate :args ((= true false))) % 0.36/0.61 (step @p8 :rule refl :args (@t76)) % 0.36/0.61 (step @p9 :rule refl :args (@t26)) % 0.36/0.61 (step @p10 :rule refl :args (@t77)) % 0.36/0.61 (step @p11 :rule refl :args (@t19)) % 0.36/0.61 (step @p12 :rule cong :premises (@p11 @p10) :args ((= @t19 @t77))) % 0.36/0.61 (step @p13 :rule symm :premises (@p12)) % 0.36/0.61 (step @p14 :rule eq_resolve :premises (@p11 @p13)) % 0.36/0.61 (step @p15 :rule refl :args (@t78)) % 0.36/0.61 (step @p16 :rule refl :args (@t21)) % 0.36/0.61 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t21 @t78))) % 0.36/0.61 (step @p18 :rule symm :premises (@p17)) % 0.36/0.61 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.36/0.61 (step @p20 :rule cong :premises (@p19 @p14) :args (@t22)) % 0.36/0.61 (step @p21 :rule cong :premises (@p20) :args (@t79)) % 0.36/0.61 (step @p22 :rule nary_cong :premises (@p21 @p9) :args (@t80)) % 0.36/0.61 (step @p23 :rule cong :premises (@p22) :args ((forall @t23 @t80))) % 0.36/0.61 (step @p24 :rule bool-impl-elim :args (@t22 @t26)) % 0.36/0.61 (step @p25 :rule cong :premises (@p24) :args (@t27)) % 0.36/0.61 (step @p26 :rule trans :premises (@p25 @p23)) % 0.36/0.61 (step @p27 :rule refl :args (tptp.setukpairinjR)) % 0.36/0.61 (step @p28 :rule cong :premises (@p27 @p26) :args (@t28)) % 0.36/0.61 (step @p29 :rule eq_resolve :premises (@p3 @p28)) % 0.36/0.61 (step @p30 :rule cong :premises (@p29 @p8) :args (@t81)) % 0.36/0.61 (step @p31 :rule refl :args (@t17)) % 0.36/0.61 (step @p32 :rule nary_cong :premises (@p21 @p31) :args (@t82)) % 0.36/0.61 (step @p33 :rule cong :premises (@p32) :args ((forall @t23 @t82))) % 0.36/0.61 (step @p34 :rule bool-impl-elim :args (@t22 @t17)) % 0.36/0.61 (step @p35 :rule cong :premises 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@p280 @p279) :args (@t167)) % 0.36/0.61 (step @p282 :rule cong :premises (@p281) :args ((forall @t6 @t167))) % 0.36/0.61 (step @p283 :rule aci_norm :args ((= (or @t131 (or @t166 @t165)) @t167))) % 0.36/0.61 (step @p284 :rule bool-and-de-morgan :args (@t31 @t47 true)) % 0.36/0.61 (step @p285 :rule nary_cong :premises (@p199 @p284) :args ((or @t131 (not (and @t31 @t47))))) % 0.36/0.61 (step @p286 :rule bool-and-de-morgan :args (@t36 @t31 (and @t47))) % 0.36/0.61 (step @p287 :rule trans :premises (@p286 @p285)) % 0.36/0.61 (step @p288 :rule trans :premises (@p287 @p283)) % 0.36/0.61 (step @p289 :rule cong :premises (@p288) :args (@t168)) % 0.36/0.61 (step @p290 :rule trans :premises (@p289 @p282)) % 0.36/0.61 (step @p291 :rule cong :premises (@p290) :args (@t169)) % 0.36/0.61 (step @p292 :rule exists-elim :args ((= @t49 @t169))) % 0.36/0.61 (step @p293 :rule trans :premises (@p292 @p291)) % 0.36/0.61 (step @p294 :rule nary_cong :premises (@p245 @p293) :args (@t50)) % 0.36/0.61 (step @p295 :rule cong :premises (@p294) :args (@t52)) % 0.36/0.61 (step @p296 :rule trans :premises (@p295 @p277)) % 0.36/0.61 (step @p297 :rule cong :premises (@p296) :args (@t54)) % 0.36/0.61 (step @p298 :rule ho_cong :premises (@p226 @p297)) % 0.36/0.61 (step @p299 :rule cong :premises (@p298) :args (@t58)) % 0.36/0.61 (step @p300 :rule trans :premises (@p6 @p299)) % 0.36/0.61 (step @p301 :rule ho_cong :premises (@p300 @p43)) % 0.36/0.61 (step @p302 :rule ho_cong :premises (@p301 @p232)) % 0.36/0.61 (step @p303 :rule ho_cong :premises (@p302 @p230)) % 0.36/0.61 (step @p304 :rule ho_cong :premises (@p238 @p303)) % 0.36/0.61 (step @p305 :rule cong :premises (@p304 @p206) :args (@t35)) % 0.36/0.61 (step @p306 :rule cong :premises (@p241 @p305) :args (@t37)) % 0.36/0.61 (step @p307 :rule cong :premises (@p306) :args (@t38)) % 0.36/0.61 (step @p308 :rule cong :premises (@p245 @p307) :args (@t40)) % 0.36/0.61 (step @p309 :rule cong :premises (@p308) :args (@t42)) % 0.36/0.61 (step @p310 :rule cong 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@p456 @t190) % 0.36/0.61 (step @p342 :rule skolemize :premises (@p319)) % 0.36/0.61 (step-pop @p457 :rule scope :premises (@p342)) % 0.36/0.61 (step @p343 :rule process_scope :premises (@p457) :args (@t195)) % 0.36/0.61 (step @p345 :rule eq_resolve :premises (@p343 @p340)) % 0.36/0.61 (step @p346 :rule implies_elim :premises (@p345)) % 0.36/0.61 (step @p347 :rule eq_resolve :premises (@p346 @p322)) % 0.36/0.61 (step @p348 :rule chain_m_resolution :premises (@p347 @p319) :args (@t189 @t196 (@list @t76))) % 0.36/0.61 (step @p349 :rule cnf_or_neg :args (@t188 3)) % 0.36/0.61 (step @p350 :rule chain_m_resolution :premises (@p349 @p348) :args ((not @t173) @t196 @t197)) % 0.36/0.61 (step @p351 :rule false_intro :premises (@p350)) % 0.36/0.61 (step @p352 :rule not_implies_elim1 :premises (@p318)) % 0.36/0.61 (step @p353 :rule instantiate :premises (@p352) :args (@t201)) % 0.36/0.61 (step @p354 :rule eq-symm :args (@t202 @t179)) % 0.36/0.61 (step @p355 :rule beta-reduce :args ((= @t203 @t179))) % 0.36/0.61 (step @p356 :rule refl :args (@t202)) % 0.36/0.61 (step @p357 :rule cong :premises (@p356 @p355) :args (@t204)) % 0.36/0.61 (step @p358 :rule trans :premises (@p357 @p354)) % 0.36/0.61 (step @p359 :rule cong :premises (@p358) :args (@t205)) % 0.36/0.61 (step @p360 :rule quant-unused-vars :args ((= (forall @t53 true) true))) % 0.36/0.61 (step @p361 :rule eq-refl :args (@t203)) % 0.36/0.61 (step @p362 :rule cong :premises (@p361) :args ((forall @t53 (= @t203 @t203)))) % 0.36/0.61 (step @p363 :rule trans :premises (@p362 @p360)) % 0.36/0.61 (step @p364 :rule refl :args (@t203)) % 0.36/0.61 (step @p365 :rule refl :args (@t18)) % 0.36/0.61 (step @p366 :rule ho_cong :premises (@p325 @p365)) % 0.36/0.61 (step @p367 :rule cong :premises (@p366 @p364) :args (@t204)) % 0.36/0.61 (step @p368 :rule cong :premises (@p367) :args (@t205)) % 0.36/0.61 (step @p369 :rule trans :premises (@p368 @p363)) % 0.36/0.61 (step @p370 :rule true_elim :premises (@p369)) % 0.36/0.61 (step @p371 :rule eq_resolve :premises (@p370 @p359)) % 0.36/0.61 (step @p372 :rule eq-symm :args (@t183 @t63)) % 0.36/0.61 (step @p373 :rule cong :premises (@p372) :args (@t206)) % 0.36/0.61 (step @p374 :rule refl :args (@t174)) % 0.36/0.61 (step @p375 :rule refl :args (@t176)) % 0.36/0.61 (step @p376 :rule refl :args (@t178)) % 0.36/0.61 (step @p377 :rule nary_cong :premises (@p376 @p375 @p374 @p373) :args (@t207)) % 0.36/0.61 (step @p378 :rule cong :premises (@p377) :args (@t208)) % 0.36/0.61 (step @p379 :rule cong :premises (@p378) :args (@t209)) % 0.36/0.61 (step @p380 :rule refl :args (@t210)) % 0.36/0.61 (step @p381 :rule cong :premises (@p380 @p379) :args ((= @t210 @t209))) % 0.36/0.61 (step @p382 :rule eq-symm :args (@t209 @t210)) % 0.36/0.61 (step @p383 :rule trans :premises (@p382 @p381)) % 0.36/0.61 (step @p384 :rule refl :args (@t211)) % 0.36/0.61 (step @p385 :rule cong :premises (@p384 @p383) :args ((=> @t211 @t212))) % 0.36/0.61 (assume-push @p458 @t211) % 0.36/0.61 (step @p387 :rule instantiate :premises (@p371) :args ((@list @t183))) % 0.36/0.61 (step-pop @p459 :rule scope :premises (@p387)) % 0.36/0.61 (step @p388 :rule process_scope :premises (@p459) :args (@t212)) % 0.36/0.61 (step @p390 :rule eq_resolve :premises (@p388 @p385)) % 0.36/0.61 (step @p391 :rule implies_elim :premises (@p390)) % 0.36/0.61 (step @p392 :rule chain_m_resolution :premises (@p391 @p371) :args (@t214 (@list false) (@list @t211))) % 0.36/0.61 (step @p393 :rule not_implies_elim1 :premises (@p316)) % 0.36/0.61 (step @p394 :rule instantiate :premises (@p393) :args ((@list @t182 @t181 @t183))) % 0.36/0.61 (step @p395 :rule bool-double-not-elim :args (@t184)) % 0.36/0.61 (step @p396 :rule refl :args (@t188)) % 0.36/0.61 (step @p397 :rule nary_cong :premises (@p396 @p395) :args ((or @t188 (not @t185)))) % 0.36/0.61 (step @p398 :rule cnf_or_neg :args (@t188 2)) % 0.36/0.61 (step @p399 :rule eq_resolve :premises (@p398 @p397)) % 0.36/0.61 (step @p400 :rule reordering :premises (@p399) :args ((or @t184 @t188))) % 0.36/0.61 (step @p401 :rule chain_m_resolution :premises (@p400 @p348) :args (@t184 @t196 @t197)) % 0.36/0.61 (step @p402 :rule cnf_or_pos :args (@t215)) % 0.36/0.61 (step @p403 :rule reordering :premises (@p402) :args ((or @t185 @t210 (not @t215)))) % 0.36/0.61 (step @p404 :rule chain_m_resolution :premises (@p403 @p401 @p394) :args (@t210 @t216 (@list @t184 @t215))) % 0.36/0.61 (step @p405 :rule cnf_equiv_pos1 :args (@t214)) % 0.36/0.61 (step @p406 :rule reordering :premises (@p405) :args ((or (not @t210) @t213 (not @t214)))) % 0.36/0.61 (step @p407 :rule chain_m_resolution :premises (@p406 @p404 @p392) :args (@t213 @t216 (@list @t210 @t214))) % 0.36/0.61 (step @p408 :rule refl :args (@t225)) % 0.36/0.61 (step @p409 :rule bool-double-not-elim :args (@t198)) % 0.36/0.61 (step @p410 :rule nary_cong :premises (@p409 @p408) :args ((or (not @t213) @t225))) % 0.36/0.61 (step @p411 :rule eq-symm :args (@t217 @t183)) % 0.36/0.61 (step @p412 :rule cong :premises (@p411) :args (@t226)) % 0.36/0.61 (step @p413 :rule refl :args (@t221)) % 0.36/0.61 (step @p414 :rule refl :args (@t222)) % 0.36/0.61 (step @p415 :rule refl :args (@t223)) % 0.36/0.61 (step @p416 :rule nary_cong :premises (@p415 @p414 @p413 @p412) :args (@t227)) % 0.36/0.61 (step @p417 :rule cong :premises (@p416) :args (@t228)) % 0.36/0.61 (step @p418 :rule refl :args (@t213)) % 0.36/0.61 (step @p419 :rule cong :premises (@p418 @p417) :args ((=> @t213 @t228))) % 0.36/0.61 (assume-push @p460 @t213) % 0.36/0.61 (step @p421 :rule skolemize :premises (@p407)) % 0.36/0.61 (step-pop @p461 :rule scope :premises (@p421)) % 0.36/0.61 (step @p422 :rule process_scope :premises (@p461) :args (@t228)) % 0.36/0.61 (step @p424 :rule eq_resolve :premises (@p422 @p419)) % 0.36/0.61 (step @p425 :rule implies_elim :premises (@p424)) % 0.36/0.61 (step @p426 :rule eq_resolve :premises (@p425 @p410)) % 0.36/0.61 (step @p427 :rule chain_m_resolution :premises (@p426 @p407) :args (@t225 @t196 (@list @t198))) % 0.36/0.61 (step @p428 :rule bool-double-not-elim :args (@t218)) % 0.36/0.61 (step @p429 :rule refl :args (@t224)) % 0.36/0.61 (step @p430 :rule nary_cong :premises (@p429 @p428) :args ((or @t224 (not @t219)))) % 0.36/0.61 (step @p431 :rule cnf_or_neg :args (@t224 3)) % 0.36/0.61 (step @p432 :rule eq_resolve :premises (@p431 @p430)) % 0.36/0.61 (step @p433 :rule reordering :premises (@p432) :args ((or @t218 @t224))) % 0.36/0.61 (step @p434 :rule chain_m_resolution :premises (@p433 @p427) :args (@t218 @t196 @t229)) % 0.36/0.61 (step @p435 :rule cnf_or_pos :args (@t231)) % 0.36/0.61 (step @p436 :rule reordering :premises (@p435) :args ((or @t219 @t230 (not @t231)))) % 0.36/0.61 (step @p437 :rule chain_m_resolution :premises (@p436 @p434 @p353) :args (@t230 @t216 (@list @t218 @t231))) % 0.36/0.61 (step @p438 :rule symm :premises (@p437)) % 0.36/0.61 (step @p439 :rule not_implies_elim1 :premises (@p317)) % 0.36/0.61 (step @p440 :rule instantiate :premises (@p439) :args (@t201)) % 0.36/0.61 (step @p441 :rule cnf_or_pos :args (@t233)) % 0.36/0.61 (step @p442 :rule reordering :premises (@p441) :args ((or @t219 @t232 (not @t233)))) % 0.36/0.61 (step @p443 :rule chain_m_resolution :premises (@p442 @p434 @p440) :args (@t232 @t216 (@list @t218 @t233))) % 0.36/0.61 (step @p444 :rule symm :premises (@p443)) % 0.36/0.61 (step @p445 :rule cong :premises (@p444 @p438) :args (@t220)) % 0.36/0.61 (step @p446 :rule bool-double-not-elim :args (@t220)) % 0.36/0.61 (step @p447 :rule nary_cong :premises (@p429 @p446) :args ((or @t224 (not @t221)))) % 0.36/0.61 (step @p448 :rule cnf_or_neg :args (@t224 2)) % 0.36/0.61 (step @p449 :rule eq_resolve :premises (@p448 @p447)) % 0.36/0.61 (step @p450 :rule reordering :premises (@p449) :args ((or @t220 @t224))) % 0.36/0.61 (step @p451 :rule chain_m_resolution :premises (@p450 @p427) :args (@t220 @t196 @t229)) % 0.36/0.61 (step @p452 :rule true_intro :premises (@p451)) % 0.36/0.61 (step @p453 :rule symm :premises (@p452)) % 0.36/0.61 (step @p454 :rule trans :premises (@p453 @p445 @p351)) % 0.36/0.61 (step @p455 false :rule eq_resolve :premises (@p454 @p7)) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------