%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU764^2 : 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 : n018.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 08:53:06 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU764^2 : 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 : n018.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 17:51:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.49 %----Proving TH0 % 0.38/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (declare-const tptp.demorgan2 Bool) % 0.38/0.61 (declare-const tptp.demorgan1 Bool) % 0.38/0.61 (declare-const tptp.binintersect (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.setminus (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.binunionT_lem Bool) % 0.38/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.61 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.61 (define @t1 () (@var "A" $$unsorted)) % 0.38/0.61 (define @t2 () (_ tptp.powerset @t1)) % 0.38/0.61 (define @t3 () (@var "Y" $$unsorted)) % 0.38/0.61 (define @t4 () (@var "X" $$unsorted)) % 0.38/0.61 (define @t5 () (_ (_ tptp.binunion @t4) @t3)) % 0.38/0.61 (define @t6 () (_ (_ tptp.in @t5) @t2)) % 0.38/0.61 (define @t7 () (_ tptp.in @t3)) % 0.38/0.61 (define @t8 () (_ @t7 @t2)) % 0.38/0.61 (define @t9 () (@list @t3)) % 0.38/0.61 (define @t10 () (forall @t9 (=> @t8 @t6))) % 0.38/0.61 (define @t11 () (_ tptp.in @t4)) % 0.38/0.61 (define @t12 () (_ @t11 @t2)) % 0.38/0.61 (define @t13 () (=> @t12 @t10)) % 0.38/0.61 (define @t14 () (@list @t1 @t4)) % 0.38/0.61 (define @t15 () (forall @t14 @t13)) % 0.38/0.61 (define @t16 () (= tptp.binunionT_lem @t15)) % 0.38/0.61 (define @t17 () (_ tptp.setminus @t1)) % 0.38/0.61 (define @t18 () (_ @t17 @t3)) % 0.38/0.61 (define @t19 () (_ @t17 @t4)) % 0.38/0.61 (define @t20 () (_ (_ tptp.binunion @t19) @t18)) % 0.38/0.61 (define @t21 () (_ (_ tptp.binintersect @t4) @t3)) % 0.38/0.61 (define @t22 () (_ @t17 @t21)) % 0.38/0.61 (define @t23 () (= @t22 @t20)) % 0.38/0.61 (define @t24 () (forall @t9 (=> @t8 @t23))) % 0.38/0.61 (define @t25 () (=> @t12 @t24)) % 0.38/0.61 (define @t26 () (forall @t14 @t25)) % 0.38/0.61 (define @t27 () (= tptp.demorgan1 @t26)) % 0.38/0.61 (define @t28 () (_ (_ tptp.binintersect @t19) @t18)) % 0.38/0.61 (define @t29 () (_ @t17 @t5)) % 0.38/0.61 (define @t30 () (= @t29 @t28)) % 0.38/0.61 (define @t31 () (forall @t9 (=> @t8 @t30))) % 0.38/0.61 (define @t32 () (=> @t12 @t31)) % 0.38/0.61 (define @t33 () (forall @t14 @t32)) % 0.38/0.61 (define @t34 () (= tptp.demorgan2 @t33)) % 0.38/0.61 (define @t35 () (@var "W" $$unsorted)) % 0.38/0.61 (define @t36 () (_ @t17 @t35)) % 0.38/0.61 (define @t37 () (@var "Z" $$unsorted)) % 0.38/0.61 (define @t38 () (_ @t17 @t37)) % 0.38/0.61 (define @t39 () (_ (_ tptp.binintersect @t38) @t36)) % 0.38/0.61 (define @t40 () (_ (_ tptp.binunion @t28) @t39)) % 0.38/0.61 (define @t41 () (_ (_ tptp.binunion @t37) @t35)) % 0.38/0.61 (define @t42 () (_ (_ tptp.binintersect @t5) @t41)) % 0.38/0.61 (define @t43 () (_ @t17 @t42)) % 0.38/0.61 (define @t44 () (= @t43 @t40)) % 0.38/0.61 (define @t45 () (_ tptp.in @t35)) % 0.38/0.61 (define @t46 () (_ @t45 @t2)) % 0.38/0.61 (define @t47 () (@list @t35)) % 0.38/0.61 (define @t48 () (forall @t47 (=> @t46 @t44))) % 0.38/0.61 (define @t49 () (_ tptp.in @t37)) % 0.38/0.61 (define @t50 () (_ @t49 @t2)) % 0.38/0.61 (define @t51 () (=> @t50 @t48)) % 0.38/0.61 (define @t52 () (@list @t37)) % 0.38/0.61 (define @t53 () (forall @t52 @t51)) % 0.38/0.61 (define @t54 () (=> @t8 @t53)) % 0.38/0.61 (define @t55 () (forall @t9 @t54)) % 0.38/0.61 (define @t56 () (=> @t12 @t55)) % 0.38/0.61 (define @t57 () (forall @t14 @t56)) % 0.38/0.61 (define @t58 () (=> tptp.demorgan2 @t57)) % 0.38/0.61 (define @t59 () (=> tptp.demorgan1 @t58)) % 0.38/0.61 (define @t60 () (=> tptp.binunionT_lem @t59)) % 0.38/0.61 (define @t61 () (not @t60)) % 0.38/0.61 (define @t62 () (@var "BOUND_VARIABLE_7686" $$unsorted)) % 0.38/0.61 (define @t63 () (@var "BOUND_VARIABLE_7684" $$unsorted)) % 0.38/0.61 (define @t64 () (@var "BOUND_VARIABLE_7682" $$unsorted)) % 0.38/0.61 (define @t65 () (tptp.setminus @t1 @t4)) % 0.38/0.61 (define @t66 () (= (tptp.setminus @t1 (tptp.binintersect (tptp.binunion @t4 @t64) (tptp.binunion @t63 @t62))) (tptp.binunion (tptp.binintersect @t65 (tptp.setminus @t1 @t64)) (tptp.binintersect (tptp.setminus @t1 @t63) (tptp.setminus @t1 @t62))))) % 0.38/0.61 (define @t67 () (tptp.powerset @t1)) % 0.38/0.61 (define @t68 () (not (tptp.in @t62 @t67))) % 0.38/0.61 (define @t69 () (not (tptp.in @t63 @t67))) % 0.38/0.61 (define @t70 () (not (tptp.in @t64 @t67))) % 0.38/0.61 (define @t71 () (tptp.in @t4 @t67)) % 0.38/0.61 (define @t72 () (not @t71)) % 0.38/0.61 (define @t73 () (or @t72 @t70 @t69 @t68 @t66)) % 0.38/0.61 (define @t74 () (@list @t1 @t4 @t64 @t63 @t62)) % 0.38/0.61 (define @t75 () (forall @t74 @t73)) % 0.38/0.61 (define @t76 () (@var "BOUND_VARIABLE_7581" $$unsorted)) % 0.38/0.61 (define @t77 () (= (tptp.setminus @t1 (tptp.binunion @t4 @t76)) (tptp.binintersect @t65 (tptp.setminus @t1 @t76)))) % 0.38/0.61 (define @t78 () (not (tptp.in @t76 @t67))) % 0.38/0.61 (define @t79 () (or @t72 @t78 @t77)) % 0.38/0.61 (define @t80 () (or @t78 @t77)) % 0.38/0.61 (define @t81 () (or @t72 @t80)) % 0.38/0.61 (define @t82 () (@list @t1 @t4 @t76)) % 0.38/0.61 (define @t83 () (forall @t82 @t81)) % 0.38/0.61 (define @t84 () (@list @t76)) % 0.38/0.61 (define @t85 () (forall @t84 @t81)) % 0.38/0.61 (define @t86 () (forall @t84 @t80)) % 0.38/0.61 (define @t87 () (@list @t3)) % 0.38/0.61 (define @t88 () (or @t72 @t86)) % 0.38/0.61 (define @t89 () (tptp.setminus @t1 @t3)) % 0.38/0.61 (define @t90 () (tptp.binintersect @t65 @t89)) % 0.38/0.61 (define @t91 () (tptp.binunion @t4 @t3)) % 0.38/0.61 (define @t92 () (tptp.setminus @t1 @t91)) % 0.38/0.61 (define @t93 () (tptp.in @t3 @t67)) % 0.38/0.61 (define @t94 () (not @t93)) % 0.38/0.61 (define @t95 () (forall @t9 (or @t94 (= @t92 @t90)))) % 0.38/0.61 (define @t96 () (not @t12)) % 0.38/0.61 (define @t97 () (or @t96 @t95)) % 0.38/0.61 (define @t98 () (not @t8)) % 0.38/0.61 (define @t99 () (or @t98 @t30)) % 0.38/0.61 (define @t100 () (=> tptp.demorgan2 @t75)) % 0.38/0.61 (define @t101 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.38/0.61 (define @t102 () (= (tptp.setminus @t1 (tptp.binintersect @t4 @t101)) (tptp.binunion @t65 (tptp.setminus @t1 @t101)))) % 0.38/0.61 (define @t103 () (not (tptp.in @t101 @t67))) % 0.38/0.61 (define @t104 () (or @t103 @t102)) % 0.38/0.61 (define @t105 () (or @t72 @t104)) % 0.38/0.61 (define @t106 () (forall (@list @t1 @t4 @t101) @t105)) % 0.38/0.61 (define @t107 () (@list @t101)) % 0.38/0.61 (define @t108 () (forall @t107 @t105)) % 0.38/0.61 (define @t109 () (forall @t107 @t104)) % 0.38/0.61 (define @t110 () (or @t72 @t109)) % 0.38/0.61 (define @t111 () (tptp.binunion @t65 @t89)) % 0.38/0.61 (define @t112 () (tptp.binintersect @t4 @t3)) % 0.38/0.61 (define @t113 () (tptp.setminus @t1 @t112)) % 0.38/0.61 (define @t114 () (forall @t9 (or @t94 (= @t113 @t111)))) % 0.38/0.61 (define @t115 () (or @t96 @t114)) % 0.38/0.61 (define @t116 () (or @t98 @t23)) % 0.38/0.61 (define @t117 () (=> tptp.demorgan1 @t100)) % 0.38/0.61 (define @t118 () (@var "BOUND_VARIABLE_7515" $$unsorted)) % 0.38/0.61 (define @t119 () (tptp.in (tptp.binunion @t4 @t118) @t67)) % 0.38/0.61 (define @t120 () (not (tptp.in @t118 @t67))) % 0.38/0.61 (define @t121 () (or @t72 @t120 @t119)) % 0.38/0.61 (define @t122 () (or @t120 @t119)) % 0.38/0.61 (define @t123 () (or @t72 @t122)) % 0.38/0.61 (define @t124 () (@list @t1 @t4 @t118)) % 0.38/0.61 (define @t125 () (forall @t124 @t123)) % 0.38/0.61 (define @t126 () (@list @t118)) % 0.38/0.61 (define @t127 () (forall @t126 @t123)) % 0.38/0.61 (define @t128 () (forall @t126 @t122)) % 0.38/0.61 (define @t129 () (or @t72 @t128)) % 0.38/0.61 (define @t130 () (tptp.in @t91 @t67)) % 0.38/0.61 (define @t131 () (forall @t9 (or @t94 @t130))) % 0.38/0.61 (define @t132 () (or @t96 @t131)) % 0.38/0.61 (define @t133 () (or @t98 @t6)) % 0.38/0.61 (define @t134 () (=> tptp.binunionT_lem @t117)) % 0.38/0.61 (define @t135 () (or @t70 @t69 @t68 @t66)) % 0.38/0.61 (define @t136 () (or @t72 @t135)) % 0.38/0.61 (define @t137 () (forall @t74 @t136)) % 0.38/0.61 (define @t138 () (@list @t64 @t63 @t62)) % 0.38/0.61 (define @t139 () (forall @t138 @t136)) % 0.38/0.61 (define @t140 () (forall @t138 @t135)) % 0.38/0.61 (define @t141 () (@var "BOUND_VARIABLE_7656" $$unsorted)) % 0.38/0.61 (define @t142 () (@var "BOUND_VARIABLE_7654" $$unsorted)) % 0.38/0.61 (define @t143 () (or @t72 @t140)) % 0.38/0.61 (define @t144 () (= (tptp.setminus @t1 (tptp.binintersect @t91 (tptp.binunion @t142 @t141))) (tptp.binunion @t90 (tptp.binintersect (tptp.setminus @t1 @t142) (tptp.setminus @t1 @t141))))) % 0.38/0.61 (define @t145 () (not (tptp.in @t141 @t67))) % 0.38/0.61 (define @t146 () (not (tptp.in @t142 @t67))) % 0.38/0.61 (define @t147 () (or @t94 @t146 @t145 @t144)) % 0.38/0.61 (define @t148 () (@list @t3 @t142 @t141)) % 0.38/0.61 (define @t149 () (forall @t148 @t147)) % 0.38/0.61 (define @t150 () (or @t96 @t149)) % 0.38/0.61 (define @t151 () (or @t146 @t145 @t144)) % 0.38/0.61 (define @t152 () (or @t94 @t151)) % 0.38/0.61 (define @t153 () (forall @t148 @t152)) % 0.38/0.61 (define @t154 () (@list @t142 @t141)) % 0.38/0.61 (define @t155 () (forall @t154 @t152)) % 0.38/0.61 (define @t156 () (forall @t154 @t151)) % 0.38/0.61 (define @t157 () (@var "BOUND_VARIABLE_7631" $$unsorted)) % 0.38/0.61 (define @t158 () (or @t94 @t156)) % 0.38/0.61 (define @t159 () (tptp.setminus @t1 @t37)) % 0.38/0.61 (define @t160 () (= (tptp.setminus @t1 (tptp.binintersect @t91 (tptp.binunion @t37 @t157))) (tptp.binunion @t90 (tptp.binintersect @t159 (tptp.setminus @t1 @t157))))) % 0.38/0.61 (define @t161 () (not (tptp.in @t157 @t67))) % 0.38/0.61 (define @t162 () (tptp.in @t37 @t67)) % 0.38/0.61 (define @t163 () (not @t162)) % 0.38/0.61 (define @t164 () (or @t163 @t161 @t160)) % 0.38/0.61 (define @t165 () (@list @t37 @t157)) % 0.38/0.61 (define @t166 () (forall @t165 @t164)) % 0.38/0.61 (define @t167 () (or @t98 @t166)) % 0.38/0.61 (define @t168 () (or @t161 @t160)) % 0.38/0.61 (define @t169 () (or @t163 @t168)) % 0.38/0.61 (define @t170 () (forall @t165 @t169)) % 0.38/0.61 (define @t171 () (@list @t157)) % 0.38/0.61 (define @t172 () (forall @t171 @t169)) % 0.38/0.61 (define @t173 () (forall @t171 @t168)) % 0.38/0.61 (define @t174 () (or @t163 @t173)) % 0.38/0.61 (define @t175 () (tptp.setminus @t1 @t35)) % 0.38/0.61 (define @t176 () (tptp.binintersect @t159 @t175)) % 0.38/0.61 (define @t177 () (tptp.binunion @t90 @t176)) % 0.38/0.61 (define @t178 () (tptp.binunion @t37 @t35)) % 0.38/0.61 (define @t179 () (tptp.binintersect @t91 @t178)) % 0.38/0.61 (define @t180 () (tptp.setminus @t1 @t179)) % 0.38/0.61 (define @t181 () (tptp.in @t35 @t67)) % 0.38/0.61 (define @t182 () (forall @t47 (or (not @t181) (= @t180 @t177)))) % 0.38/0.61 (define @t183 () (not @t50)) % 0.38/0.61 (define @t184 () (or @t183 @t182)) % 0.38/0.61 (define @t185 () (not @t46)) % 0.38/0.61 (define @t186 () (or @t185 @t44)) % 0.38/0.61 (define @t187 () (@quantifiers_skolemize @t75 4)) % 0.38/0.61 (define @t188 () (@quantifiers_skolemize @t75 3)) % 0.38/0.61 (define @t189 () (tptp.binunion @t188 @t187)) % 0.38/0.61 (define @t190 () (@quantifiers_skolemize @t75 2)) % 0.38/0.61 (define @t191 () (@quantifiers_skolemize @t75 1)) % 0.38/0.61 (define @t192 () (tptp.binunion @t191 @t190)) % 0.38/0.61 (define @t193 () (@quantifiers_skolemize @t75 0)) % 0.38/0.61 (define @t194 () (tptp.binintersect (tptp.setminus @t193 @t188) (tptp.setminus @t193 @t187))) % 0.38/0.61 (define @t195 () (tptp.binintersect (tptp.setminus @t193 @t191) (tptp.setminus @t193 @t190))) % 0.38/0.61 (define @t196 () (tptp.setminus @t193 (tptp.binintersect @t192 @t189))) % 0.38/0.61 (define @t197 () (= @t196 (tptp.binunion @t195 @t194))) % 0.38/0.61 (define @t198 () (tptp.powerset @t193)) % 0.38/0.61 (define @t199 () (tptp.in @t187 @t198)) % 0.38/0.61 (define @t200 () (not @t199)) % 0.38/0.61 (define @t201 () (tptp.in @t188 @t198)) % 0.38/0.61 (define @t202 () (not @t201)) % 0.38/0.61 (define @t203 () (tptp.in @t190 @t198)) % 0.38/0.61 (define @t204 () (not @t203)) % 0.38/0.61 (define @t205 () (tptp.in @t191 @t198)) % 0.38/0.61 (define @t206 () (not @t205)) % 0.38/0.61 (define @t207 () (or @t206 @t204 @t202 @t200 @t197)) % 0.38/0.61 (define @t208 () (@list true)) % 0.38/0.61 (define @t209 () (@list @t207)) % 0.38/0.61 (define @t210 () (tptp.setminus @t193 @t189)) % 0.38/0.61 (define @t211 () (or @t202 @t200 (= @t210 @t194))) % 0.38/0.61 (define @t212 () (forall @t82 @t79)) % 0.38/0.61 (define @t213 () (@list @t193 @t188 @t187)) % 0.38/0.61 (define @t214 () (= @t194 @t210)) % 0.38/0.61 (define @t215 () (or @t202 @t200 @t214)) % 0.38/0.61 (define @t216 () (@list false)) % 0.38/0.61 (define @t217 () (@list @t212)) % 0.38/0.61 (define @t218 () (@list false false false)) % 0.38/0.61 (define @t219 () (tptp.setminus @t193 @t192)) % 0.38/0.61 (define @t220 () (or @t206 @t204 (= @t219 @t195))) % 0.38/0.61 (define @t221 () (@list @t193 @t191 @t190)) % 0.38/0.61 (define @t222 () (= @t195 @t219)) % 0.38/0.61 (define @t223 () (or @t206 @t204 @t222)) % 0.38/0.61 (define @t224 () (tptp.binunion @t219 @t210)) % 0.38/0.61 (define @t225 () (= @t196 @t224)) % 0.38/0.61 (define @t226 () (tptp.in @t192 @t198)) % 0.38/0.61 (define @t227 () (or @t206 @t204 @t226)) % 0.38/0.61 (define @t228 () (tptp.in @t189 @t198)) % 0.38/0.61 (define @t229 () (not @t228)) % 0.38/0.61 (define @t230 () (not @t226)) % 0.38/0.61 (define @t231 () (or @t230 @t229 @t225)) % 0.38/0.61 (define @t232 () (or @t202 @t200 @t228)) % 0.38/0.61 (define @t233 () (not @t232)) % 0.38/0.61 (define @t234 () (forall @t124 @t121)) % 0.38/0.61 (assume @p1 @t16) % 0.38/0.61 (assume @p2 @t27) % 0.38/0.61 (assume @p3 @t34) % 0.38/0.61 (assume @p4 @t61) % 0.38/0.61 (assume @p5 true) % 0.38/0.61 (step @p6 :rule refl :args (@t75)) % 0.38/0.61 (step @p7 :rule aci_norm :args ((= @t81 @t79))) % 0.38/0.61 (step @p8 :rule cong :premises (@p7) :args (@t83)) % 0.38/0.61 (step @p9 :rule quant-merge-prenex :args ((= (forall @t14 @t85) @t83))) % 0.38/0.61 (step @p10 :rule alpha_equiv :args (@t86 (@list @t76) @t87)) % 0.38/0.61 (step @p11 :rule refl :args (@t72)) % 0.38/0.61 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t88)) % 0.38/0.61 (step @p13 :rule quant-miniscope-or :args ((= @t85 @t88))) % 0.38/0.61 (step @p14 :rule trans :premises (@p13 @p12)) % 0.38/0.61 (step @p15 :rule symm :premises (@p14)) % 0.38/0.61 (step @p16 :rule cong :premises (@p15) :args ((forall @t14 (or @t72 @t95)))) % 0.38/0.61 (step @p17 :rule trans :premises (@p16 @p9)) % 0.38/0.61 (step @p18 :rule trans :premises (@p17 @p8)) % 0.38/0.61 (step @p19 :rule refl :args (@t95)) % 0.38/0.61 (step @p20 :rule refl :args ((tptp.in @t4 @t2))) % 0.38/0.61 (step @p21 :rule refl :args (@t67)) % 0.38/0.61 (step @p22 :rule refl :args (@t4)) % 0.38/0.61 (step @p23 :rule cong :premises (@p22 @p21) :args (@t71)) % 0.38/0.61 (step @p24 :rule trans :premises (@p23 @p20)) % 0.38/0.61 (step @p25 :rule refl :args (@t11)) % 0.38/0.61 (step @p26 :rule ho_cong :premises (@p25 @p21)) % 0.38/0.61 (step @p27 :rule cong :premises (@p26 @p24) :args ((= (_ @t11 @t67) @t71))) % 0.38/0.61 (step @p28 :rule symm :premises (@p27)) % 0.38/0.61 (step @p29 :rule refl :args (@t12)) % 0.38/0.61 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.38/0.61 (step @p31 :rule refl :args (@t2)) % 0.38/0.61 (step @p32 :rule cong :premises (@p31 @p21) :args ((= @t2 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0.38/0.61 (step @p274 :rule ho_cong :premises (@p268 @p34)) % 0.38/0.61 (step @p275 :rule trans :premises (@p274 @p273)) % 0.38/0.61 (step @p276 :rule cong :premises (@p275) :args (@t183)) % 0.38/0.61 (step @p277 :rule nary_cong :premises (@p276 @p263) :args (@t184)) % 0.38/0.61 (step @p278 :rule cong :premises (@p277) :args ((forall @t52 @t184))) % 0.38/0.61 (step @p279 :rule trans :premises (@p278 @p262)) % 0.38/0.61 (step @p280 :rule bool-impl-elim :args (@t50 @t182)) % 0.38/0.61 (step @p281 :rule cong :premises (@p280) :args ((forall @t52 (=> @t50 @t182)))) % 0.38/0.61 (step @p282 :rule trans :premises (@p281 @p279)) % 0.38/0.61 (step @p283 :rule refl :args ((tptp.binunion @t28 @t39))) % 0.38/0.61 (step @p284 :rule refl :args ((tptp.binintersect @t38 @t36))) % 0.38/0.61 (step @p285 :rule refl :args (@t175)) % 0.38/0.61 (step @p286 :rule refl :args (@t159)) % 0.38/0.61 (step @p287 :rule cong :premises (@p286 @p285) :args (@t176)) % 0.38/0.61 (step @p288 :rule trans :premises (@p287 @p284)) % 0.38/0.61 (step @p289 :rule cong :premises (@p48 @p288) :args (@t177)) % 0.38/0.61 (step @p290 :rule trans :premises (@p289 @p283)) % 0.38/0.61 (step @p291 :rule ho_cong :premises (@p132 @p48)) % 0.38/0.61 (step @p292 :rule ho_cong :premises (@p291 @p288)) % 0.38/0.61 (step @p293 :rule cong :premises (@p292 @p290) :args ((= (_ (_ tptp.binunion @t90) @t176) @t177))) % 0.38/0.61 (step @p294 :rule symm :premises (@p293)) % 0.38/0.61 (step @p295 :rule refl :args (@t40)) % 0.38/0.61 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.38/0.61 (step @p297 :rule ho_cong :premises (@p49 @p286)) % 0.38/0.61 (step @p298 :rule ho_cong :premises (@p297 @p285)) % 0.38/0.61 (step @p299 :rule cong :premises (@p298 @p288) :args ((= (_ (_ tptp.binintersect @t159) @t175) @t176))) % 0.38/0.61 (step @p300 :rule symm :premises (@p299)) % 0.38/0.61 (step @p301 :rule refl :args (@t39)) % 0.38/0.61 (step @p302 :rule eq_resolve :premises (@p301 @p300)) % 0.38/0.61 (step @p303 :rule refl :args (@t36)) % 0.38/0.61 (step @p304 :rule cong :premises (@p303 @p285) :args ((= @t36 @t175))) % 0.38/0.61 (step @p305 :rule symm :premises (@p304)) % 0.38/0.61 (step @p306 :rule eq_resolve :premises (@p303 @p305)) % 0.38/0.61 (step @p307 :rule refl :args (@t38)) % 0.38/0.61 (step @p308 :rule cong :premises (@p307 @p286) :args ((= @t38 @t159))) % 0.38/0.61 (step @p309 :rule symm :premises (@p308)) % 0.38/0.61 (step @p310 :rule eq_resolve :premises (@p307 @p309)) % 0.38/0.61 (step @p311 :rule ho_cong :premises (@p49 @p310)) % 0.38/0.61 (step @p312 :rule ho_cong :premises (@p311 @p306)) % 0.38/0.61 (step @p313 :rule trans :premises (@p312 @p302)) % 0.38/0.61 (step @p314 :rule ho_cong :premises (@p132 @p66)) % 0.38/0.61 (step @p315 :rule ho_cong :premises (@p314 @p313)) % 0.38/0.61 (step @p316 :rule trans :premises (@p315 @p296)) % 0.38/0.61 (step @p317 :rule refl :args ((tptp.setminus @t1 @t42))) % 0.38/0.61 (step @p318 :rule refl :args ((tptp.binintersect @t5 @t41))) % 0.38/0.61 (step @p319 :rule refl :args (@t178)) % 0.38/0.61 (step @p320 :rule cong :premises (@p68 @p319) :args (@t179)) % 0.38/0.61 (step @p321 :rule trans :premises (@p320 @p318)) % 0.38/0.61 (step @p322 :rule cong :premises (@p69 @p321) :args (@t180)) % 0.38/0.61 (step @p323 :rule trans :premises (@p322 @p317)) % 0.38/0.61 (step @p324 :rule ho_cong :premises (@p72 @p321)) % 0.38/0.61 (step @p325 :rule cong :premises (@p324 @p323) :args ((= (_ @t17 @t179) @t180))) % 0.38/0.61 (step @p326 :rule symm :premises (@p325)) % 0.38/0.61 (step @p327 :rule refl :args (@t43)) % 0.38/0.61 (step @p328 :rule eq_resolve :premises (@p327 @p326)) % 0.38/0.61 (step @p329 :rule ho_cong :premises (@p49 @p68)) % 0.38/0.61 (step @p330 :rule ho_cong :premises (@p329 @p319)) % 0.38/0.61 (step @p331 :rule cong :premises (@p330 @p321) :args ((= (_ (_ tptp.binintersect @t91) @t178) @t179))) % 0.38/0.61 (step @p332 :rule symm :premises (@p331)) % 0.38/0.61 (step @p333 :rule refl :args (@t42)) % 0.38/0.61 (step @p334 :rule eq_resolve :premises (@p333 @p332)) % 0.38/0.61 (step @p335 :rule refl :args (@t41)) % 0.38/0.61 (step @p336 :rule cong :premises (@p335 @p319) :args ((= @t41 @t178))) % 0.38/0.61 (step @p337 :rule symm :premises (@p336)) % 0.38/0.61 (step @p338 :rule eq_resolve :premises (@p335 @p337)) % 0.38/0.61 (step @p339 :rule ho_cong :premises (@p49 @p81)) % 0.38/0.61 (step @p340 :rule ho_cong :premises (@p339 @p338)) % 0.38/0.61 (step @p341 :rule trans :premises (@p340 @p334)) % 0.38/0.61 (step @p342 :rule ho_cong :premises (@p72 @p341)) % 0.38/0.61 (step @p343 :rule trans :premises (@p342 @p328)) % 0.38/0.61 (step @p344 :rule cong :premises (@p343 @p316) :args (@t44)) % 0.38/0.61 (step @p345 :rule refl :args ((tptp.in @t35 @t2))) % 0.38/0.61 (step @p346 :rule refl :args (@t35)) % 0.38/0.61 (step @p347 :rule cong :premises (@p346 @p21) :args (@t181)) % 0.38/0.61 (step @p348 :rule trans :premises (@p347 @p345)) % 0.38/0.61 (step @p349 :rule refl :args (@t45)) % 0.38/0.61 (step @p350 :rule ho_cong :premises (@p349 @p21)) % 0.38/0.61 (step @p351 :rule cong :premises (@p350 @p348) :args ((= (_ @t45 @t67) @t181))) % 0.38/0.61 (step @p352 :rule symm :premises (@p351)) % 0.38/0.61 (step @p353 :rule refl :args (@t46)) % 0.38/0.61 (step @p354 :rule eq_resolve :premises (@p353 @p352)) % 0.38/0.61 (step @p355 :rule ho_cong :premises (@p349 @p34)) % 0.38/0.61 (step @p356 :rule trans :premises (@p355 @p354)) % 0.38/0.61 (step @p357 :rule cong :premises (@p356) :args (@t185)) % 0.38/0.61 (step @p358 :rule nary_cong :premises (@p357 @p344) :args (@t186)) % 0.38/0.61 (step @p359 :rule cong :premises (@p358) :args ((forall @t47 @t186))) % 0.38/0.61 (step @p360 :rule bool-impl-elim :args (@t46 @t44)) % 0.38/0.61 (step @p361 :rule cong :premises (@p360) :args (@t48)) % 0.38/0.61 (step @p362 :rule trans :premises (@p361 @p359)) % 0.38/0.61 (step @p363 :rule refl :args (@t50)) % 0.38/0.61 (step @p364 :rule cong :premises (@p363 @p362) :args (@t51)) % 0.38/0.61 (step @p365 :rule cong :premises (@p364) :args (@t53)) % 0.38/0.61 (step @p366 :rule trans :premises (@p365 @p282)) % 0.38/0.61 (step @p367 :rule refl :args (@t8)) % 0.38/0.61 (step @p368 :rule cong :premises (@p367 @p366) :args (@t54)) % 0.38/0.61 (step @p369 :rule cong :premises (@p368) :args (@t55)) % 0.38/0.61 (step @p370 :rule trans :premises (@p369 @p250)) % 0.38/0.61 (step @p371 :rule cong :premises (@p103 @p370) :args (@t56)) % 0.38/0.61 (step @p372 :rule cong :premises (@p371) :args (@t57)) % 0.38/0.61 (step @p373 :rule trans :premises (@p372 @p231)) % 0.38/0.61 (step @p374 :rule cong :premises (@p107 @p373) :args (@t58)) % 0.38/0.61 (step @p375 :rule cong :premises (@p166 @p374) :args (@t59)) % 0.38/0.61 (step @p376 :rule cong :premises (@p209 @p375) :args (@t60)) % 0.38/0.61 (step @p377 :rule cong :premises (@p376) :args (@t61)) % 0.38/0.61 (step @p378 :rule trans :premises (@p377 @p213)) % 0.38/0.61 (step @p379 :rule eq_resolve :premises (@p4 @p378)) % 0.38/0.61 (step @p380 :rule not_implies_elim1 :premises (@p379)) % 0.38/0.61 (step @p381 :rule not_implies_elim2 :premises (@p379)) % 0.38/0.61 (step @p382 :rule not_implies_elim1 :premises (@p381)) % 0.38/0.61 (step @p383 :rule instantiate :premises (@p382) :args ((@list @t193 @t192 @t189))) % 0.38/0.61 (step @p384 :rule not_implies_elim2 :premises (@p381)) % 0.38/0.61 (step @p385 :rule not_implies_elim2 :premises (@p384)) % 0.38/0.61 (step @p386 :rule skolemize :premises (@p385)) % 0.38/0.61 (step @p387 :rule cnf_or_neg :args (@t207 4)) % 0.38/0.61 (step @p388 :rule chain_m_resolution :premises (@p387 @p386) :args ((not @t197) @t208 @t209)) % 0.38/0.61 (step @p389 :rule false_intro :premises (@p388)) % 0.38/0.61 (step @p390 :rule not_implies_elim1 :premises (@p384)) % 0.38/0.61 (step @p391 :rule eq-symm :args (@t210 @t194)) % 0.38/0.61 (step @p392 :rule refl :args (@t200)) % 0.38/0.61 (step @p393 :rule refl :args (@t202)) % 0.38/0.61 (step @p394 :rule nary_cong :premises (@p393 @p392 @p391) :args (@t211)) % 0.38/0.61 (step @p395 :rule refl :args (@t212)) % 0.38/0.61 (step @p396 :rule cong :premises (@p395 @p394) :args ((=> @t212 @t211))) % 0.38/0.61 (assume-push @p470 @t212) % 0.38/0.61 (step @p398 :rule instantiate :premises (@p390) :args (@t213)) % 0.38/0.61 (step-pop @p471 :rule scope :premises (@p398)) % 0.38/0.61 (step @p399 :rule process_scope :premises (@p471) :args (@t211)) % 0.38/0.61 (step @p401 :rule eq_resolve :premises (@p399 @p396)) % 0.38/0.61 (step @p402 :rule implies_elim :premises (@p401)) % 0.38/0.61 (step @p403 :rule chain_m_resolution :premises (@p402 @p390) :args (@t215 @t216 @t217)) % 0.38/0.61 (step @p404 :rule bool-double-not-elim :args (@t199)) % 0.38/0.61 (step @p405 :rule refl :args (@t207)) % 0.38/0.61 (step @p406 :rule nary_cong :premises (@p405 @p404) :args ((or @t207 (not @t200)))) % 0.38/0.61 (step @p407 :rule cnf_or_neg :args (@t207 3)) % 0.38/0.61 (step @p408 :rule eq_resolve :premises (@p407 @p406)) % 0.38/0.61 (step @p409 :rule reordering :premises (@p408) :args ((or @t199 @t207))) % 0.38/0.61 (step @p410 :rule chain_m_resolution :premises (@p409 @p386) :args (@t199 @t208 @t209)) % 0.38/0.61 (step @p411 :rule bool-double-not-elim :args (@t201)) % 0.38/0.61 (step @p412 :rule nary_cong :premises (@p405 @p411) :args ((or @t207 (not @t202)))) % 0.38/0.61 (step @p413 :rule cnf_or_neg :args (@t207 2)) % 0.38/0.61 (step @p414 :rule eq_resolve :premises (@p413 @p412)) % 0.38/0.61 (step @p415 :rule reordering :premises (@p414) :args ((or @t201 @t207))) % 0.38/0.61 (step @p416 :rule chain_m_resolution :premises (@p415 @p386) :args (@t201 @t208 @t209)) % 0.38/0.61 (step @p417 :rule cnf_or_pos :args (@t215)) % 0.38/0.61 (step @p418 :rule reordering :premises (@p417) :args ((or @t202 @t200 @t214 (not @t215)))) % 0.38/0.61 (step @p419 :rule chain_m_resolution :premises (@p418 @p416 @p410 @p403) :args (@t214 @t218 (@list @t201 @t199 @t215))) % 0.38/0.61 (step @p420 :rule symm :premises (@p419)) % 0.38/0.61 (step @p421 :rule eq-symm :args (@t219 @t195)) % 0.38/0.61 (step @p422 :rule refl :args (@t204)) % 0.38/0.61 (step @p423 :rule refl :args (@t206)) % 0.38/0.61 (step @p424 :rule nary_cong :premises (@p423 @p422 @p421) :args (@t220)) % 0.38/0.61 (step @p425 :rule cong :premises (@p395 @p424) :args ((=> @t212 @t220))) % 0.38/0.61 (assume-push @p472 @t212) % 0.38/0.61 (step @p427 :rule instantiate :premises (@p390) :args (@t221)) % 0.38/0.61 (step-pop @p473 :rule scope :premises (@p427)) % 0.38/0.61 (step @p428 :rule process_scope :premises (@p473) :args (@t220)) % 0.38/0.61 (step @p430 :rule eq_resolve :premises (@p428 @p425)) % 0.38/0.61 (step @p431 :rule implies_elim :premises (@p430)) % 0.38/0.61 (step @p432 :rule chain_m_resolution :premises (@p431 @p390) :args (@t223 @t216 @t217)) % 0.38/0.61 (step @p433 :rule bool-double-not-elim :args (@t203)) % 0.38/0.61 (step @p434 :rule nary_cong :premises (@p405 @p433) :args ((or @t207 (not @t204)))) % 0.38/0.61 (step @p435 :rule cnf_or_neg :args (@t207 1)) % 0.38/0.61 (step @p436 :rule eq_resolve :premises (@p435 @p434)) % 0.38/0.61 (step @p437 :rule reordering :premises (@p436) :args ((or @t203 @t207))) % 0.38/0.61 (step @p438 :rule chain_m_resolution :premises (@p437 @p386) :args (@t203 @t208 @t209)) % 0.38/0.61 (step @p439 :rule bool-double-not-elim :args (@t205)) % 0.38/0.61 (step @p440 :rule nary_cong :premises (@p405 @p439) :args ((or @t207 (not @t206)))) % 0.38/0.61 (step @p441 :rule cnf_or_neg :args (@t207 0)) % 0.38/0.61 (step @p442 :rule eq_resolve :premises (@p441 @p440)) % 0.38/0.61 (step @p443 :rule reordering :premises (@p442) :args ((or @t205 @t207))) % 0.38/0.61 (step @p444 :rule chain_m_resolution :premises (@p443 @p386) :args (@t205 @t208 @t209)) % 0.38/0.61 (step @p445 :rule cnf_or_pos :args (@t223)) % 0.38/0.61 (step @p446 :rule reordering :premises (@p445) :args ((or @t206 @t204 @t222 (not @t223)))) % 0.38/0.61 (step @p447 :rule chain_m_resolution :premises (@p446 @p444 @p438 @p432) :args (@t222 @t218 (@list @t205 @t203 @t223))) % 0.38/0.61 (step @p448 :rule symm :premises (@p447)) % 0.38/0.61 (step @p449 :rule cong :premises (@p448 @p420) :args (@t224)) % 0.38/0.61 (step @p450 :rule refl :args (@t196)) % 0.38/0.61 (step @p451 :rule cong :premises (@p450 @p449) :args (@t225)) % 0.38/0.61 (step @p452 :rule trans :premises (@p451 @p389)) % 0.38/0.61 (step @p453 :rule false_elim :premises (@p452)) % 0.38/0.61 (step @p454 :rule instantiate :premises (@p380) :args (@t221)) % 0.38/0.61 (step @p455 :rule cnf_or_pos :args (@t227)) % 0.38/0.61 (step @p456 :rule reordering :premises (@p455) :args ((or @t206 @t204 @t226 (not @t227)))) % 0.38/0.61 (step @p457 :rule chain_m_resolution :premises (@p456 @p444 @p438 @p454) :args (@t226 @t218 (@list @t205 @t203 @t227))) % 0.38/0.61 (step @p458 :rule cnf_or_pos :args (@t231)) % 0.38/0.61 (step @p459 :rule reordering :premises (@p458) :args ((or @t230 @t229 @t225 (not @t231)))) % 0.38/0.61 (step @p460 :rule chain_m_resolution :premises (@p459 @p457 @p453 @p383) :args (@t229 (@list false true false) (@list @t226 @t225 @t231))) % 0.38/0.61 (step @p461 :rule cnf_or_pos :args (@t232)) % 0.38/0.61 (step @p462 :rule reordering :premises (@p461) :args ((or @t202 @t200 @t228 @t233))) % 0.38/0.61 (step @p463 :rule chain_m_resolution :premises (@p462 @p416 @p410 @p460) :args (@t233 (@list false false true) (@list @t201 @t199 @t228))) % 0.38/0.61 (assume-push @p474 @t234) % 0.38/0.61 (step @p465 :rule instantiate :premises (@p380) :args (@t213)) % 0.38/0.61 (step-pop @p475 :rule scope :premises (@p465)) % 0.38/0.61 (step @p466 :rule process_scope :premises (@p475) :args (@t232)) % 0.38/0.61 (step @p468 :rule implies_elim :premises (@p466)) % 0.38/0.61 (step @p469 false :rule chain_m_resolution :premises (@p468 @p463 @p380) :args (false (@list true false) (@list @t232 @t234))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------