%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG074+1 : TPTP v9.2.1. Released v2.7.0. % 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 08:05:09 AM UTC 2026 % Result : Theorem 0.36s 0.60s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG074+1 : TPTP v9.2.1. Released v2.7.0. % 0.13/0.13 % 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 : Wed Jun 3 01:39:02 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.60 % SZS status Theorem % 0.36/0.60 % SZS output start Proof % 0.36/0.60 ( % 0.36/0.60 (declare-sort $$unsorted 0) % 0.36/0.60 (declare-const tptp.j (-> $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.h (-> $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.sorti2 (-> $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.op2 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.60 (declare-const tptp.sorti1 (-> $$unsorted Bool)) % 0.36/0.60 (declare-const tptp.op1 (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.60 (define @t1 () (@var "V" $$unsorted)) % 0.36/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.60 (define @t3 () (tptp.op1 @t2 @t1)) % 0.36/0.60 (define @t4 () (tptp.sorti1 @t3)) % 0.36/0.60 (define @t5 () (tptp.sorti1 @t1)) % 0.36/0.60 (define @t6 () (@list @t1)) % 0.36/0.60 (define @t7 () (forall @t6 (=> @t5 @t4))) % 0.36/0.60 (define @t8 () (tptp.sorti1 @t2)) % 0.36/0.60 (define @t9 () (=> @t8 @t7)) % 0.36/0.60 (define @t10 () (@list @t2)) % 0.36/0.60 (define @t11 () (forall @t10 @t9)) % 0.36/0.60 (define @t12 () (tptp.op2 @t2 @t1)) % 0.36/0.60 (define @t13 () (tptp.sorti2 @t1)) % 0.36/0.60 (define @t14 () (tptp.sorti2 @t2)) % 0.36/0.60 (define @t15 () (tptp.op1 @t3 @t2)) % 0.36/0.60 (define @t16 () (not (= @t15 @t1))) % 0.36/0.60 (define @t17 () (tptp.op1 @t3 @t1)) % 0.36/0.60 (define @t18 () (tptp.op1 @t1 @t2)) % 0.36/0.60 (define @t19 () (not (= @t18 @t3))) % 0.36/0.60 (define @t20 () (and @t5 @t19 (= @t17 @t2) @t16)) % 0.36/0.60 (define @t21 () (exists @t6 @t20)) % 0.36/0.60 (define @t22 () (and @t8 @t21)) % 0.36/0.60 (define @t23 () (exists @t10 @t22)) % 0.36/0.60 (define @t24 () (tptp.op2 @t12 @t2)) % 0.36/0.60 (define @t25 () (not (= @t24 @t1))) % 0.36/0.60 (define @t26 () (tptp.op2 @t12 @t1)) % 0.36/0.60 (define @t27 () (tptp.op2 @t1 @t2)) % 0.36/0.60 (define @t28 () (not (= @t27 @t12))) % 0.36/0.60 (define @t29 () (and @t13 @t28 (= @t26 @t2) @t25)) % 0.36/0.60 (define @t30 () (exists @t6 @t29)) % 0.36/0.60 (define @t31 () (and @t14 @t30)) % 0.36/0.60 (define @t32 () (exists @t10 @t31)) % 0.36/0.60 (define @t33 () (not @t32)) % 0.36/0.60 (define @t34 () (@var "X2" $$unsorted)) % 0.36/0.60 (define @t35 () (tptp.j (tptp.h @t34))) % 0.36/0.60 (define @t36 () (tptp.sorti1 @t34)) % 0.36/0.60 (define @t37 () (=> @t36 (= @t35 @t34))) % 0.36/0.60 (define @t38 () (@list @t34)) % 0.36/0.60 (define @t39 () (forall @t38 @t37)) % 0.36/0.60 (define @t40 () (@var "X1" $$unsorted)) % 0.36/0.60 (define @t41 () (tptp.h (tptp.j @t40))) % 0.36/0.60 (define @t42 () (tptp.sorti2 @t40)) % 0.36/0.60 (define @t43 () (=> @t42 (= @t41 @t40))) % 0.36/0.60 (define @t44 () (@list @t40)) % 0.36/0.60 (define @t45 () (forall @t44 @t43)) % 0.36/0.60 (define @t46 () (@var "Z" $$unsorted)) % 0.36/0.60 (define @t47 () (@var "Y" $$unsorted)) % 0.36/0.60 (define @t48 () (tptp.j @t47)) % 0.36/0.60 (define @t49 () (= (tptp.j (tptp.op2 @t47 @t46)) (tptp.op1 @t48 (tptp.j @t46)))) % 0.36/0.60 (define @t50 () (tptp.sorti2 @t46)) % 0.36/0.60 (define @t51 () (@list @t46)) % 0.36/0.60 (define @t52 () (forall @t51 (=> @t50 @t49))) % 0.36/0.60 (define @t53 () (tptp.sorti2 @t47)) % 0.36/0.60 (define @t54 () (=> @t53 @t52)) % 0.36/0.60 (define @t55 () (@list @t47)) % 0.36/0.60 (define @t56 () (forall @t55 @t54)) % 0.36/0.60 (define @t57 () (@var "X" $$unsorted)) % 0.36/0.60 (define @t58 () (@var "W" $$unsorted)) % 0.36/0.60 (define @t59 () (tptp.h @t58)) % 0.36/0.60 (define @t60 () (= (tptp.h (tptp.op1 @t58 @t57)) (tptp.op2 @t59 (tptp.h @t57)))) % 0.36/0.60 (define @t61 () (tptp.sorti1 @t57)) % 0.36/0.60 (define @t62 () (@list @t57)) % 0.36/0.60 (define @t63 () (forall @t62 (=> @t61 @t60))) % 0.36/0.60 (define @t64 () (tptp.sorti1 @t58)) % 0.36/0.60 (define @t65 () (=> @t64 @t63)) % 0.36/0.60 (define @t66 () (@list @t58)) % 0.36/0.60 (define @t67 () (forall @t66 @t65)) % 0.36/0.60 (define @t68 () (and @t67 @t56 @t45 @t39)) % 0.36/0.60 (define @t69 () (not @t68)) % 0.36/0.60 (define @t70 () (tptp.sorti1 (tptp.j @t1))) % 0.36/0.60 (define @t71 () (forall @t6 (=> @t13 @t70))) % 0.36/0.60 (define @t72 () (tptp.sorti2 (tptp.h @t2))) % 0.36/0.60 (define @t73 () (forall @t10 (=> @t8 @t72))) % 0.36/0.60 (define @t74 () (and @t73 @t71)) % 0.36/0.60 (define @t75 () (=> @t74 @t69)) % 0.36/0.60 (define @t76 () (not @t75)) % 0.36/0.60 (define @t77 () (@var "BOUND_VARIABLE_7585" $$unsorted)) % 0.36/0.60 (define @t78 () (tptp.op1 @t2 @t77)) % 0.36/0.60 (define @t79 () (= @t77 (tptp.op1 @t78 @t2))) % 0.36/0.60 (define @t80 () (not (= @t2 (tptp.op1 @t78 @t77)))) % 0.36/0.60 (define @t81 () (= @t78 (tptp.op1 @t77 @t2))) % 0.36/0.60 (define @t82 () (not (tptp.sorti1 @t77))) % 0.36/0.60 (define @t83 () (not @t8)) % 0.36/0.60 (define @t84 () (or @t83 @t82 @t81 @t80 @t79)) % 0.36/0.60 (define @t85 () (or @t82 @t81 @t80 @t79)) % 0.36/0.60 (define @t86 () (or @t83 @t85)) % 0.36/0.60 (define @t87 () (@list @t2 @t77)) % 0.36/0.60 (define @t88 () (forall @t87 @t86)) % 0.36/0.60 (define @t89 () (@list @t77)) % 0.36/0.60 (define @t90 () (forall @t89 @t86)) % 0.36/0.60 (define @t91 () (forall @t89 @t85)) % 0.36/0.60 (define @t92 () (@list @t1)) % 0.36/0.60 (define @t93 () (or @t83 @t91)) % 0.36/0.60 (define @t94 () (= @t1 @t15)) % 0.36/0.60 (define @t95 () (= @t2 @t17)) % 0.36/0.60 (define @t96 () (not @t95)) % 0.36/0.60 (define @t97 () (= @t3 @t18)) % 0.36/0.60 (define @t98 () (not @t5)) % 0.36/0.60 (define @t99 () (forall @t6 (or @t98 @t97 @t96 @t94))) % 0.36/0.60 (define @t100 () (not @t99)) % 0.36/0.60 (define @t101 () (and @t8 @t100)) % 0.36/0.60 (define @t102 () (forall @t10 (not @t101))) % 0.36/0.60 (define @t103 () (not @t102)) % 0.36/0.60 (define @t104 () (not @t94)) % 0.36/0.60 (define @t105 () (not @t104)) % 0.36/0.60 (define @t106 () (not @t97)) % 0.36/0.60 (define @t107 () (not @t106)) % 0.36/0.60 (define @t108 () (or @t98 @t107 @t96 @t105)) % 0.36/0.60 (define @t109 () (and @t5 @t106 @t95 @t104)) % 0.36/0.60 (define @t110 () (forall @t6 (not @t109))) % 0.36/0.60 (define @t111 () (not @t110)) % 0.36/0.60 (define @t112 () (forall @t87 @t84)) % 0.36/0.60 (define @t113 () (@quantifiers_skolemize @t112 0)) % 0.36/0.60 (define @t114 () (@quantifiers_skolemize @t112 1)) % 0.36/0.60 (define @t115 () (tptp.op1 @t113 @t114)) % 0.36/0.60 (define @t116 () (tptp.op1 @t115 @t113)) % 0.36/0.60 (define @t117 () (= @t114 @t116)) % 0.36/0.60 (define @t118 () (tptp.op1 @t115 @t114)) % 0.36/0.60 (define @t119 () (= @t113 @t118)) % 0.36/0.60 (define @t120 () (not @t119)) % 0.36/0.60 (define @t121 () (tptp.op1 @t114 @t113)) % 0.36/0.60 (define @t122 () (= @t115 @t121)) % 0.36/0.60 (define @t123 () (tptp.sorti1 @t114)) % 0.36/0.60 (define @t124 () (not @t123)) % 0.36/0.60 (define @t125 () (tptp.sorti1 @t113)) % 0.36/0.60 (define @t126 () (not @t125)) % 0.36/0.60 (define @t127 () (or @t126 @t124 @t122 @t120 @t117)) % 0.36/0.60 (define @t128 () (@list true)) % 0.36/0.60 (define @t129 () (@list @t127)) % 0.36/0.60 (define @t130 () (= @t34 @t35)) % 0.36/0.60 (define @t131 () (= @t40 @t41)) % 0.36/0.60 (define @t132 () (@var "BOUND_VARIABLE_7683" $$unsorted)) % 0.36/0.60 (define @t133 () (= (tptp.j (tptp.op2 @t47 @t132)) (tptp.op1 @t48 (tptp.j @t132)))) % 0.36/0.60 (define @t134 () (not (tptp.sorti2 @t132))) % 0.36/0.60 (define @t135 () (not @t53)) % 0.36/0.60 (define @t136 () (or @t134 @t133)) % 0.36/0.60 (define @t137 () (or @t135 @t136)) % 0.36/0.60 (define @t138 () (forall (@list @t47 @t132) @t137)) % 0.36/0.60 (define @t139 () (@list @t132)) % 0.36/0.60 (define @t140 () (forall @t139 @t137)) % 0.36/0.60 (define @t141 () (forall @t139 @t136)) % 0.36/0.60 (define @t142 () (or @t135 @t141)) % 0.36/0.60 (define @t143 () (forall @t51 (or (not @t50) @t49))) % 0.36/0.60 (define @t144 () (@var "BOUND_VARIABLE_7660" $$unsorted)) % 0.36/0.60 (define @t145 () (= (tptp.h (tptp.op1 @t58 @t144)) (tptp.op2 @t59 (tptp.h @t144)))) % 0.36/0.60 (define @t146 () (not (tptp.sorti1 @t144))) % 0.36/0.60 (define @t147 () (not @t64)) % 0.36/0.60 (define @t148 () (or @t146 @t145)) % 0.36/0.60 (define @t149 () (or @t147 @t148)) % 0.36/0.60 (define @t150 () (forall (@list @t58 @t144) @t149)) % 0.36/0.60 (define @t151 () (@list @t144)) % 0.36/0.60 (define @t152 () (forall @t151 @t149)) % 0.36/0.60 (define @t153 () (forall @t151 @t148)) % 0.36/0.60 (define @t154 () (or @t147 @t153)) % 0.36/0.60 (define @t155 () (forall @t62 (or (not @t61) @t60))) % 0.36/0.60 (define @t156 () (@list @t113 @t114)) % 0.36/0.60 (define @t157 () (tptp.h @t114)) % 0.36/0.60 (define @t158 () (tptp.h @t113)) % 0.36/0.60 (define @t159 () (tptp.op2 @t158 @t157)) % 0.36/0.60 (define @t160 () (tptp.h @t115)) % 0.36/0.60 (define @t161 () (= @t160 @t159)) % 0.36/0.60 (define @t162 () (or @t126 @t124 @t161)) % 0.36/0.60 (define @t163 () (@list false false false)) % 0.36/0.60 (define @t164 () (@list @t114)) % 0.36/0.60 (define @t165 () (tptp.j @t157)) % 0.36/0.60 (define @t166 () (= @t114 @t165)) % 0.36/0.60 (define @t167 () (or @t124 @t166)) % 0.36/0.60 (define @t168 () (@list false false)) % 0.36/0.60 (define @t169 () (@list @t115 @t113)) % 0.36/0.60 (define @t170 () (@var "BOUND_VARIABLE_7530" $$unsorted)) % 0.36/0.60 (define @t171 () (tptp.sorti1 (tptp.op1 @t2 @t170))) % 0.36/0.60 (define @t172 () (not (tptp.sorti1 @t170))) % 0.36/0.60 (define @t173 () (or @t172 @t171)) % 0.36/0.60 (define @t174 () (or @t83 @t173)) % 0.36/0.60 (define @t175 () (forall (@list @t2 @t170) @t174)) % 0.36/0.60 (define @t176 () (@list @t170)) % 0.36/0.60 (define @t177 () (forall @t176 @t174)) % 0.36/0.60 (define @t178 () (forall @t176 @t173)) % 0.36/0.60 (define @t179 () (or @t83 @t178)) % 0.36/0.60 (define @t180 () (forall @t6 (or @t98 @t4))) % 0.36/0.60 (define @t181 () (tptp.sorti1 @t115)) % 0.36/0.60 (define @t182 () (or @t126 @t124 @t181)) % 0.36/0.60 (define @t183 () (tptp.op2 @t160 @t158)) % 0.36/0.60 (define @t184 () (tptp.h @t116)) % 0.36/0.60 (define @t185 () (= @t184 @t183)) % 0.36/0.60 (define @t186 () (not @t181)) % 0.36/0.60 (define @t187 () (or @t186 @t126 @t185)) % 0.36/0.60 (define @t188 () (tptp.sorti1 @t116)) % 0.36/0.60 (define @t189 () (or @t186 @t126 @t188)) % 0.36/0.60 (define @t190 () (= @t116 (tptp.j @t184))) % 0.36/0.60 (define @t191 () (not @t188)) % 0.36/0.60 (define @t192 () (or @t191 @t190)) % 0.36/0.60 (define @t193 () (@var "BOUND_VARIABLE_7626" $$unsorted)) % 0.36/0.60 (define @t194 () (tptp.op2 @t2 @t193)) % 0.36/0.60 (define @t195 () (= @t193 (tptp.op2 @t194 @t2))) % 0.36/0.60 (define @t196 () (not (= @t2 (tptp.op2 @t194 @t193)))) % 0.36/0.60 (define @t197 () (= @t194 (tptp.op2 @t193 @t2))) % 0.36/0.60 (define @t198 () (not (tptp.sorti2 @t193))) % 0.36/0.60 (define @t199 () (not @t14)) % 0.36/0.60 (define @t200 () (or @t199 @t198 @t197 @t196 @t195)) % 0.36/0.60 (define @t201 () (@list @t2 @t193)) % 0.36/0.60 (define @t202 () (or @t198 @t197 @t196 @t195)) % 0.36/0.60 (define @t203 () (or @t199 @t202)) % 0.36/0.60 (define @t204 () (forall @t201 @t203)) % 0.36/0.60 (define @t205 () (@list @t193)) % 0.36/0.60 (define @t206 () (forall @t205 @t203)) % 0.36/0.60 (define @t207 () (forall @t205 @t202)) % 0.36/0.60 (define @t208 () (or @t199 @t207)) % 0.36/0.60 (define @t209 () (= @t1 @t24)) % 0.36/0.60 (define @t210 () (= @t2 @t26)) % 0.36/0.60 (define @t211 () (not @t210)) % 0.36/0.60 (define @t212 () (= @t12 @t27)) % 0.36/0.60 (define @t213 () (not @t13)) % 0.36/0.60 (define @t214 () (forall @t6 (or @t213 @t212 @t211 @t209))) % 0.36/0.60 (define @t215 () (not @t214)) % 0.36/0.60 (define @t216 () (and @t14 @t215)) % 0.36/0.60 (define @t217 () (forall @t10 (not @t216))) % 0.36/0.60 (define @t218 () (not @t217)) % 0.36/0.60 (define @t219 () (not @t209)) % 0.36/0.60 (define @t220 () (not @t219)) % 0.36/0.60 (define @t221 () (not @t212)) % 0.36/0.60 (define @t222 () (not @t221)) % 0.36/0.60 (define @t223 () (or @t213 @t222 @t211 @t220)) % 0.36/0.60 (define @t224 () (and @t13 @t221 @t210 @t219)) % 0.36/0.60 (define @t225 () (forall @t6 (not @t224))) % 0.36/0.60 (define @t226 () (not @t225)) % 0.36/0.60 (define @t227 () (@list @t158 @t157)) % 0.36/0.60 (define @t228 () (tptp.op2 @t160 @t157)) % 0.36/0.60 (define @t229 () (= (tptp.h @t118) @t228)) % 0.36/0.60 (define @t230 () (or @t186 @t124 @t229)) % 0.36/0.60 (define @t231 () (tptp.sorti2 @t157)) % 0.36/0.60 (define @t232 () (or @t124 @t231)) % 0.36/0.60 (define @t233 () (@list @t113)) % 0.36/0.60 (define @t234 () (tptp.sorti2 @t158)) % 0.36/0.60 (define @t235 () (or @t126 @t234)) % 0.36/0.60 (define @t236 () (tptp.j @t158)) % 0.36/0.60 (define @t237 () (tptp.j @t159)) % 0.36/0.60 (define @t238 () (= @t237 (tptp.op1 @t236 @t165))) % 0.36/0.60 (define @t239 () (not @t231)) % 0.36/0.60 (define @t240 () (not @t234)) % 0.36/0.60 (define @t241 () (or @t240 @t239 @t238)) % 0.36/0.60 (define @t242 () (tptp.op1 @t165 @t236)) % 0.36/0.60 (define @t243 () (tptp.op2 @t157 @t158)) % 0.36/0.60 (define @t244 () (= (tptp.j @t243) @t242)) % 0.36/0.60 (define @t245 () (or @t239 @t240 @t244)) % 0.36/0.60 (define @t246 () (= @t113 @t236)) % 0.36/0.60 (define @t247 () (or @t126 @t246)) % 0.36/0.60 (define @t248 () (tptp.h @t121)) % 0.36/0.60 (define @t249 () (= @t248 @t243)) % 0.36/0.60 (define @t250 () (or @t124 @t126 @t249)) % 0.36/0.60 (define @t251 () (= @t159 @t243)) % 0.36/0.60 (define @t252 () (and @t161 @t249 @t246 @t166 @t251 @t244 @t238)) % 0.36/0.60 (define @t253 () (not @t251)) % 0.36/0.60 (define @t254 () (not @t166)) % 0.36/0.60 (define @t255 () (not @t161)) % 0.36/0.60 (define @t256 () (tptp.op2 @t159 @t158)) % 0.36/0.60 (define @t257 () (= @t157 @t256)) % 0.36/0.60 (define @t258 () (= @t158 (tptp.op2 @t159 @t157))) % 0.36/0.60 (define @t259 () (not @t258)) % 0.36/0.60 (define @t260 () (or @t240 @t239 @t251 @t259 @t257)) % 0.36/0.60 (define @t261 () (and @t161 @t185 @t166 @t257 @t190)) % 0.36/0.60 (assume @p1 @t11) % 0.36/0.60 (assume @p2 (forall @t10 (=> @t14 (forall @t6 (=> @t13 (tptp.sorti2 @t12)))))) % 0.36/0.60 (assume @p3 @t23) % 0.36/0.60 (assume @p4 @t33) % 0.36/0.60 (assume @p5 @t76) % 0.36/0.60 (assume @p6 true) % 0.36/0.60 (step @p7 :rule aci_norm :args ((= @t86 @t84))) % 0.36/0.60 (step @p8 :rule cong :premises (@p7) :args (@t88)) % 0.36/0.60 (step @p9 :rule quant-merge-prenex :args ((= (forall @t10 @t90) @t88))) % 0.36/0.60 (step @p10 :rule alpha_equiv :args (@t91 (@list @t77) @t92)) % 0.36/0.60 (step @p11 :rule refl :args (@t83)) % 0.36/0.60 (step @p12 :rule nary_cong 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% 0.36/0.60 (step @p87 :rule symm :premises (@p86)) % 0.36/0.60 (step @p88 :rule cong :premises (@p87) :args ((forall @t55 (or @t135 @t143)))) % 0.36/0.60 (step @p89 :rule trans :premises (@p88 @p81)) % 0.36/0.60 (step @p90 :rule trans :premises (@p89 @p80)) % 0.36/0.60 (step @p91 :rule bool-impl-elim :args (@t53 @t143)) % 0.36/0.60 (step @p92 :rule cong :premises (@p91) :args ((forall @t55 (=> @t53 @t143)))) % 0.36/0.60 (step @p93 :rule trans :premises (@p92 @p90)) % 0.36/0.60 (step @p94 :rule bool-impl-elim :args (@t50 @t49)) % 0.36/0.60 (step @p95 :rule cong :premises (@p94) :args (@t52)) % 0.36/0.60 (step @p96 :rule refl :args (@t53)) % 0.36/0.60 (step @p97 :rule cong :premises (@p96 @p95) :args (@t54)) % 0.36/0.60 (step @p98 :rule cong :premises (@p97) :args (@t56)) % 0.36/0.60 (step @p99 :rule trans :premises (@p98 @p93)) % 0.36/0.60 (step @p100 :rule aci_norm :args ((= @t149 (or @t147 @t146 @t145)))) % 0.36/0.60 (step @p101 :rule cong :premises (@p100) :args (@t150)) % 0.36/0.60 (step @p102 :rule quant-merge-prenex :args ((= (forall @t66 @t152) @t150))) % 0.36/0.60 (step @p103 :rule alpha_equiv :args (@t153 (@list @t144) (@list @t57))) % 0.36/0.60 (step @p104 :rule refl :args (@t147)) % 0.36/0.60 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t154)) % 0.36/0.60 (step @p106 :rule quant-miniscope-or :args ((= @t152 @t154))) % 0.36/0.60 (step @p107 :rule trans :premises (@p106 @p105)) % 0.36/0.60 (step @p108 :rule symm :premises (@p107)) % 0.36/0.60 (step @p109 :rule cong :premises (@p108) :args ((forall @t66 (or @t147 @t155)))) % 0.36/0.60 (step @p110 :rule trans :premises (@p109 @p102)) % 0.36/0.60 (step @p111 :rule trans :premises (@p110 @p101)) % 0.36/0.60 (step @p112 :rule bool-impl-elim :args (@t64 @t155)) % 0.36/0.60 (step @p113 :rule cong :premises (@p112) :args ((forall @t66 (=> @t64 @t155)))) % 0.36/0.60 (step @p114 :rule trans :premises (@p113 @p111)) % 0.36/0.60 (step @p115 :rule bool-impl-elim :args (@t61 @t60)) % 0.36/0.60 (step @p116 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(@t26 @t2)) % 0.36/0.60 (step @p237 :rule eq-symm :args (@t27 @t12)) % 0.36/0.60 (step @p238 :rule cong :premises (@p237) :args (@t28)) % 0.36/0.60 (step @p239 :rule refl :args (@t13)) % 0.36/0.60 (step @p240 :rule nary_cong :premises (@p239 @p238 @p236 @p235) :args (@t29)) % 0.36/0.60 (step @p241 :rule cong :premises (@p240) :args (@t30)) % 0.36/0.60 (step @p242 :rule trans :premises (@p241 @p233)) % 0.36/0.60 (step @p243 :rule refl :args (@t14)) % 0.36/0.60 (step @p244 :rule nary_cong :premises (@p243 @p242) :args (@t31)) % 0.36/0.60 (step @p245 :rule cong :premises (@p244) :args (@t32)) % 0.36/0.60 (step @p246 :rule trans :premises (@p245 @p213)) % 0.36/0.60 (step @p247 :rule cong :premises (@p246) :args (@t33)) % 0.36/0.60 (step @p248 :rule trans :premises (@p247 @p192)) % 0.36/0.60 (step @p249 :rule eq_resolve :premises (@p4 @p248)) % 0.36/0.60 (step @p250 :rule instantiate :premises (@p249) :args (@t227)) % 0.36/0.60 (step @p251 :rule refl :args (@t157)) % 0.36/0.60 (step @p252 :rule cong :premises (@p150 @p251) :args (@t228)) % 0.36/0.60 (step @p253 :rule instantiate :premises (@p133) :args ((@list @t115 @t114))) % 0.36/0.60 (step @p254 :rule cnf_or_pos :args (@t230)) % 0.36/0.60 (step @p255 :rule reordering :premises (@p254) :args ((or @t124 @t186 @t229 (not @t230)))) % 0.36/0.60 (step @p256 :rule chain_m_resolution :premises (@p255 @p141 @p180 @p253) :args (@t229 @t163 (@list @t123 @t181 @t230))) % 0.36/0.60 (step @p257 :rule bool-double-not-elim :args (@t119)) % 0.36/0.60 (step @p258 :rule nary_cong :premises (@p136 @p257) :args ((or @t127 (not @t120)))) % 0.36/0.60 (step @p259 :rule cnf_or_neg :args (@t127 3)) % 0.36/0.60 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 0.36/0.60 (step @p261 :rule reordering :premises (@p260) :args ((or @t119 @t127))) % 0.36/0.60 (step @p262 :rule chain_m_resolution :premises (@p261 @p62) :args (@t119 @t128 @t129)) % 0.36/0.60 (step @p263 :rule cong :premises (@p262) :args (@t158)) % 0.36/0.60 (step @p264 :rule trans :premises (@p263 @p256 @p252)) % 0.36/0.60 (step @p265 :rule and_elim :premises (@p132) :args (1)) % 0.36/0.60 (step @p266 :rule instantiate :premises (@p265) :args (@t227)) % 0.36/0.60 (step @p267 :rule not_implies_elim1 :premises (@p130)) % 0.36/0.60 (step @p268 :rule and_elim :premises (@p267) :args (0)) % 0.36/0.60 (step @p269 :rule instantiate :premises (@p268) :args (@t164)) % 0.36/0.60 (step @p270 :rule cnf_or_pos :args (@t232)) % 0.36/0.60 (step @p271 :rule reordering :premises (@p270) :args ((or @t124 @t231 (not @t232)))) % 0.36/0.60 (step @p272 :rule chain_m_resolution :premises (@p271 @p141 @p269) :args (@t231 @t168 (@list @t123 @t232))) % 0.36/0.60 (step @p273 :rule instantiate :premises (@p268) :args (@t233)) % 0.36/0.60 (step @p274 :rule cnf_or_pos :args (@t235)) % 0.36/0.60 (step @p275 :rule reordering :premises (@p274) :args ((or @t126 @t234 (not @t235)))) % 0.36/0.60 (step @p276 :rule chain_m_resolution :premises (@p275 @p147 @p273) :args (@t234 @t168 (@list @t125 @t235))) % 0.36/0.60 (step @p277 :rule cnf_or_pos :args (@t241)) % 0.36/0.60 (step @p278 :rule reordering :premises (@p277) :args ((or @t240 @t239 @t238 (not @t241)))) % 0.36/0.60 (step @p279 :rule chain_m_resolution :premises (@p278 @p276 @p272 @p266) :args (@t238 @t163 (@list @t234 @t231 @t241))) % 0.36/0.60 (step @p280 :rule instantiate :premises (@p265) :args ((@list @t157 @t158))) % 0.36/0.60 (step @p281 :rule cnf_or_pos :args (@t245)) % 0.36/0.60 (step @p282 :rule reordering :premises (@p281) :args ((or @t240 @t239 @t244 (not @t245)))) % 0.36/0.60 (step @p283 :rule chain_m_resolution :premises (@p282 @p276 @p272 @p280) :args (@t244 @t163 (@list @t234 @t231 @t245))) % 0.36/0.60 (step @p284 :rule instantiate :premises (@p151) :args (@t233)) % 0.36/0.60 (step @p285 :rule cnf_or_pos :args (@t247)) % 0.36/0.60 (step @p286 :rule reordering :premises (@p285) :args ((or @t126 @t246 (not @t247)))) % 0.36/0.60 (step @p287 :rule chain_m_resolution :premises (@p286 @p147 @p284) :args (@t246 @t168 (@list @t125 @t247))) % 0.36/0.60 (step @p288 :rule instantiate :premises (@p133) :args ((@list @t114 @t113))) % 0.36/0.60 (step @p289 :rule cnf_or_pos :args (@t250)) % 0.36/0.60 (step @p290 :rule reordering :premises (@p289) :args ((or @t126 @t124 @t249 (not @t250)))) % 0.36/0.60 (step @p291 :rule chain_m_resolution :premises (@p290 @p147 @p141 @p288) :args (@t249 @t163 (@list @t125 @t123 @t250))) % 0.36/0.60 (step @p292 :rule cnf_or_neg :args (@t127 2)) % 0.36/0.60 (step @p293 :rule chain_m_resolution :premises (@p292 @p62) :args ((not @t122) @t128 @t129)) % 0.36/0.60 (assume-push @p383 @t161) % 0.36/0.60 (assume-push @p384 @t249) % 0.36/0.60 (assume-push @p385 @t246) % 0.36/0.60 (assume-push @p386 @t166) % 0.36/0.60 (assume-push @p387 @t251) % 0.36/0.60 (assume-push @p388 @t244) % 0.36/0.60 (assume-push @p389 @t238) % 0.36/0.60 (assume-push @p390 @t166) % 0.36/0.60 (assume-push @p391 @t246) % 0.36/0.60 (assume-push @p392 @t244) % 0.36/0.60 (assume-push @p393 @t249) % 0.36/0.60 (assume-push @p394 @t251) % 0.36/0.60 (assume-push @p395 @t161) % 0.36/0.60 (assume-push @p396 @t238) % 0.36/0.60 (step @p308 :rule symm :premises (@p287)) % 0.36/0.60 (step @p309 :rule symm :premises (@p155)) % 0.36/0.60 (step @p310 :rule cong :premises (@p309 @p308) :args (@t242)) % 0.36/0.60 (step @p311 :rule cong :premises (@p291) :args ((tptp.j @t248))) % 0.36/0.60 (step @p312 :rule symm :premises (@p291)) % 0.36/0.60 (step @p313 :rule trans :premises (@p150 @p387 @p312)) % 0.36/0.60 (step @p314 :rule cong :premises (@p313) :args ((tptp.j @t160))) % 0.36/0.60 (step @p315 :rule symm :premises (@p150)) % 0.36/0.60 (step @p316 :rule cong :premises (@p315) :args (@t237)) % 0.36/0.60 (step @p317 :rule symm :premises (@p279)) % 0.36/0.60 (step @p318 :rule cong :premises (@p287 @p155) :args (@t115)) % 0.36/0.60 (step @p319 :rule trans :premises (@p318 @p317 @p316 @p314 @p311 @p283 @p310)) % 0.36/0.60 (step-pop @p397 :rule scope :premises (@p319)) % 0.36/0.60 (step-pop @p398 :rule scope :premises (@p397)) % 0.36/0.60 (step-pop @p399 :rule scope :premises (@p398)) % 0.36/0.60 (step-pop @p400 :rule scope :premises (@p399)) % 0.36/0.60 (step-pop @p401 :rule scope :premises (@p400)) % 0.36/0.60 (step-pop @p402 :rule scope :premises (@p401)) % 0.36/0.60 (step-pop @p403 :rule scope :premises (@p402)) % 0.36/0.60 (step @p320 :rule process_scope :premises (@p403) :args (@t122)) % 0.36/0.60 (step @p328 :rule and_intro :premises (@p155 @p287 @p283 @p291 @p387 @p150 @p279)) % 0.36/0.60 (step @p329 :rule modus_ponens :premises (@p328 @p320)) % 0.36/0.60 (step-pop @p404 :rule scope :premises (@p329)) % 0.36/0.60 (step-pop @p405 :rule scope :premises (@p404)) % 0.36/0.60 (step-pop @p406 :rule scope :premises (@p405)) % 0.36/0.60 (step-pop @p407 :rule scope :premises (@p406)) % 0.36/0.60 (step-pop @p408 :rule scope :premises (@p407)) % 0.36/0.60 (step-pop @p409 :rule scope :premises (@p408)) % 0.36/0.60 (step-pop @p410 :rule scope :premises (@p409)) % 0.36/0.60 (step @p330 :rule process_scope :premises (@p410) :args (@t122)) % 0.36/0.60 (step @p338 :rule implies_elim :premises (@p330)) % 0.36/0.60 (step @p339 :rule cnf_and_neg :args (@t252)) % 0.36/0.60 (step @p340 :rule resolution :premises (@p339 @p338) :args (true @t252)) % 0.36/0.60 (step @p341 :rule reordering :premises (@p340) :args ((or @t122 @t255 (not @t249) (not @t246) @t254 @t253 (not @t244) (not @t238)))) % 0.36/0.60 (step @p342 :rule chain_m_resolution :premises (@p341 @p293 @p150 @p291 @p287 @p155 @p283 @p279) :args (@t253 (@list true false false false false false false) (@list @t122 @t161 @t249 @t246 @t166 @t244 @t238))) % 0.36/0.60 (step @p343 :rule cnf_or_pos :args (@t260)) % 0.36/0.60 (step @p344 :rule reordering :premises (@p343) :args ((or @t240 @t239 @t251 @t259 @t257 (not @t260)))) % 0.36/0.60 (step @p345 :rule chain_m_resolution :premises (@p344 @p276 @p272 @p342 @p264 @p250) :args (@t257 (@list false false true false false) (@list @t234 @t231 @t251 @t258 @t260))) % 0.36/0.60 (assume-push @p411 @t161) % 0.36/0.60 (assume-push @p412 @t185) % 0.36/0.60 (assume-push @p413 @t166) % 0.36/0.60 (assume-push @p414 @t257) % 0.36/0.60 (assume-push @p415 @t190) % 0.36/0.60 (assume-push @p416 @t190) % 0.36/0.60 (assume-push @p417 @t185) % 0.36/0.60 (assume-push @p418 @t161) % 0.36/0.60 (assume-push @p419 @t257) % 0.36/0.60 (assume-push @p420 @t166) % 0.36/0.60 (step @p356 :rule symm :premises (@p191)) % 0.36/0.60 (step @p357 :rule symm :premises (@p183)) % 0.36/0.60 (step @p358 :rule cong :premises (@p357) :args ((tptp.j @t183))) % 0.36/0.60 (step @p359 :rule refl :args (@t158)) % 0.36/0.60 (step @p315 :rule symm :premises (@p150)) % 0.36/0.60 (step @p360 :rule cong :premises (@p315 @p359) :args (@t256)) % 0.36/0.60 (step @p361 :rule trans :premises (@p414 @p360)) % 0.36/0.60 (step @p362 :rule cong :premises (@p361) :args (@t165)) % 0.36/0.60 (step @p363 :rule trans :premises (@p155 @p362 @p358 @p356)) % 0.36/0.60 (step-pop @p421 :rule scope :premises (@p363)) % 0.36/0.60 (step-pop @p422 :rule scope :premises (@p421)) % 0.36/0.60 (step-pop @p423 :rule scope :premises (@p422)) % 0.36/0.60 (step-pop @p424 :rule scope :premises (@p423)) % 0.36/0.60 (step-pop @p425 :rule scope :premises (@p424)) % 0.36/0.60 (step @p364 :rule process_scope :premises (@p425) :args (@t117)) % 0.36/0.60 (step @p370 :rule and_intro :premises (@p191 @p183 @p150 @p414 @p155)) % 0.36/0.60 (step @p371 :rule modus_ponens :premises (@p370 @p364)) % 0.36/0.60 (step-pop @p426 :rule scope :premises (@p371)) % 0.36/0.60 (step-pop @p427 :rule scope :premises (@p426)) % 0.36/0.60 (step-pop @p428 :rule scope :premises (@p427)) % 0.36/0.60 (step-pop @p429 :rule scope :premises (@p428)) % 0.36/0.60 (step-pop @p430 :rule scope :premises (@p429)) % 0.36/0.60 (step @p372 :rule process_scope :premises (@p430) :args (@t117)) % 0.36/0.60 (step @p378 :rule implies_elim :premises (@p372)) % 0.36/0.60 (step @p379 :rule cnf_and_neg :args (@t261)) % 0.36/0.60 (step @p380 :rule resolution :premises (@p379 @p378) :args (true @t261)) % 0.36/0.60 (step @p381 :rule reordering :premises (@p380) :args ((or @t117 @t255 (not @t185) @t254 (not @t257) (not @t190)))) % 0.36/0.60 (step @p382 false :rule chain_m_resolution :premises (@p381 @p345 @p191 @p183 @p155 @p150 @p64) :args (false (@list false false false false false true) (@list @t257 @t190 @t185 @t166 @t161 @t117))) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------