%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN054+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:42:50 AM UTC 2026 % Result : Theorem 0.40s 0.62s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN054+2 : TPTP v9.2.1. Released v7.3.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n021.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 12:39:05 EDT 2026 % 0.18/0.34 % CPUTime : % 0.32/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.62 % SZS status Theorem % 0.40/0.62 % SZS output start Proof % 0.40/0.62 ( % 0.40/0.62 (declare-sort $$unsorted 0) % 0.40/0.62 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.40/0.62 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.40/0.62 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.40/0.62 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.40/0.62 (define @t1 () (@var "Y24" $$unsorted)) % 0.40/0.62 (define @t2 () (@var "X19" $$unsorted)) % 0.40/0.62 (define @t3 () (= @t2 @t1)) % 0.40/0.62 (define @t4 () (tptp.r1 @t2)) % 0.40/0.62 (define @t5 () (and @t4 @t3)) % 0.40/0.62 (define @t6 () (not @t3)) % 0.40/0.62 (define @t7 () (not @t4)) % 0.40/0.62 (define @t8 () (and @t7 @t6)) % 0.40/0.62 (define @t9 () (or @t8 @t5)) % 0.40/0.62 (define @t10 () (@list @t2)) % 0.40/0.62 (define @t11 () (forall @t10 @t9)) % 0.40/0.62 (define @t12 () (@list @t1)) % 0.40/0.62 (define @t13 () (exists @t12 @t11)) % 0.40/0.62 (define @t14 () (@var "Y21" $$unsorted)) % 0.40/0.62 (define @t15 () (@var "X12" $$unsorted)) % 0.40/0.62 (define @t16 () (= @t15 @t14)) % 0.40/0.62 (define @t17 () (@var "X11" $$unsorted)) % 0.40/0.62 (define @t18 () (tptp.r2 @t17 @t15)) % 0.40/0.62 (define @t19 () (@var "Y22" $$unsorted)) % 0.40/0.62 (define @t20 () (@var "X15" $$unsorted)) % 0.40/0.62 (define @t21 () (= @t20 @t19)) % 0.40/0.62 (define @t22 () (@var "X14" $$unsorted)) % 0.40/0.62 (define @t23 () (@var "X13" $$unsorted)) % 0.40/0.62 (define @t24 () (tptp.r3 @t23 @t22 @t20)) % 0.40/0.62 (define @t25 () (and @t24 @t21)) % 0.40/0.62 (define @t26 () (not @t21)) % 0.40/0.62 (define @t27 () (not @t24)) % 0.40/0.62 (define @t28 () (and @t27 @t26)) % 0.40/0.62 (define @t29 () (or @t28 @t25)) % 0.40/0.62 (define @t30 () (@list @t20)) % 0.40/0.62 (define @t31 () (forall @t30 @t29)) % 0.40/0.62 (define @t32 () (@list @t19)) % 0.40/0.62 (define @t33 () (exists @t32 @t31)) % 0.40/0.62 (define @t34 () (forall (@list @t23 @t22) @t33)) % 0.40/0.62 (define @t35 () (@var "Y23" $$unsorted)) % 0.40/0.62 (define @t36 () (@var "X18" $$unsorted)) % 0.40/0.62 (define @t37 () (= @t36 @t35)) % 0.40/0.62 (define @t38 () (@var "X17" $$unsorted)) % 0.40/0.62 (define @t39 () (@var "X16" $$unsorted)) % 0.40/0.62 (define @t40 () (tptp.r4 @t39 @t38 @t36)) % 0.40/0.62 (define @t41 () (@var "Y7" $$unsorted)) % 0.40/0.62 (define @t42 () (@var "X8" $$unsorted)) % 0.40/0.62 (define @t43 () (@var "X1" $$unsorted)) % 0.40/0.62 (define @t44 () (tptp.r3 @t43 @t42 @t41)) % 0.40/0.62 (define @t45 () (@var "Y4" $$unsorted)) % 0.40/0.62 (define @t46 () (tptp.r2 @t41 @t45)) % 0.40/0.62 (define @t47 () (and @t46 @t44)) % 0.40/0.62 (define @t48 () (@list @t41)) % 0.40/0.62 (define @t49 () (exists @t48 @t47)) % 0.40/0.62 (define @t50 () (@var "Y5" $$unsorted)) % 0.40/0.62 (define @t51 () (= @t50 @t45)) % 0.40/0.62 (define @t52 () (@var "Y15" $$unsorted)) % 0.40/0.62 (define @t53 () (tptp.r3 @t43 @t52 @t50)) % 0.40/0.62 (define @t54 () (tptp.r2 @t42 @t52)) % 0.40/0.62 (define @t55 () (and @t54 @t53)) % 0.40/0.62 (define @t56 () (@list @t52)) % 0.40/0.62 (define @t57 () (exists @t56 @t55)) % 0.40/0.62 (define @t58 () (and @t57 @t51)) % 0.40/0.62 (define @t59 () (@list @t50)) % 0.40/0.62 (define @t60 () (exists @t59 @t58)) % 0.40/0.62 (define @t61 () (and @t60 @t49)) % 0.40/0.62 (define @t62 () (@list @t45)) % 0.40/0.62 (define @t63 () (exists @t62 @t61)) % 0.40/0.62 (define @t64 () (forall (@list @t43 @t42) @t63)) % 0.40/0.62 (define @t65 () (@var "Y6" $$unsorted)) % 0.40/0.62 (define @t66 () (@var "X9" $$unsorted)) % 0.40/0.62 (define @t67 () (@var "X2" $$unsorted)) % 0.40/0.62 (define @t68 () (@var "Y2" $$unsorted)) % 0.40/0.62 (define @t69 () (@list @t65)) % 0.40/0.62 (define @t70 () (@var "Y3" $$unsorted)) % 0.40/0.62 (define @t71 () (@var "Y14" $$unsorted)) % 0.40/0.62 (define @t72 () (@list @t70)) % 0.40/0.62 (define @t73 () (@list @t68)) % 0.40/0.62 (define @t74 () (@var "X10" $$unsorted)) % 0.40/0.62 (define @t75 () (@var "X3" $$unsorted)) % 0.40/0.62 (define @t76 () (@var "Y12" $$unsorted)) % 0.40/0.62 (define @t77 () (@var "Y13" $$unsorted)) % 0.40/0.62 (define @t78 () (@var "X4" $$unsorted)) % 0.40/0.62 (define @t79 () (@var "Y9" $$unsorted)) % 0.40/0.62 (define @t80 () (= @t79 @t78)) % 0.40/0.62 (define @t81 () (@var "Y16" $$unsorted)) % 0.40/0.62 (define @t82 () (tptp.r3 @t78 @t81 @t79)) % 0.40/0.62 (define @t83 () (tptp.r1 @t81)) % 0.40/0.62 (define @t84 () (and @t83 @t82)) % 0.40/0.62 (define @t85 () (@list @t81)) % 0.40/0.62 (define @t86 () (exists @t85 @t84)) % 0.40/0.62 (define @t87 () (and @t86 @t80)) % 0.40/0.62 (define @t88 () (@list @t79)) % 0.40/0.62 (define @t89 () (exists @t88 @t87)) % 0.40/0.62 (define @t90 () (forall (@list @t78) @t89)) % 0.40/0.62 (define @t91 () (@var "Y18" $$unsorted)) % 0.40/0.62 (define @t92 () (@var "Y8" $$unsorted)) % 0.40/0.62 (define @t93 () (@var "Y17" $$unsorted)) % 0.40/0.62 (define @t94 () (@var "X5" $$unsorted)) % 0.40/0.62 (define @t95 () (@var "Y11" $$unsorted)) % 0.40/0.62 (define @t96 () (@var "X6" $$unsorted)) % 0.40/0.62 (define @t97 () (@var "Y1" $$unsorted)) % 0.40/0.62 (define @t98 () (@var "Y19" $$unsorted)) % 0.40/0.62 (define @t99 () (@var "Y10" $$unsorted)) % 0.40/0.62 (define @t100 () (@var "X7" $$unsorted)) % 0.40/0.62 (define @t101 () (@var "Y20" $$unsorted)) % 0.40/0.62 (define @t102 () (tptp.r2 @t65 @t70)) % 0.40/0.62 (define @t103 () (tptp.r1 @t65)) % 0.40/0.62 (define @t104 () (and @t103 @t102)) % 0.40/0.62 (define @t105 () (exists @t69 @t104)) % 0.40/0.62 (define @t106 () (and (= @t97 @t70) @t105)) % 0.40/0.62 (define @t107 () (exists @t72 @t106)) % 0.40/0.62 (define @t108 () (tptp.r2 @t50 @t68)) % 0.40/0.62 (define @t109 () (tptp.r1 @t50)) % 0.40/0.62 (define @t110 () (and @t109 @t108)) % 0.40/0.62 (define @t111 () (exists @t59 @t110)) % 0.40/0.62 (define @t112 () (tptp.r3 @t45 @t68 @t97)) % 0.40/0.62 (define @t113 () (tptp.r1 @t45)) % 0.40/0.62 (define @t114 () (and @t113 @t112)) % 0.40/0.62 (define @t115 () (exists @t62 @t114)) % 0.40/0.62 (define @t116 () (and @t115 @t111)) % 0.40/0.62 (define @t117 () (exists @t73 @t116)) % 0.40/0.62 (define @t118 () (and @t117 @t107)) % 0.40/0.62 (define @t119 () (@list @t97)) % 0.40/0.62 (define @t120 () (exists @t119 @t118)) % 0.40/0.62 (define @t121 () (not @t120)) % 0.40/0.62 (define @t122 () (@var "BOUND_VARIABLE_8240" $$unsorted)) % 0.40/0.62 (define @t123 () (not (tptp.r2 @t122 @t97))) % 0.40/0.62 (define @t124 () (not (tptp.r1 @t122))) % 0.40/0.62 (define @t125 () (@var "BOUND_VARIABLE_8225" $$unsorted)) % 0.40/0.62 (define @t126 () (@var "BOUND_VARIABLE_8229" $$unsorted)) % 0.40/0.62 (define @t127 () (not (tptp.r2 @t126 @t125))) % 0.40/0.62 (define @t128 () (not (tptp.r1 @t126))) % 0.40/0.62 (define @t129 () (@var "BOUND_VARIABLE_8227" $$unsorted)) % 0.40/0.62 (define @t130 () (not (tptp.r3 @t129 @t125 @t97))) % 0.40/0.62 (define @t131 () (not (tptp.r1 @t129))) % 0.40/0.62 (define @t132 () (or @t131 @t130 @t128 @t127 @t124 @t123)) % 0.40/0.62 (define @t133 () (@list @t97 @t125 @t129 @t126 @t122)) % 0.40/0.62 (define @t134 () (or @t124 @t123)) % 0.40/0.62 (define @t135 () (or @t131 @t130 @t128 @t127)) % 0.40/0.62 (define @t136 () (or @t135 @t134)) % 0.40/0.62 (define @t137 () (forall @t133 @t136)) % 0.40/0.62 (define @t138 () (forall (@list @t125 @t129 @t126 @t122) @t136)) % 0.40/0.62 (define @t139 () (forall (@list @t122) @t134)) % 0.40/0.62 (define @t140 () (@var "BOUND_VARIABLE_8195" $$unsorted)) % 0.40/0.62 (define @t141 () (@list @t140)) % 0.40/0.62 (define @t142 () (forall (@list @t125 @t129 @t126) @t135)) % 0.40/0.62 (define @t143 () (@var "BOUND_VARIABLE_8165" $$unsorted)) % 0.40/0.62 (define @t144 () (@var "BOUND_VARIABLE_8158" $$unsorted)) % 0.40/0.62 (define @t145 () (or @t142 @t139)) % 0.40/0.62 (define @t146 () (not (tptp.r2 @t140 @t97))) % 0.40/0.62 (define @t147 () (not (tptp.r1 @t140))) % 0.40/0.62 (define @t148 () (or @t147 @t146)) % 0.40/0.62 (define @t149 () (@list @t140)) % 0.40/0.62 (define @t150 () (forall @t149 @t148)) % 0.40/0.62 (define @t151 () (not (tptp.r2 @t143 @t68))) % 0.40/0.62 (define @t152 () (not (tptp.r1 @t143))) % 0.40/0.62 (define @t153 () (not (tptp.r3 @t144 @t68 @t97))) % 0.40/0.62 (define @t154 () (not (tptp.r1 @t144))) % 0.40/0.62 (define @t155 () (or @t154 @t153 @t152 @t151)) % 0.40/0.62 (define @t156 () (@list @t68 @t144 @t143)) % 0.40/0.62 (define @t157 () (forall @t156 @t155)) % 0.40/0.62 (define @t158 () (not @t150)) % 0.40/0.62 (define @t159 () (not @t157)) % 0.40/0.62 (define @t160 () (and @t159 @t158)) % 0.40/0.62 (define @t161 () (forall @t119 (not @t160))) % 0.40/0.62 (define @t162 () (not @t161)) % 0.40/0.62 (define @t163 () (not (= @t97 @t97))) % 0.40/0.62 (define @t164 () (or @t163 @t147 @t146)) % 0.40/0.62 (define @t165 () (not (tptp.r2 @t140 @t70))) % 0.40/0.62 (define @t166 () (= @t70 @t97)) % 0.40/0.62 (define @t167 () (not @t166)) % 0.40/0.62 (define @t168 () (or @t167 @t167 @t147 @t165)) % 0.40/0.62 (define @t169 () (or @t167 @t147 @t165)) % 0.40/0.62 (define @t170 () (forall @t72 @t169)) % 0.40/0.62 (define @t171 () (forall @t149 @t170)) % 0.40/0.62 (define @t172 () (forall (@list @t140 @t70) @t169)) % 0.40/0.62 (define @t173 () (@list @t70 @t140)) % 0.40/0.62 (define @t174 () (or @t147 @t165)) % 0.40/0.62 (define @t175 () (or @t167 @t174)) % 0.40/0.62 (define @t176 () (forall @t173 @t175)) % 0.40/0.62 (define @t177 () (forall @t149 @t175)) % 0.40/0.62 (define @t178 () (forall @t149 @t174)) % 0.40/0.62 (define @t179 () (or @t167 @t178)) % 0.40/0.62 (define @t180 () (forall @t69 (or (not @t103) (not @t102)))) % 0.40/0.62 (define @t181 () (not @t180)) % 0.40/0.62 (define @t182 () (and @t166 @t181)) % 0.40/0.62 (define @t183 () (forall @t72 (not @t182))) % 0.40/0.62 (define @t184 () (not @t183)) % 0.40/0.62 (define @t185 () (forall @t69 (not @t104))) % 0.40/0.62 (define @t186 () (not @t185)) % 0.40/0.62 (define @t187 () (or @t152 @t151)) % 0.40/0.62 (define @t188 () (or @t154 @t153)) % 0.40/0.62 (define @t189 () (or @t188 @t187)) % 0.40/0.62 (define @t190 () (forall @t156 @t189)) % 0.40/0.62 (define @t191 () (forall (@list @t144 @t143) @t189)) % 0.40/0.62 (define @t192 () (forall (@list @t143) @t187)) % 0.40/0.62 (define @t193 () (forall (@list @t144) @t188)) % 0.40/0.62 (define @t194 () (or @t193 @t192)) % 0.40/0.62 (define @t195 () (forall @t59 (or (not @t109) (not @t108)))) % 0.40/0.62 (define @t196 () (forall @t62 (or (not @t113) (not @t112)))) % 0.40/0.62 (define @t197 () (not @t195)) % 0.40/0.62 (define @t198 () (not @t196)) % 0.40/0.62 (define @t199 () (and @t198 @t197)) % 0.40/0.62 (define @t200 () (forall @t73 (not @t199))) % 0.40/0.62 (define @t201 () (not @t200)) % 0.40/0.62 (define @t202 () (forall @t59 (not @t110))) % 0.40/0.62 (define @t203 () (not @t202)) % 0.40/0.62 (define @t204 () (forall @t62 (not @t114))) % 0.40/0.62 (define @t205 () (not @t204)) % 0.40/0.62 (define @t206 () (tptp.r1 @t1)) % 0.40/0.62 (define @t207 () (@var "BOUND_VARIABLE_7643" $$unsorted)) % 0.40/0.62 (define @t208 () (tptp.r1 @t207)) % 0.40/0.62 (define @t209 () (not @t208)) % 0.40/0.62 (define @t210 () (@list @t207)) % 0.40/0.62 (define @t211 () (forall @t210 (or @t209 (and @t208 (= @t1 @t207))))) % 0.40/0.62 (define @t212 () (forall @t12 (or (not @t211) (not @t206)))) % 0.40/0.62 (define @t213 () (@quantifiers_skolemize @t212 0)) % 0.40/0.62 (define @t214 () (@var "BOUND_VARIABLE_8022" $$unsorted)) % 0.40/0.62 (define @t215 () (not (tptp.r1 @t214))) % 0.40/0.62 (define @t216 () (@list @t214)) % 0.40/0.62 (define @t217 () (@quantifiers_skolemize (forall @t216 (or @t215 (not (tptp.r3 @t213 @t214 @t213)))) 0)) % 0.40/0.62 (define @t218 () (@var "BOUND_VARIABLE_7886" $$unsorted)) % 0.40/0.62 (define @t219 () (not (tptp.r2 @t218 @t45))) % 0.40/0.62 (define @t220 () (@var "BOUND_VARIABLE_7879" $$unsorted)) % 0.40/0.62 (define @t221 () (@list @t45 @t220 @t218)) % 0.40/0.62 (define @t222 () (forall @t221 (or (not (tptp.r2 @t213 @t220)) (not (tptp.r3 @t213 @t220 @t45)) @t219 (not (tptp.r3 @t213 @t213 @t218))))) % 0.40/0.62 (define @t223 () (@quantifiers_skolemize @t222 1)) % 0.40/0.62 (define @t224 () (@quantifiers_skolemize @t222 0)) % 0.40/0.62 (define @t225 () (not (tptp.r3 @t78 @t214 @t78))) % 0.40/0.62 (define @t226 () (not (= @t78 @t78))) % 0.40/0.62 (define @t227 () (or @t226 @t215 @t225)) % 0.40/0.62 (define @t228 () (not (tptp.r3 @t78 @t214 @t79))) % 0.40/0.62 (define @t229 () (= @t78 @t79)) % 0.40/0.62 (define @t230 () (not @t229)) % 0.40/0.62 (define @t231 () (or @t230 @t230 @t215 @t228)) % 0.40/0.62 (define @t232 () (or @t230 @t215 @t228)) % 0.40/0.62 (define @t233 () (forall @t88 @t232)) % 0.40/0.62 (define @t234 () (forall @t216 @t233)) % 0.40/0.62 (define @t235 () (forall (@list @t214 @t79) @t232)) % 0.40/0.62 (define @t236 () (@list @t79 @t214)) % 0.40/0.62 (define @t237 () (or @t215 @t228)) % 0.40/0.62 (define @t238 () (or @t237 @t230)) % 0.40/0.62 (define @t239 () (forall @t236 @t238)) % 0.40/0.62 (define @t240 () (forall @t216 @t238)) % 0.40/0.62 (define @t241 () (forall @t216 @t237)) % 0.40/0.62 (define @t242 () (or @t241 @t230)) % 0.40/0.62 (define @t243 () (forall @t85 (or (not @t83) (not @t82)))) % 0.40/0.62 (define @t244 () (not @t243)) % 0.40/0.62 (define @t245 () (and @t244 @t229)) % 0.40/0.62 (define @t246 () (forall @t88 (not @t245))) % 0.40/0.62 (define @t247 () (not @t246)) % 0.40/0.62 (define @t248 () (forall @t85 (not @t84))) % 0.40/0.62 (define @t249 () (not @t248)) % 0.40/0.62 (define @t250 () (@list @t213)) % 0.40/0.62 (define @t251 () (tptp.r1 @t217)) % 0.40/0.62 (define @t252 () (tptp.r3 @t213 @t217 @t213)) % 0.40/0.62 (define @t253 () (not @t252)) % 0.40/0.62 (define @t254 () (not @t251)) % 0.40/0.62 (define @t255 () (or @t254 @t253)) % 0.40/0.62 (define @t256 () (@list true)) % 0.40/0.62 (define @t257 () (@list @t255)) % 0.40/0.62 (define @t258 () (not (tptp.r3 @t43 @t42 @t218))) % 0.40/0.62 (define @t259 () (not (tptp.r3 @t43 @t220 @t45))) % 0.40/0.62 (define @t260 () (not (tptp.r2 @t42 @t220))) % 0.40/0.62 (define @t261 () (or @t219 @t258)) % 0.40/0.62 (define @t262 () (or @t260 @t259)) % 0.40/0.62 (define @t263 () (or @t262 @t261)) % 0.40/0.62 (define @t264 () (forall @t221 @t263)) % 0.40/0.62 (define @t265 () (forall (@list @t220 @t218) @t263)) % 0.40/0.62 (define @t266 () (forall (@list @t218) @t261)) % 0.40/0.62 (define @t267 () (forall (@list @t220) @t262)) % 0.40/0.62 (define @t268 () (@var "BOUND_VARIABLE_7841" $$unsorted)) % 0.40/0.62 (define @t269 () (@list @t268)) % 0.40/0.62 (define @t270 () (or @t267 @t266)) % 0.40/0.62 (define @t271 () (forall @t48 (or (not @t46) (not @t44)))) % 0.40/0.62 (define @t272 () (not (tptp.r3 @t43 @t268 @t45))) % 0.40/0.62 (define @t273 () (not (tptp.r2 @t42 @t268))) % 0.40/0.62 (define @t274 () (or @t273 @t272)) % 0.40/0.62 (define @t275 () (@list @t268)) % 0.40/0.62 (define @t276 () (forall @t275 @t274)) % 0.40/0.62 (define @t277 () (not @t271)) % 0.40/0.62 (define @t278 () (not @t276)) % 0.40/0.62 (define @t279 () (and @t278 @t277)) % 0.40/0.62 (define @t280 () (forall @t62 (not @t279))) % 0.40/0.62 (define @t281 () (not @t280)) % 0.40/0.62 (define @t282 () (forall @t48 (not @t47))) % 0.40/0.62 (define @t283 () (not @t282)) % 0.40/0.62 (define @t284 () (not (= @t45 @t45))) % 0.40/0.62 (define @t285 () (or @t284 @t273 @t272)) % 0.40/0.62 (define @t286 () (not (tptp.r3 @t43 @t268 @t50))) % 0.40/0.62 (define @t287 () (= @t45 @t50)) % 0.40/0.62 (define @t288 () (not @t287)) % 0.40/0.62 (define @t289 () (or @t288 @t288 @t273 @t286)) % 0.40/0.62 (define @t290 () (or @t288 @t273 @t286)) % 0.40/0.62 (define @t291 () (forall @t59 @t290)) % 0.40/0.62 (define @t292 () (forall @t275 @t291)) % 0.40/0.62 (define @t293 () (forall (@list @t268 @t50) @t290)) % 0.40/0.62 (define @t294 () (@list @t50 @t268)) % 0.40/0.62 (define @t295 () (or @t273 @t286)) % 0.40/0.62 (define @t296 () (or @t295 @t288)) % 0.40/0.62 (define @t297 () (forall @t294 @t296)) % 0.40/0.62 (define @t298 () (forall @t275 @t296)) % 0.40/0.62 (define @t299 () (forall @t275 @t295)) % 0.40/0.62 (define @t300 () (or @t299 @t288)) % 0.40/0.62 (define @t301 () (forall @t56 (or (not @t54) (not @t53)))) % 0.40/0.62 (define @t302 () (not @t301)) % 0.40/0.62 (define @t303 () (and @t302 @t287)) % 0.40/0.62 (define @t304 () (forall @t59 (not @t303))) % 0.40/0.62 (define @t305 () (not @t304)) % 0.40/0.62 (define @t306 () (forall @t56 (not @t55))) % 0.40/0.62 (define @t307 () (not @t306)) % 0.40/0.62 (define @t308 () (@list @t213 @t213)) % 0.40/0.62 (define @t309 () (tptp.r3 @t213 @t223 @t224)) % 0.40/0.62 (define @t310 () (@quantifiers_skolemize @t222 2)) % 0.40/0.62 (define @t311 () (tptp.r3 @t213 @t213 @t310)) % 0.40/0.62 (define @t312 () (not @t311)) % 0.40/0.62 (define @t313 () (tptp.r2 @t310 @t224)) % 0.40/0.62 (define @t314 () (not @t313)) % 0.40/0.62 (define @t315 () (not @t309)) % 0.40/0.62 (define @t316 () (tptp.r2 @t213 @t223)) % 0.40/0.62 (define @t317 () (not @t316)) % 0.40/0.62 (define @t318 () (or @t317 @t315 @t314 @t312)) % 0.40/0.62 (define @t319 () (@list @t318)) % 0.40/0.62 (define @t320 () (and @t211 @t206)) % 0.40/0.62 (define @t321 () (forall @t12 (not @t320))) % 0.40/0.62 (define @t322 () (not @t321)) % 0.40/0.62 (define @t323 () (= @t1 @t1)) % 0.40/0.62 (define @t324 () (and @t206 @t323)) % 0.40/0.62 (define @t325 () (not @t323)) % 0.40/0.62 (define @t326 () (or @t325 @t324)) % 0.40/0.62 (define @t327 () (@var "BOUND_VARIABLE_7652" $$unsorted)) % 0.40/0.62 (define @t328 () (= @t1 @t327)) % 0.40/0.62 (define @t329 () (and (tptp.r1 @t327) @t328)) % 0.40/0.62 (define @t330 () (not @t328)) % 0.40/0.62 (define @t331 () (@list @t327)) % 0.40/0.62 (define @t332 () (or @t330 @t330 @t329)) % 0.40/0.62 (define @t333 () (or @t330 @t329)) % 0.40/0.62 (define @t334 () (forall @t331 @t333)) % 0.40/0.62 (define @t335 () (= @t1 @t2)) % 0.40/0.62 (define @t336 () (and @t4 @t335)) % 0.40/0.62 (define @t337 () (not @t335)) % 0.40/0.62 (define @t338 () (or @t337 @t336)) % 0.40/0.62 (define @t339 () (forall @t10 @t338)) % 0.40/0.62 (define @t340 () (@list @t2)) % 0.40/0.62 (define @t341 () (or @t7 @t336)) % 0.40/0.62 (define @t342 () (forall @t10 @t341)) % 0.40/0.62 (define @t343 () (and @t342 @t339)) % 0.40/0.62 (define @t344 () (tptp.r1 @t213)) % 0.40/0.62 (define @t345 () (not @t344)) % 0.40/0.62 (define @t346 () (forall @t210 (or @t209 (and @t208 (= @t207 @t213))))) % 0.40/0.62 (define @t347 () (not @t346)) % 0.40/0.62 (define @t348 () (or @t347 @t345)) % 0.40/0.62 (define @t349 () (not @t348)) % 0.40/0.62 (define @t350 () (not @t212)) % 0.40/0.62 (define @t351 () (and @t208 (= @t213 @t207))) % 0.40/0.62 (define @t352 () (or @t209 @t351)) % 0.40/0.62 (define @t353 () (forall @t210 @t352)) % 0.40/0.62 (define @t354 () (not @t353)) % 0.40/0.62 (define @t355 () (or @t354 @t345)) % 0.40/0.62 (define @t356 () (not @t355)) % 0.40/0.62 (define @t357 () (@list @t348)) % 0.40/0.62 (define @t358 () (not (tptp.r2 @t217 @t224))) % 0.40/0.62 (define @t359 () (or @t345 @t315 @t345 @t317 @t254 @t358)) % 0.40/0.62 (define @t360 () (and @t251 (= @t217 @t213))) % 0.40/0.62 (define @t361 () (or @t254 @t360)) % 0.40/0.62 (define @t362 () (= @t213 @t217)) % 0.40/0.62 (define @t363 () (and @t251 @t362)) % 0.40/0.62 (define @t364 () (or @t254 @t363)) % 0.40/0.62 (define @t365 () (@list false)) % 0.40/0.62 (define @t366 () (@list false false)) % 0.40/0.62 (define @t367 () (@var "BOUND_VARIABLE_7738" $$unsorted)) % 0.40/0.62 (define @t368 () (= @t19 @t367)) % 0.40/0.62 (define @t369 () (tptp.r3 @t23 @t22 @t367)) % 0.40/0.62 (define @t370 () (@list @t367)) % 0.40/0.62 (define @t371 () (forall @t370 (or (not @t369) (and @t369 @t368)))) % 0.40/0.62 (define @t372 () (tptp.r3 @t23 @t22 @t19)) % 0.40/0.62 (define @t373 () (and @t371 @t372)) % 0.40/0.62 (define @t374 () (forall @t32 (not @t373))) % 0.40/0.62 (define @t375 () (not @t374)) % 0.40/0.62 (define @t376 () (= @t19 @t19)) % 0.40/0.62 (define @t377 () (and @t372 @t376)) % 0.40/0.62 (define @t378 () (not @t376)) % 0.40/0.62 (define @t379 () (or @t378 @t377)) % 0.40/0.62 (define @t380 () (@var "BOUND_VARIABLE_7747" $$unsorted)) % 0.40/0.62 (define @t381 () (= @t19 @t380)) % 0.40/0.62 (define @t382 () (and (tptp.r3 @t23 @t22 @t380) @t381)) % 0.40/0.62 (define @t383 () (not @t381)) % 0.40/0.62 (define @t384 () (@list @t380)) % 0.40/0.62 (define @t385 () (or @t383 @t383 @t382)) % 0.40/0.62 (define @t386 () (or @t383 @t382)) % 0.40/0.62 (define @t387 () (forall @t384 @t386)) % 0.40/0.62 (define @t388 () (= @t19 @t20)) % 0.40/0.62 (define @t389 () (and @t24 @t388)) % 0.40/0.62 (define @t390 () (not @t388)) % 0.40/0.62 (define @t391 () (or @t390 @t389)) % 0.40/0.62 (define @t392 () (forall @t30 @t391)) % 0.40/0.62 (define @t393 () (@list @t20)) % 0.40/0.62 (define @t394 () (or @t27 @t389)) % 0.40/0.62 (define @t395 () (forall @t30 @t394)) % 0.40/0.62 (define @t396 () (and @t395 @t392)) % 0.40/0.62 (define @t397 () (tptp.r3 @t213 @t213 @t367)) % 0.40/0.62 (define @t398 () (not @t397)) % 0.40/0.62 (define @t399 () (forall @t32 (or (not (forall @t370 (or @t398 (and @t397 @t368)))) (not (tptp.r3 @t213 @t213 @t19))))) % 0.40/0.62 (define @t400 () (@quantifiers_skolemize @t399 0)) % 0.40/0.62 (define @t401 () (not (tptp.r3 @t213 @t213 @t400))) % 0.40/0.62 (define @t402 () (forall @t370 (or @t398 (and @t397 (= @t367 @t400))))) % 0.40/0.62 (define @t403 () (not @t402)) % 0.40/0.62 (define @t404 () (or @t403 @t401)) % 0.40/0.62 (define @t405 () (not @t404)) % 0.40/0.62 (define @t406 () (not @t399)) % 0.40/0.62 (define @t407 () (and @t397 (= @t400 @t367))) % 0.40/0.62 (define @t408 () (or @t398 @t407)) % 0.40/0.62 (define @t409 () (forall @t370 @t408)) % 0.40/0.62 (define @t410 () (not @t409)) % 0.40/0.62 (define @t411 () (or @t410 @t401)) % 0.40/0.62 (define @t412 () (not @t411)) % 0.40/0.62 (define @t413 () (tptp.r3 @t213 @t213 @t213)) % 0.40/0.62 (define @t414 () (= @t213 @t400)) % 0.40/0.62 (define @t415 () (and @t413 @t414)) % 0.40/0.62 (define @t416 () (not @t413)) % 0.40/0.62 (define @t417 () (or @t416 @t415)) % 0.40/0.62 (define @t418 () (and @t311 (= @t310 @t400))) % 0.40/0.62 (define @t419 () (or @t312 @t418)) % 0.40/0.62 (define @t420 () (= @t400 @t310)) % 0.40/0.62 (define @t421 () (and @t311 @t420)) % 0.40/0.62 (define @t422 () (or @t312 @t421)) % 0.40/0.62 (assume @p1 @t13) % 0.40/0.62 (assume @p2 (forall (@list @t17) (exists (@list @t14) (forall (@list @t15) (or (and (not @t18) (not @t16)) (and @t18 @t16)))))) % 0.40/0.62 (assume @p3 @t34) % 0.40/0.62 (assume @p4 (forall (@list @t39 @t38) (exists (@list @t35) (forall (@list @t36) (or (and (not @t40) (not @t37)) (and @t40 @t37)))))) % 0.40/0.62 (assume @p5 @t64) % 0.40/0.62 (assume @p6 (forall (@list @t67 @t66) (exists @t73 (and (exists @t72 (and (exists (@list @t71) (and (tptp.r2 @t66 @t71) (tptp.r4 @t67 @t71 @t70))) (= @t70 @t68))) (exists @t69 (and (tptp.r3 @t65 @t67 @t68) (tptp.r4 @t67 @t66 @t65))))))) % 0.40/0.62 (assume @p7 (forall (@list @t75 @t74) (or (forall (@list @t76) (or (forall (@list @t77) (or (not (tptp.r2 @t75 @t77)) (not (= @t77 @t76)))) (not (tptp.r2 @t74 @t76)))) (= @t75 @t74)))) % 0.40/0.62 (assume @p8 @t90) % 0.40/0.62 (assume @p9 (forall (@list @t94) (exists (@list @t92) (and (exists (@list @t93) (and (tptp.r1 @t93) (tptp.r4 @t94 @t93 @t92))) (exists (@list @t91) (and (tptp.r1 @t91) (= @t92 @t91))))))) % 0.40/0.62 (assume @p10 (forall (@list @t96) (or (exists (@list @t98) (and (tptp.r1 @t98) (= @t96 @t98))) (exists (@list @t97 @t95) (and (tptp.r2 @t97 @t95) (= @t96 @t95)))))) % 0.40/0.62 (assume @p11 (forall (@list @t100 @t99) (or (forall (@list @t101) (or (not (tptp.r1 @t101)) (not (= @t101 @t99)))) (not (tptp.r2 @t100 @t99))))) % 0.40/0.62 (assume @p12 @t121) % 0.40/0.62 (assume @p13 true) % 0.40/0.62 (step @p14 :rule evaluate :args ((= true false))) % 0.40/0.62 (step @p15 :rule bool-double-not-elim :args ((forall @t133 @t132))) % 0.40/0.62 (step @p16 :rule aci_norm :args ((= @t136 @t132))) % 0.40/0.62 (step @p17 :rule cong :premises (@p16) :args (@t137)) % 0.40/0.62 (step @p18 :rule quant-merge-prenex :args ((= (forall @t119 @t138) @t137))) % 0.40/0.62 (step @p19 :rule alpha_equiv :args (@t139 (@list @t122) @t141)) % 0.40/0.62 (step @p20 :rule alpha_equiv :args (@t142 (@list @t125 @t129 @t126) (@list @t68 @t144 @t143))) % 0.40/0.62 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t145)) % 0.40/0.62 (step @p22 :rule quant-miniscope-or :args ((= @t138 @t145))) % 0.40/0.62 (step @p23 :rule trans :premises (@p22 @p21)) % 0.40/0.62 (step @p24 :rule symm :premises (@p23)) % 0.40/0.62 (step @p25 :rule cong :premises (@p24) :args ((forall @t119 (or @t157 @t150)))) % 0.40/0.62 (step @p26 :rule trans :premises (@p25 @p18)) % 0.40/0.62 (step @p27 :rule trans :premises (@p26 @p17)) % 0.40/0.62 (step @p28 :rule bool-double-not-elim :args (@t150)) % 0.40/0.62 (step @p29 :rule bool-double-not-elim :args (@t157)) % 0.40/0.62 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or (not @t159) (not @t158)))) % 0.40/0.62 (step @p31 :rule bool-and-de-morgan :args (@t159 @t158 true)) % 0.40/0.62 (step @p32 :rule trans :premises (@p31 @p30)) % 0.40/0.62 (step @p33 :rule cong :premises (@p32) :args (@t161)) % 0.40/0.62 (step @p34 :rule trans :premises (@p33 @p27)) % 0.40/0.62 (step @p35 :rule cong :premises (@p34) :args (@t162)) % 0.40/0.62 (step @p36 :rule exists-elim :args ((= (exists @t119 @t160) @t162))) % 0.40/0.62 (step @p37 :rule trans :premises (@p36 @p35)) % 0.40/0.62 (step @p38 :rule aci_norm :args ((= (or false @t147 @t146) @t148))) % 0.40/0.62 (step @p39 :rule refl :args (@t146)) % 0.40/0.62 (step @p40 :rule refl :args (@t147)) % 0.40/0.62 (step @p41 :rule evaluate :args ((not true))) % 0.40/0.62 (step @p42 :rule eq-refl :args (@t97)) % 0.40/0.62 (step @p43 :rule cong :premises (@p42) :args (@t163)) % 0.40/0.62 (step @p44 :rule trans :premises (@p43 @p41)) % 0.40/0.62 (step @p45 :rule nary_cong :premises (@p44 @p40 @p39) :args (@t164)) % 0.40/0.62 (step @p46 :rule trans :premises (@p45 @p38)) % 0.40/0.62 (step @p47 :rule cong :premises (@p46) :args ((forall @t149 @t164))) % 0.40/0.62 (step @p48 :rule quant-var-elim-eq :args ((= (forall @t72 @t168) @t164))) % 0.40/0.62 (step @p49 :rule aci_norm :args ((= @t169 @t168))) % 0.40/0.62 (step @p50 :rule cong :premises (@p49) :args (@t170)) % 0.40/0.62 (step @p51 :rule trans :premises (@p50 @p48)) % 0.40/0.62 (step @p52 :rule cong :premises (@p51) :args (@t171)) % 0.40/0.62 (step @p53 :rule quant-merge-prenex :args ((= @t171 @t172))) % 0.40/0.62 (step @p54 :rule symm :premises (@p53)) % 0.40/0.62 (step @p55 :rule quant_var_reordering :args ((= (forall @t173 @t169) @t172))) % 0.40/0.62 (step @p56 :rule trans :premises (@p55 @p54 @p52)) % 0.40/0.62 (step @p57 :rule trans :premises (@p56 @p47)) % 0.40/0.62 (step @p58 :rule aci_norm :args ((= @t175 @t169))) % 0.40/0.62 (step @p59 :rule cong :premises (@p58) :args (@t176)) % 0.40/0.62 (step @p60 :rule trans :premises (@p59 @p57)) % 0.40/0.62 (step @p61 :rule quant-merge-prenex :args ((= (forall @t72 @t177) @t176))) % 0.40/0.62 (step @p62 :rule alpha_equiv :args (@t178 @t141 (@list @t65))) % 0.40/0.62 (step @p63 :rule refl :args (@t167)) % 0.40/0.62 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t179)) % 0.40/0.62 (step @p65 :rule quant-miniscope-or :args ((= @t177 @t179))) % 0.40/0.62 (step @p66 :rule trans :premises (@p65 @p64)) % 0.40/0.62 (step @p67 :rule symm :premises (@p66)) % 0.40/0.62 (step @p68 :rule cong :premises (@p67) :args ((forall @t72 (or @t167 @t180)))) % 0.40/0.62 (step @p69 :rule trans :premises (@p68 @p61)) % 0.40/0.62 (step @p70 :rule trans :premises (@p69 @p60)) % 0.40/0.62 (step @p71 :rule bool-double-not-elim :args (@t180)) % 0.40/0.62 (step @p72 :rule nary_cong :premises (@p63 @p71) :args ((or @t167 (not @t181)))) % 0.40/0.62 (step @p73 :rule bool-and-de-morgan :args (@t166 @t181 true)) % 0.40/0.62 (step @p74 :rule trans :premises (@p73 @p72)) % 0.40/0.62 (step @p75 :rule cong :premises (@p74) :args (@t183)) % 0.40/0.62 (step @p76 :rule trans :premises (@p75 @p70)) % 0.40/0.62 (step @p77 :rule cong :premises (@p76) :args (@t184)) % 0.40/0.62 (step @p78 :rule exists-elim :args ((= (exists @t72 @t182) @t184))) % 0.40/0.62 (step @p79 :rule trans :premises (@p78 @p77)) % 0.40/0.62 (step @p80 :rule bool-and-de-morgan :args (@t103 @t102 true)) % 0.40/0.62 (step @p81 :rule cong :premises (@p80) :args (@t185)) % 0.40/0.62 (step @p82 :rule cong 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(@p548)) % 0.40/0.62 (step @p550 :rule trans :premises (@p549 @p541 @p384)) % 0.40/0.62 (step @p551 false :rule eq_resolve :premises (@p550 @p14)) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------