%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU706^2 : 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 : n017.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 08:52:49 AM UTC 2026 % Result : Theorem 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU706^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 17:46:46 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.36/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-sort $$unsorted 0) % 0.36/0.58 (declare-const tptp.emptyset $$unsorted) % 0.36/0.58 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.setunionsingleton Bool) % 0.36/0.58 (declare-const tptp.setunion__Cong Bool) % 0.36/0.58 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.setadjoin__Cong Bool) % 0.36/0.58 (declare-const tptp.in__Cong Bool) % 0.36/0.58 (declare-const tptp.uniqinunit Bool) % 0.36/0.58 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.36/0.58 (define @t1 () (@var "Xy" $$unsorted)) % 0.36/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.36/0.58 (define @t3 () (= @t2 @t1)) % 0.36/0.58 (define @t4 () (_ tptp.setadjoin @t1)) % 0.36/0.58 (define @t5 () (_ @t4 tptp.emptyset)) % 0.36/0.58 (define @t6 () (_ tptp.in @t2)) % 0.36/0.58 (define @t7 () (_ @t6 @t5)) % 0.36/0.58 (define @t8 () (@list @t2 @t1)) % 0.36/0.58 (define @t9 () (forall @t8 (=> @t7 @t3))) % 0.36/0.58 (define @t10 () (= tptp.uniqinunit @t9)) % 0.36/0.58 (define @t11 () (@var "B" $$unsorted)) % 0.36/0.58 (define @t12 () (_ (_ tptp.in @t1) @t11)) % 0.36/0.58 (define @t13 () (@var "A" $$unsorted)) % 0.36/0.58 (define @t14 () (_ @t6 @t13)) % 0.36/0.58 (define @t15 () (= @t14 @t12)) % 0.36/0.58 (define @t16 () (forall @t8 (=> @t3 @t15))) % 0.36/0.58 (define @t17 () (= @t13 @t11)) % 0.36/0.58 (define @t18 () (=> @t17 @t16)) % 0.36/0.58 (define @t19 () (@list @t13 @t11)) % 0.36/0.58 (define @t20 () (forall @t19 @t18)) % 0.36/0.58 (define @t21 () (= tptp.in__Cong @t20)) % 0.36/0.58 (define @t22 () (@var "Xu" $$unsorted)) % 0.36/0.58 (define @t23 () (_ @t4 @t22)) % 0.36/0.58 (define @t24 () (@var "Xz" $$unsorted)) % 0.36/0.58 (define @t25 () (_ tptp.setadjoin @t2)) % 0.36/0.58 (define @t26 () (_ @t25 @t24)) % 0.36/0.58 (define @t27 () (= @t26 @t23)) % 0.36/0.58 (define @t28 () (= @t24 @t22)) % 0.36/0.58 (define @t29 () (@list @t24 @t22)) % 0.36/0.58 (define @t30 () (forall @t29 (=> @t28 @t27))) % 0.36/0.58 (define @t31 () (=> @t3 @t30)) % 0.36/0.58 (define @t32 () (forall @t8 @t31)) % 0.36/0.58 (define @t33 () (= tptp.setadjoin__Cong @t32)) % 0.36/0.58 (define @t34 () (_ tptp.setunion @t11)) % 0.36/0.58 (define @t35 () (_ tptp.setunion @t13)) % 0.36/0.58 (define @t36 () (= @t35 @t34)) % 0.36/0.58 (define @t37 () (forall @t19 (=> @t17 @t36))) % 0.36/0.58 (define @t38 () (= tptp.setunion__Cong @t37)) % 0.36/0.58 (define @t39 () (_ @t25 tptp.emptyset)) % 0.36/0.58 (define @t40 () (_ tptp.setunion @t39)) % 0.36/0.58 (define @t41 () (@list @t2)) % 0.36/0.58 (define @t42 () (forall @t41 (= @t40 @t2))) % 0.36/0.58 (define @t43 () (= tptp.setunionsingleton @t42)) % 0.36/0.58 (define @t44 () (@var "X" $$unsorted)) % 0.36/0.58 (define @t45 () (_ tptp.setunion @t44)) % 0.36/0.58 (define @t46 () (_ @t6 @t44)) % 0.36/0.58 (define @t47 () (=> @t46 (= @t45 @t2))) % 0.36/0.58 (define @t48 () (forall @t41 @t47)) % 0.36/0.58 (define @t49 () (=> (_ tptp.singleton @t44) @t48)) % 0.36/0.58 (define @t50 () (@list @t44)) % 0.36/0.58 (define @t51 () (forall @t50 @t49)) % 0.36/0.58 (define @t52 () (=> tptp.setunionsingleton @t51)) % 0.36/0.58 (define @t53 () (=> tptp.setunion__Cong @t52)) % 0.36/0.58 (define @t54 () (=> tptp.setadjoin__Cong @t53)) % 0.36/0.58 (define @t55 () (=> tptp.in__Cong @t54)) % 0.36/0.58 (define @t56 () (=> tptp.uniqinunit @t55)) % 0.36/0.58 (define @t57 () (not @t56)) % 0.36/0.58 (define @t58 () (= @t13 @t39)) % 0.36/0.58 (define @t59 () (and @t14 @t58)) % 0.36/0.58 (define @t60 () (exists @t41 @t59)) % 0.36/0.58 (define @t61 () (@list @t13)) % 0.36/0.58 (define @t62 () (lambda @t61 @t60)) % 0.36/0.58 (define @t63 () (@var "BOUND_VARIABLE_7661" $$unsorted)) % 0.36/0.58 (define @t64 () (tptp.setadjoin @t63 tptp.emptyset)) % 0.36/0.58 (define @t65 () (tptp.setunion @t64)) % 0.36/0.58 (define @t66 () (@var "BOUND_VARIABLE_7669" $$unsorted)) % 0.36/0.58 (define @t67 () (= @t66 @t65)) % 0.36/0.58 (define @t68 () (not (tptp.in @t66 @t64))) % 0.36/0.58 (define @t69 () (not (tptp.in @t63 @t64))) % 0.36/0.58 (define @t70 () (or @t69 @t68 @t67)) % 0.36/0.58 (define @t71 () (@list @t63 @t66)) % 0.36/0.58 (define @t72 () (forall @t71 @t70)) % 0.36/0.58 (define @t73 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.36/0.58 (define @t74 () (tptp.setunion @t73)) % 0.36/0.58 (define @t75 () (=> (forall @t41 (= @t2 @t74)) @t72)) % 0.36/0.58 (define @t76 () (=> true (=> true @t75))) % 0.36/0.58 (define @t77 () (=> true @t76)) % 0.36/0.58 (define @t78 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.36/0.58 (define @t79 () (tptp.in @t2 @t78)) % 0.36/0.58 (define @t80 () (forall @t8 (or (not @t79) @t3))) % 0.36/0.58 (define @t81 () (=> @t80 @t77)) % 0.36/0.58 (define @t82 () (= @t2 @t40)) % 0.36/0.58 (define @t83 () (=> tptp.setunionsingleton @t72)) % 0.36/0.58 (define @t84 () (@list @t11)) % 0.36/0.58 (define @t85 () (tptp.setunion @t11)) % 0.36/0.58 (define @t86 () (not (= @t11 @t11))) % 0.36/0.58 (define @t87 () (or @t86 (= @t85 @t85))) % 0.36/0.58 (define @t88 () (tptp.setunion @t13)) % 0.36/0.58 (define @t89 () (= @t88 @t85)) % 0.36/0.58 (define @t90 () (not @t17)) % 0.36/0.58 (define @t91 () (or @t90 @t90 @t89)) % 0.36/0.58 (define @t92 () (or @t90 @t89)) % 0.36/0.58 (define @t93 () (forall @t61 @t92)) % 0.36/0.58 (define @t94 () (forall @t84 @t93)) % 0.36/0.58 (define @t95 () (forall (@list @t11 @t13) @t92)) % 0.36/0.58 (define @t96 () (or @t90 @t36)) % 0.36/0.58 (define @t97 () (=> tptp.setunion__Cong @t83)) % 0.36/0.58 (define @t98 () (@var "BOUND_VARIABLE_7587" $$unsorted)) % 0.36/0.58 (define @t99 () (@list @t1 @t98)) % 0.36/0.58 (define @t100 () (tptp.setadjoin @t1 @t98)) % 0.36/0.58 (define @t101 () (not (= @t1 @t1))) % 0.36/0.58 (define @t102 () (or @t101 (= @t100 @t100))) % 0.36/0.58 (define @t103 () (= @t100 (tptp.setadjoin @t2 @t98))) % 0.36/0.58 (define @t104 () (not @t3)) % 0.36/0.58 (define @t105 () (or @t104 @t104 @t103)) % 0.36/0.58 (define @t106 () (or @t104 @t103)) % 0.36/0.58 (define @t107 () (forall @t41 @t106)) % 0.36/0.58 (define @t108 () (forall @t99 @t107)) % 0.36/0.58 (define @t109 () (forall (@list @t1 @t98 @t2) @t106)) % 0.36/0.58 (define @t110 () (forall (@list @t2 @t1 @t98) @t106)) % 0.36/0.58 (define @t111 () (@list @t98)) % 0.36/0.58 (define @t112 () (forall @t111 @t106)) % 0.36/0.58 (define @t113 () (forall @t111 @t103)) % 0.36/0.58 (define @t114 () (or @t104 @t113)) % 0.36/0.58 (define @t115 () (tptp.setadjoin @t2 @t22)) % 0.36/0.58 (define @t116 () (tptp.setadjoin @t1 @t22)) % 0.36/0.58 (define @t117 () (= @t116 @t115)) % 0.36/0.58 (define @t118 () (@list @t22)) % 0.36/0.58 (define @t119 () (forall @t118 @t117)) % 0.36/0.58 (define @t120 () (not (= @t22 @t22))) % 0.36/0.58 (define @t121 () (or @t120 (= @t115 @t116))) % 0.36/0.58 (define @t122 () (tptp.setadjoin @t2 @t24)) % 0.36/0.58 (define @t123 () (= @t122 @t116)) % 0.36/0.58 (define @t124 () (not @t28)) % 0.36/0.58 (define @t125 () (or @t124 @t124 @t123)) % 0.36/0.58 (define @t126 () (@list @t24)) % 0.36/0.58 (define @t127 () (or @t124 @t123)) % 0.36/0.58 (define @t128 () (forall @t126 @t127)) % 0.36/0.58 (define @t129 () (forall @t118 @t128)) % 0.36/0.58 (define @t130 () (forall (@list @t22 @t24) @t127)) % 0.36/0.58 (define @t131 () (or @t124 @t27)) % 0.36/0.58 (define @t132 () (=> tptp.setadjoin__Cong @t97)) % 0.36/0.58 (define @t133 () (@var "BOUND_VARIABLE_7547" $$unsorted)) % 0.36/0.58 (define @t134 () (@list @t11 @t133)) % 0.36/0.58 (define @t135 () (tptp.in @t133 @t11)) % 0.36/0.58 (define @t136 () (or @t86 (= @t135 @t135))) % 0.36/0.58 (define @t137 () (= @t135 (tptp.in @t133 @t13))) % 0.36/0.58 (define @t138 () (or @t90 @t90 @t137)) % 0.36/0.58 (define @t139 () (or @t90 @t137)) % 0.36/0.58 (define @t140 () (forall @t61 @t139)) % 0.36/0.58 (define @t141 () (forall @t134 @t140)) % 0.36/0.58 (define @t142 () (forall (@list @t11 @t133 @t13) @t139)) % 0.36/0.58 (define @t143 () (forall (@list @t13 @t11 @t133) @t139)) % 0.36/0.58 (define @t144 () (@list @t133)) % 0.36/0.58 (define @t145 () (forall @t144 @t139)) % 0.36/0.58 (define @t146 () (forall @t144 @t137)) % 0.36/0.58 (define @t147 () (or @t90 @t146)) % 0.36/0.58 (define @t148 () (tptp.in @t1 @t13)) % 0.36/0.58 (define @t149 () (tptp.in @t1 @t11)) % 0.36/0.58 (define @t150 () (= @t149 @t148)) % 0.36/0.58 (define @t151 () (@list @t1)) % 0.36/0.58 (define @t152 () (forall @t151 @t150)) % 0.36/0.58 (define @t153 () (or @t101 (= @t148 @t149))) % 0.36/0.58 (define @t154 () (tptp.in @t2 @t13)) % 0.36/0.58 (define @t155 () (= @t154 @t149)) % 0.36/0.58 (define @t156 () (or @t104 @t104 @t155)) % 0.36/0.58 (define @t157 () (or @t104 @t155)) % 0.36/0.58 (define @t158 () (forall @t41 @t157)) % 0.36/0.58 (define @t159 () (forall @t151 @t158)) % 0.36/0.58 (define @t160 () (forall (@list @t1 @t2) @t157)) % 0.36/0.58 (define @t161 () (or @t104 @t15)) % 0.36/0.58 (define @t162 () (=> tptp.in__Cong @t132)) % 0.36/0.58 (define @t163 () (not @t7)) % 0.36/0.58 (define @t164 () (or @t163 @t3)) % 0.36/0.58 (define @t165 () (=> tptp.uniqinunit @t162)) % 0.36/0.58 (define @t166 () (not (= @t64 @t64))) % 0.36/0.58 (define @t167 () (or @t69 @t166 @t68 (= @t65 @t66))) % 0.36/0.58 (define @t168 () (tptp.setunion @t44)) % 0.36/0.58 (define @t169 () (= @t168 @t66)) % 0.36/0.58 (define @t170 () (not (tptp.in @t66 @t44))) % 0.36/0.58 (define @t171 () (not (= @t44 @t64))) % 0.36/0.58 (define @t172 () (not (tptp.in @t63 @t44))) % 0.36/0.58 (define @t173 () (or @t171 @t172 @t171 @t170 @t169)) % 0.36/0.58 (define @t174 () (or @t172 @t171 @t170 @t169)) % 0.36/0.58 (define @t175 () (forall @t50 @t174)) % 0.36/0.58 (define @t176 () (forall @t71 @t175)) % 0.36/0.58 (define @t177 () (forall (@list @t63 @t66 @t44) @t174)) % 0.36/0.58 (define @t178 () (@list @t44 @t63 @t66)) % 0.36/0.58 (define @t179 () (not (= @t64 @t44))) % 0.36/0.58 (define @t180 () (= @t66 @t168)) % 0.36/0.58 (define @t181 () (or @t172 @t179 @t170 @t180)) % 0.36/0.58 (define @t182 () (or @t170 @t180)) % 0.36/0.58 (define @t183 () (or @t172 @t179)) % 0.36/0.58 (define @t184 () (or @t183 @t182)) % 0.36/0.58 (define @t185 () (forall @t178 @t184)) % 0.36/0.58 (define @t186 () (forall @t71 @t184)) % 0.36/0.58 (define @t187 () (forall (@list @t66) @t182)) % 0.36/0.58 (define @t188 () (@list @t2)) % 0.36/0.58 (define @t189 () (forall (@list @t63) @t183)) % 0.36/0.58 (define @t190 () (or @t189 @t187)) % 0.36/0.58 (define @t191 () (tptp.in @t2 @t44)) % 0.36/0.58 (define @t192 () (not @t191)) % 0.36/0.58 (define @t193 () (forall @t41 (or @t192 (= @t2 @t168)))) % 0.36/0.58 (define @t194 () (forall @t41 (or @t192 (not (= @t73 @t44))))) % 0.36/0.58 (define @t195 () (not @t194)) % 0.36/0.58 (define @t196 () (= @t2 @t45)) % 0.36/0.58 (define @t197 () (not @t46)) % 0.36/0.58 (define @t198 () (or @t197 @t196)) % 0.36/0.58 (define @t199 () (not (= @t44 @t73))) % 0.36/0.58 (define @t200 () (or @t192 @t199)) % 0.36/0.58 (define @t201 () (forall @t41 @t200)) % 0.36/0.58 (define @t202 () (not @t201)) % 0.36/0.58 (define @t203 () (_ (lambda @t61 (not (forall @t41 (or (not @t154) (not (= @t13 @t73)))))) @t44)) % 0.36/0.58 (define @t204 () (=> @t203 @t48)) % 0.36/0.58 (define @t205 () (forall @t50 @t204)) % 0.36/0.58 (define @t206 () (=> tptp.setunionsingleton @t205)) % 0.36/0.58 (define @t207 () (=> tptp.setunion__Cong @t206)) % 0.36/0.58 (define @t208 () (=> tptp.setadjoin__Cong @t207)) % 0.36/0.58 (define @t209 () (=> tptp.in__Cong @t208)) % 0.36/0.58 (define @t210 () (=> tptp.uniqinunit @t209)) % 0.36/0.58 (define @t211 () (not @t58)) % 0.36/0.58 (define @t212 () (not @t14)) % 0.36/0.58 (define @t213 () (or @t212 @t211)) % 0.36/0.58 (define @t214 () (forall @t41 (not @t59))) % 0.36/0.58 (define @t215 () (not @t214)) % 0.36/0.58 (define @t216 () (@quantifiers_skolemize @t72 0)) % 0.36/0.58 (define @t217 () (@quantifiers_skolemize @t72 1)) % 0.36/0.58 (define @t218 () (tptp.setadjoin @t216 tptp.emptyset)) % 0.36/0.58 (define @t219 () (tptp.in @t217 @t218)) % 0.36/0.58 (define @t220 () (not @t219)) % 0.36/0.58 (define @t221 () (or @t220 (= @t217 @t216))) % 0.36/0.58 (define @t222 () (= @t216 @t217)) % 0.36/0.58 (define @t223 () (or @t220 @t222)) % 0.36/0.58 (define @t224 () (= @t217 (tptp.setunion @t218))) % 0.36/0.58 (define @t225 () (or (not (tptp.in @t216 @t218)) @t220 @t224)) % 0.36/0.58 (define @t226 () (@list true)) % 0.36/0.58 (define @t227 () (@list @t225)) % 0.36/0.58 (assume @p1 @t10) % 0.36/0.58 (assume @p2 @t21) % 0.36/0.58 (assume @p3 @t33) % 0.36/0.58 (assume @p4 @t38) % 0.36/0.58 (assume @p5 @t43) % 0.36/0.58 (assume @p6 @t57) % 0.36/0.58 (assume @p7 true) % 0.36/0.58 (step @p8 (= tptp.singleton @t62) :rule refl :args (@t62)) % 0.36/0.58 (step @p9 :rule evaluate :args ((= false true))) % 0.36/0.58 (step @p10 :rule bool-impl-true2 :args (@t75)) % 0.36/0.58 (step @p11 :rule bool-impl-true2 :args (@t75)) % 0.36/0.58 (step @p12 :rule refl :args (true)) % 0.36/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args (@t76)) % 0.36/0.58 (step @p14 :rule trans :premises (@p13 @p10)) % 0.36/0.58 (step @p15 :rule cong :premises (@p12 @p11) :args (@t76)) % 0.36/0.58 (step @p16 :rule cong :premises (@p12 @p15) :args (@t77)) % 0.36/0.58 (step @p17 :rule trans :premises (@p16 @p14)) % 0.36/0.58 (step @p18 :rule refl :args (@t80)) % 0.36/0.58 (step @p19 :rule cong :premises (@p18 @p17) :args (@t81)) % 0.36/0.58 (step @p20 :rule cong :premises (@p19) :args ((not @t81))) % 0.36/0.58 (step @p21 :rule refl :args (@t72)) % 0.36/0.58 (step @p22 :rule refl :args ((tptp.setunion @t39))) % 0.36/0.58 (step @p23 :rule refl :args (@t73)) % 0.36/0.58 (step @p24 :rule cong :premises (@p23) :args (@t74)) % 0.36/0.58 (step @p25 :rule trans :premises (@p24 @p22)) % 0.36/0.58 (step @p26 :rule refl :args (tptp.setunion)) % 0.36/0.58 (step @p27 :rule ho_cong :premises (@p26 @p23)) % 0.36/0.58 (step @p28 :rule cong :premises (@p27 @p25) :args ((= (_ tptp.setunion @t73) @t74))) % 0.36/0.58 (step @p29 :rule symm :premises (@p28)) % 0.36/0.58 (step @p30 :rule refl :args (@t40)) % 0.36/0.58 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.36/0.58 (step @p32 :rule refl :args (@t39)) % 0.36/0.58 (step @p33 :rule cong :premises (@p32 @p23) :args ((= @t39 @t73))) % 0.36/0.58 (step @p34 :rule symm :premises (@p33)) % 0.36/0.58 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.36/0.58 (step @p36 :rule ho_cong :premises (@p26 @p35)) % 0.36/0.58 (step @p37 :rule trans :premises (@p36 @p31)) % 0.36/0.58 (step @p38 :rule refl :args (@t2)) % 0.36/0.58 (step @p39 :rule cong :premises (@p38 @p37) :args (@t82)) % 0.36/0.58 (step @p40 :rule cong :premises (@p39) :args ((forall @t41 @t82))) % 0.36/0.58 (step @p41 :rule eq-symm :args (@t40 @t2)) % 0.36/0.58 (step @p42 :rule cong :premises (@p41) :args (@t42)) % 0.36/0.58 (step @p43 :rule trans :premises (@p42 @p40)) % 0.36/0.58 (step @p44 :rule refl :args (tptp.setunionsingleton)) % 0.36/0.58 (step @p45 :rule cong :premises (@p44 @p43) :args (@t43)) % 0.36/0.58 (step @p46 :rule eq_resolve :premises (@p5 @p45)) % 0.36/0.58 (step @p47 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0.36/0.58 (step @p289 :rule trans :premises (@p288 @p286)) % 0.36/0.58 (step @p290 :rule cong :premises (@p289) :args (@t176)) % 0.36/0.58 (step @p291 :rule quant-merge-prenex :args ((= @t176 @t177))) % 0.36/0.58 (step @p292 :rule symm :premises (@p291)) % 0.36/0.58 (step @p293 :rule quant_var_reordering :args ((= (forall @t178 @t174) @t177))) % 0.36/0.58 (step @p294 :rule trans :premises (@p293 @p292 @p290)) % 0.36/0.58 (step @p295 :rule trans :premises (@p294 @p285)) % 0.36/0.58 (step @p296 :rule eq-symm :args (@t66 @t168)) % 0.36/0.58 (step @p297 :rule refl :args (@t170)) % 0.36/0.58 (step @p298 :rule eq-symm :args (@t64 @t44)) % 0.36/0.58 (step @p299 :rule cong :premises (@p298) :args (@t179)) % 0.36/0.58 (step @p300 :rule refl :args (@t172)) % 0.36/0.58 (step @p301 :rule nary_cong :premises (@p300 @p299 @p297 @p296) :args (@t181)) % 0.36/0.58 (step @p302 :rule aci_norm :args ((= @t184 @t181))) % 0.36/0.58 (step @p303 :rule trans :premises (@p302 @p301)) % 0.36/0.58 (step @p304 :rule cong :premises (@p303) :args (@t185)) % 0.36/0.58 (step @p305 :rule trans :premises (@p304 @p295)) % 0.36/0.58 (step @p306 :rule quant-merge-prenex :args ((= (forall @t50 @t186) @t185))) % 0.36/0.58 (step @p307 :rule alpha_equiv :args (@t187 (@list @t66) @t188)) % 0.36/0.58 (step @p308 :rule alpha_equiv :args (@t189 (@list @t63) @t188)) % 0.36/0.58 (step @p309 :rule nary_cong :premises (@p308 @p307) :args (@t190)) % 0.36/0.58 (step @p310 :rule quant-miniscope-or :args ((= @t186 @t190))) % 0.36/0.58 (step @p311 :rule trans :premises (@p310 @p309)) % 0.36/0.58 (step @p312 :rule symm :premises (@p311)) % 0.36/0.58 (step @p313 :rule cong :premises (@p312) :args ((forall @t50 (or @t194 @t193)))) % 0.36/0.58 (step @p314 :rule trans :premises (@p313 @p306)) % 0.36/0.58 (step @p315 :rule trans :premises (@p314 @p305)) % 0.36/0.58 (step @p316 :rule refl :args (@t193)) % 0.36/0.58 (step @p317 :rule bool-double-not-elim :args (@t194)) % 0.36/0.58 (step @p318 :rule nary_cong :premises (@p317 @p316) :args ((or (not @t195) @t193))) % 0.36/0.58 (step @p319 :rule bool-impl-elim :args (@t195 @t193)) % 0.36/0.58 (step @p320 :rule trans :premises (@p319 @p318)) % 0.36/0.58 (step @p321 :rule cong :premises (@p320) :args ((forall @t50 (=> @t195 @t193)))) % 0.36/0.58 (step @p322 :rule trans :premises (@p321 @p315)) % 0.36/0.58 (step @p323 :rule refl :args (@t168)) % 0.36/0.58 (step @p324 :rule refl :args (@t45)) % 0.36/0.58 (step @p325 :rule cong :premises (@p324 @p323) :args ((= @t45 @t168))) % 0.36/0.58 (step @p326 :rule symm :premises (@p325)) % 0.36/0.58 (step @p327 :rule eq_resolve :premises (@p324 @p326)) % 0.36/0.58 (step @p328 :rule cong :premises (@p38 @p327) :args (@t196)) % 0.36/0.58 (step @p329 :rule refl :args (@t191)) % 0.36/0.58 (step @p330 :rule refl :args (@t46)) % 0.36/0.58 (step @p331 :rule cong :premises (@p330 @p329) :args ((= @t46 @t191))) % 0.36/0.58 (step @p332 :rule symm :premises (@p331)) % 0.36/0.58 (step @p333 :rule eq_resolve :premises (@p330 @p332)) % 0.36/0.58 (step @p334 :rule cong :premises (@p333) :args (@t197)) % 0.36/0.58 (step @p335 :rule nary_cong :premises (@p334 @p328) :args (@t198)) % 0.36/0.58 (step @p336 :rule cong :premises (@p335) :args ((forall @t41 @t198))) % 0.36/0.58 (step @p337 :rule bool-impl-elim :args (@t46 @t196)) % 0.36/0.58 (step @p338 :rule cong :premises (@p337) :args ((forall @t41 (=> @t46 @t196)))) % 0.36/0.58 (step @p339 :rule trans :premises (@p338 @p336)) % 0.36/0.58 (step @p340 :rule eq-symm :args (@t45 @t2)) % 0.36/0.58 (step @p341 :rule refl :args (@t46)) % 0.36/0.58 (step @p342 :rule cong :premises (@p341 @p340) :args (@t47)) % 0.36/0.58 (step @p343 :rule cong :premises (@p342) :args (@t48)) % 0.36/0.58 (step @p344 :rule trans :premises (@p343 @p339)) % 0.36/0.58 (step @p345 :rule eq-symm :args (@t44 @t73)) % 0.36/0.58 (step @p346 :rule cong :premises (@p345) :args (@t199)) % 0.36/0.58 (step @p347 :rule refl :args (@t192)) % 0.36/0.58 (step @p348 :rule nary_cong :premises (@p347 @p346) :args (@t200)) % 0.36/0.58 (step @p349 :rule cong :premises (@p348) :args (@t201)) % 0.36/0.58 (step @p350 :rule cong :premises (@p349) :args (@t202)) % 0.36/0.58 (step @p351 :rule beta-reduce :args ((= @t203 @t202))) % 0.36/0.58 (step @p352 :rule trans :premises (@p351 @p350)) % 0.36/0.58 (step @p353 :rule cong :premises (@p352 @p344) :args (@t204)) % 0.36/0.58 (step @p354 :rule cong :premises (@p353) :args (@t205)) % 0.36/0.58 (step @p355 :rule trans :premises (@p354 @p322)) % 0.36/0.58 (step @p356 :rule cong :premises (@p44 @p355) :args (@t206)) % 0.36/0.58 (step @p357 :rule cong :premises (@p89 @p356) :args (@t207)) % 0.36/0.58 (step @p358 :rule cong :premises (@p169 @p357) :args (@t208)) % 0.36/0.58 (step @p359 :rule cong :premises (@p241 @p358) :args (@t209)) % 0.36/0.58 (step @p360 :rule cong :premises (@p270 @p359) :args (@t210)) % 0.36/0.58 (step @p361 :rule cong :premises (@p360) :args ((not @t210))) % 0.36/0.58 (step @p362 :rule refl :args (@t48)) % 0.36/0.58 (step @p363 :rule refl :args (@t44)) % 0.36/0.58 (step @p364 :rule refl :args (@t13)) % 0.36/0.58 (step @p365 :rule cong :premises (@p364 @p35) :args (@t58)) % 0.36/0.58 (step @p366 :rule cong :premises (@p365) :args (@t211)) % 0.36/0.58 (step @p367 :rule cong :premises (@p229) :args (@t212)) % 0.36/0.58 (step @p368 :rule nary_cong :premises (@p367 @p366) :args (@t213)) % 0.36/0.58 (step @p369 :rule cong :premises (@p368) :args ((forall @t41 @t213))) % 0.36/0.58 (step @p370 :rule bool-and-de-morgan :args (@t14 @t58 true)) % 0.36/0.58 (step @p371 :rule cong :premises (@p370) :args (@t214)) % 0.36/0.58 (step @p372 :rule trans :premises (@p371 @p369)) % 0.36/0.58 (step @p373 :rule cong :premises (@p372) :args (@t215)) % 0.36/0.58 (step @p374 :rule exists-elim :args ((= @t60 @t215))) % 0.36/0.58 (step @p375 :rule trans :premises (@p374 @p373)) % 0.36/0.58 (step @p376 :rule cong :premises (@p375) :args (@t62)) % 0.36/0.58 (step @p377 :rule trans :premises (@p8 @p376)) % 0.36/0.58 (step @p378 :rule ho_cong :premises (@p377 @p363)) % 0.36/0.58 (step @p379 :rule cong :premises (@p378 @p362) :args (@t49)) % 0.36/0.58 (step @p380 :rule cong :premises (@p379) :args (@t51)) % 0.36/0.58 (step @p381 :rule cong :premises (@p44 @p380) :args (@t52)) % 0.36/0.58 (step @p382 :rule cong :premises (@p89 @p381) :args (@t53)) % 0.36/0.58 (step @p383 :rule cong :premises (@p169 @p382) :args (@t54)) % 0.36/0.58 (step @p384 :rule cong :premises (@p241 @p383) :args (@t55)) % 0.36/0.58 (step @p385 :rule cong :premises (@p270 @p384) :args (@t56)) % 0.36/0.58 (step @p386 :rule cong :premises (@p385) :args (@t57)) % 0.36/0.58 (step @p387 :rule trans :premises (@p386 @p361)) % 0.36/0.58 (step @p388 :rule trans :premises (@p387 @p275)) % 0.36/0.58 (step @p389 :rule eq_resolve :premises (@p6 @p388)) % 0.36/0.58 (step @p390 :rule not_implies_elim2 :premises (@p389)) % 0.36/0.58 (step @p391 :rule not_implies_elim1 :premises (@p390)) % 0.36/0.58 (step @p392 :rule instantiate :premises (@p391) :args ((@list @t216))) % 0.36/0.58 (step @p393 :rule not_implies_elim1 :premises (@p389)) % 0.36/0.58 (step @p394 :rule eq-symm :args (@t217 @t216)) % 0.36/0.58 (step @p395 :rule refl :args (@t220)) % 0.36/0.58 (step @p396 :rule nary_cong :premises (@p395 @p394) :args (@t221)) % 0.36/0.58 (step @p397 :rule cong :premises (@p18 @p396) :args ((=> @t80 @t221))) % 0.36/0.58 (assume-push @p426 @t80) % 0.36/0.58 (step @p399 :rule instantiate :premises (@p393) :args ((@list @t217 @t216))) % 0.36/0.58 (step-pop @p427 :rule scope :premises (@p399)) % 0.36/0.58 (step @p400 :rule process_scope :premises (@p427) :args (@t221)) % 0.36/0.58 (step @p402 :rule eq_resolve :premises (@p400 @p397)) % 0.36/0.58 (step @p403 :rule implies_elim :premises (@p402)) % 0.36/0.58 (step @p404 :rule chain_m_resolution :premises (@p403 @p393) :args (@t223 (@list false) (@list @t80))) % 0.36/0.58 (step @p405 :rule not_implies_elim2 :premises (@p390)) % 0.36/0.58 (step @p406 :rule skolemize :premises (@p405)) % 0.36/0.58 (step @p407 :rule bool-double-not-elim :args (@t219)) % 0.36/0.58 (step @p408 :rule refl :args (@t225)) % 0.36/0.58 (step @p409 :rule nary_cong :premises (@p408 @p407) :args ((or @t225 (not @t220)))) % 0.36/0.58 (step @p410 :rule cnf_or_neg :args (@t225 1)) % 0.36/0.58 (step @p411 :rule eq_resolve :premises (@p410 @p409)) % 0.36/0.58 (step @p412 :rule reordering :premises (@p411) :args ((or @t219 @t225))) % 0.36/0.58 (step @p413 :rule chain_m_resolution :premises (@p412 @p406) :args (@t219 @t226 @t227)) % 0.36/0.58 (step @p414 :rule cnf_or_pos :args (@t223)) % 0.36/0.58 (step @p415 :rule reordering :premises (@p414) :args ((or @t220 @t222 (not @t223)))) % 0.36/0.58 (step @p416 :rule chain_m_resolution :premises (@p415 @p413 @p404) :args (@t222 (@list false false) (@list @t219 @t223))) % 0.36/0.58 (step @p417 :rule symm :premises (@p416)) % 0.36/0.58 (step @p418 :rule trans :premises (@p417 @p392)) % 0.36/0.58 (step @p419 :rule true_intro :premises (@p418)) % 0.36/0.58 (step @p420 :rule cnf_or_neg :args (@t225 2)) % 0.36/0.58 (step @p421 :rule chain_m_resolution :premises (@p420 @p406) :args ((not @t224) @t226 @t227)) % 0.36/0.58 (step @p422 :rule false_intro :premises (@p421)) % 0.36/0.58 (step @p423 :rule symm :premises (@p422)) % 0.36/0.58 (step @p424 :rule trans :premises (@p423 @p419)) % 0.36/0.58 (step @p425 false :rule eq_resolve :premises (@p424 @p9)) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------