%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM535+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 08:39:45 AM UTC 2026 % Result : Theorem 0.44s 0.69s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM535+1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n029.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 11:28:32 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.69 % SZS status Theorem % 0.44/0.69 % SZS output start Proof % 0.44/0.69 ( % 0.44/0.69 (declare-sort $$unsorted 0) % 0.44/0.69 (declare-const tptp.xx $$unsorted) % 0.44/0.69 (declare-const tptp.xS $$unsorted) % 0.44/0.69 (declare-const tptp.sdtmndt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.69 (declare-const tptp.slcrc0 $$unsorted) % 0.44/0.69 (declare-const tptp.isCountable0 (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.isFinite0 (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.aSubsetOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.44/0.69 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.44/0.69 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.69 (define @t2 () (tptp.aSet0 @t1)) % 0.44/0.69 (define @t3 () (@list @t1)) % 0.44/0.69 (define @t4 () (@var "W1" $$unsorted)) % 0.44/0.69 (define @t5 () (tptp.aElement0 @t4)) % 0.44/0.69 (define @t6 () (tptp.aElementOf0 @t4 @t1)) % 0.44/0.69 (define @t7 () (@list @t4)) % 0.44/0.69 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.44/0.69 (define @t9 () (=> @t2 @t8)) % 0.44/0.69 (define @t10 () (forall @t3 @t9)) % 0.44/0.69 (define @t11 () (tptp.isFinite0 @t1)) % 0.44/0.69 (define @t12 () (exists @t7 @t6)) % 0.44/0.69 (define @t13 () (not @t12)) % 0.44/0.69 (define @t14 () (and @t2 @t13)) % 0.44/0.69 (define @t15 () (= @t1 tptp.slcrc0)) % 0.44/0.69 (define @t16 () (= @t15 @t14)) % 0.44/0.69 (define @t17 () (forall @t3 @t16)) % 0.44/0.69 (define @t18 () (tptp.isCountable0 @t1)) % 0.44/0.69 (define @t19 () (and @t2 @t18)) % 0.44/0.69 (define @t20 () (@var "W2" $$unsorted)) % 0.44/0.69 (define @t21 () (tptp.aElementOf0 @t20 @t1)) % 0.44/0.69 (define @t22 () (tptp.aElementOf0 @t20 @t4)) % 0.44/0.69 (define @t23 () (@list @t20)) % 0.44/0.69 (define @t24 () (forall @t23 (=> @t22 @t21))) % 0.44/0.69 (define @t25 () (tptp.aSet0 @t4)) % 0.44/0.69 (define @t26 () (and @t25 @t24)) % 0.44/0.69 (define @t27 () (tptp.aSubsetOf0 @t4 @t1)) % 0.44/0.69 (define @t28 () (= @t27 @t26)) % 0.44/0.69 (define @t29 () (forall @t7 @t28)) % 0.44/0.69 (define @t30 () (=> @t2 @t29)) % 0.44/0.69 (define @t31 () (forall @t3 @t30)) % 0.44/0.69 (define @t32 () (tptp.aSubsetOf0 @t1 @t4)) % 0.44/0.69 (define @t33 () (@list @t1 @t4)) % 0.44/0.69 (define @t34 () (tptp.aSet0 @t20)) % 0.44/0.69 (define @t35 () (@var "W3" $$unsorted)) % 0.44/0.69 (define @t36 () (= @t35 @t4)) % 0.44/0.69 (define @t37 () (tptp.aElementOf0 @t35 @t1)) % 0.44/0.69 (define @t38 () (or @t37 @t36)) % 0.44/0.69 (define @t39 () (tptp.aElement0 @t35)) % 0.44/0.69 (define @t40 () (and @t39 @t38)) % 0.44/0.69 (define @t41 () (tptp.aElementOf0 @t35 @t20)) % 0.44/0.69 (define @t42 () (= @t41 @t40)) % 0.44/0.69 (define @t43 () (@list @t35)) % 0.44/0.69 (define @t44 () (forall @t43 @t42)) % 0.44/0.69 (define @t45 () (and @t34 @t44)) % 0.44/0.69 (define @t46 () (tptp.sdtpldt0 @t1 @t4)) % 0.44/0.69 (define @t47 () (= @t20 @t46)) % 0.44/0.69 (define @t48 () (= @t47 @t45)) % 0.44/0.69 (define @t49 () (forall @t23 @t48)) % 0.44/0.69 (define @t50 () (and @t2 @t5)) % 0.44/0.69 (define @t51 () (=> @t50 @t49)) % 0.44/0.69 (define @t52 () (forall @t33 @t51)) % 0.44/0.69 (define @t53 () (not @t36)) % 0.44/0.69 (define @t54 () (and @t39 @t37 @t53)) % 0.44/0.69 (define @t55 () (= @t41 @t54)) % 0.44/0.69 (define @t56 () (forall @t43 @t55)) % 0.44/0.69 (define @t57 () (and @t34 @t56)) % 0.44/0.69 (define @t58 () (tptp.sdtmndt0 @t1 @t4)) % 0.44/0.69 (define @t59 () (= @t20 @t58)) % 0.44/0.69 (define @t60 () (= @t59 @t57)) % 0.44/0.69 (define @t61 () (forall @t23 @t60)) % 0.44/0.69 (define @t62 () (=> @t50 @t61)) % 0.44/0.69 (define @t63 () (forall @t33 @t62)) % 0.44/0.69 (define @t64 () (tptp.aSet0 tptp.xS)) % 0.44/0.69 (define @t65 () (tptp.aElementOf0 tptp.xx tptp.xS)) % 0.44/0.69 (define @t66 () (tptp.sdtmndt0 tptp.xS tptp.xx)) % 0.44/0.69 (define @t67 () (tptp.sdtpldt0 @t66 tptp.xx)) % 0.44/0.69 (define @t68 () (tptp.aSubsetOf0 @t67 tptp.xS)) % 0.44/0.69 (define @t69 () (tptp.aSubsetOf0 tptp.xS @t67)) % 0.44/0.69 (define @t70 () (forall @t7 (not (tptp.aElementOf0 @t4 tptp.xS)))) % 0.44/0.69 (define @t71 () (@list tptp.xx)) % 0.44/0.69 (define @t72 () (not @t65)) % 0.44/0.69 (define @t73 () (not @t70)) % 0.44/0.69 (define @t74 () (@list false)) % 0.44/0.69 (define @t75 () (@quantifiers_skolemize @t70 0)) % 0.44/0.69 (define @t76 () (tptp.aElementOf0 @t75 tptp.xS)) % 0.44/0.69 (define @t77 () (not @t76)) % 0.44/0.69 (define @t78 () (not @t77)) % 0.44/0.69 (define @t79 () (@list true)) % 0.44/0.69 (define @t80 () (@var "BOUND_VARIABLE_7699" $$unsorted)) % 0.44/0.69 (define @t81 () (tptp.aElementOf0 @t35 @t80)) % 0.44/0.69 (define @t82 () (= @t4 @t35)) % 0.44/0.69 (define @t83 () (and @t39 @t37 (not @t82))) % 0.44/0.69 (define @t84 () (forall @t43 (= @t81 @t83))) % 0.44/0.69 (define @t85 () (tptp.aSet0 @t80)) % 0.44/0.69 (define @t86 () (and @t85 @t84)) % 0.44/0.69 (define @t87 () (= (= @t80 @t58) @t86)) % 0.44/0.69 (define @t88 () (not @t5)) % 0.44/0.69 (define @t89 () (not @t2)) % 0.44/0.69 (define @t90 () (or @t89 @t88 @t87)) % 0.44/0.69 (define @t91 () (@list @t1 @t4 @t80)) % 0.44/0.69 (define @t92 () (forall @t91 @t90)) % 0.44/0.69 (define @t93 () (@list @t80)) % 0.44/0.69 (define @t94 () (forall @t93 @t90)) % 0.44/0.69 (define @t95 () (forall @t93 @t87)) % 0.44/0.69 (define @t96 () (@list @t20)) % 0.44/0.69 (define @t97 () (or @t89 @t88 @t95)) % 0.44/0.69 (define @t98 () (forall @t23 (= @t59 (and @t34 (forall @t43 (= @t41 @t83)))))) % 0.44/0.69 (define @t99 () (or @t89 @t88 @t98)) % 0.44/0.69 (define @t100 () (or @t89 @t88)) % 0.44/0.69 (define @t101 () (not @t50)) % 0.44/0.69 (define @t102 () (tptp.aElementOf0 @t35 @t66)) % 0.44/0.69 (define @t103 () (= @t35 tptp.xx)) % 0.44/0.69 (define @t104 () (tptp.aElementOf0 @t35 tptp.xS)) % 0.44/0.69 (define @t105 () (forall @t43 (= (and @t39 @t104 (not @t103)) @t102))) % 0.44/0.69 (define @t106 () (tptp.aSet0 @t66)) % 0.44/0.69 (define @t107 () (and @t106 @t105)) % 0.44/0.69 (define @t108 () (= tptp.xx @t35)) % 0.44/0.69 (define @t109 () (not @t108)) % 0.44/0.69 (define @t110 () (and @t39 @t104 @t109)) % 0.44/0.69 (define @t111 () (= @t110 @t102)) % 0.44/0.69 (define @t112 () (forall @t43 @t111)) % 0.44/0.69 (define @t113 () (and @t106 @t112)) % 0.44/0.69 (define @t114 () (= (= @t66 @t66) @t113)) % 0.44/0.69 (define @t115 () (tptp.aElement0 tptp.xx)) % 0.44/0.69 (define @t116 () (not @t115)) % 0.44/0.69 (define @t117 () (not @t64)) % 0.44/0.69 (define @t118 () (or @t117 @t116 @t114)) % 0.44/0.69 (define @t119 () (forall @t91 (or @t89 @t88 (= (= @t58 @t80) (and @t85 (forall @t43 (= @t83 @t81))))))) % 0.44/0.69 (define @t120 () (or @t117 @t116 @t107)) % 0.44/0.69 (define @t121 () (@var "BOUND_VARIABLE_7546" $$unsorted)) % 0.44/0.69 (define @t122 () (tptp.aElement0 @t121)) % 0.44/0.69 (define @t123 () (not (tptp.aElementOf0 @t121 @t1))) % 0.44/0.69 (define @t124 () (or @t123 @t122)) % 0.44/0.69 (define @t125 () (or @t89 @t124)) % 0.44/0.69 (define @t126 () (forall (@list @t1 @t121) @t125)) % 0.44/0.69 (define @t127 () (@list @t121)) % 0.44/0.69 (define @t128 () (forall @t127 @t125)) % 0.44/0.69 (define @t129 () (forall @t127 @t124)) % 0.44/0.69 (define @t130 () (@list @t4)) % 0.44/0.69 (define @t131 () (or @t89 @t129)) % 0.44/0.69 (define @t132 () (not @t6)) % 0.44/0.69 (define @t133 () (forall @t7 (or @t132 @t5))) % 0.44/0.69 (define @t134 () (or @t117 @t72 @t115)) % 0.44/0.69 (define @t135 () (@list false false false)) % 0.44/0.69 (define @t136 () (not @t107)) % 0.44/0.69 (define @t137 () (@list @t107)) % 0.44/0.69 (define @t138 () (and @t39 (or @t104 (= @t35 @t75)))) % 0.44/0.69 (define @t139 () (tptp.aElementOf0 @t35 @t67)) % 0.44/0.69 (define @t140 () (forall @t43 (= @t139 @t138))) % 0.44/0.69 (define @t141 () (@quantifiers_skolemize @t140 0)) % 0.44/0.69 (define @t142 () (= tptp.xx @t141)) % 0.44/0.69 (define @t143 () (not @t142)) % 0.44/0.69 (define @t144 () (tptp.aElementOf0 @t141 tptp.xS)) % 0.44/0.69 (define @t145 () (tptp.aElement0 @t141)) % 0.44/0.69 (define @t146 () (and @t145 @t144 @t143)) % 0.44/0.69 (define @t147 () (tptp.aElementOf0 @t141 @t66)) % 0.44/0.69 (define @t148 () (= @t141 tptp.xx)) % 0.44/0.69 (define @t149 () (not @t148)) % 0.44/0.69 (define @t150 () (and @t145 @t144 @t149)) % 0.44/0.69 (define @t151 () (= @t150 @t147)) % 0.44/0.69 (define @t152 () (@list @t141)) % 0.44/0.69 (define @t153 () (= @t147 @t146)) % 0.44/0.69 (define @t154 () (@list @t105)) % 0.44/0.69 (define @t155 () (@var "BOUND_VARIABLE_7668" $$unsorted)) % 0.44/0.69 (define @t156 () (tptp.aElementOf0 @t35 @t155)) % 0.44/0.69 (define @t157 () (and @t39 (or @t37 @t82))) % 0.44/0.69 (define @t158 () (forall @t43 (= @t156 @t157))) % 0.44/0.69 (define @t159 () (tptp.aSet0 @t155)) % 0.44/0.69 (define @t160 () (and @t159 @t158)) % 0.44/0.69 (define @t161 () (= (= @t155 @t46) @t160)) % 0.44/0.69 (define @t162 () (or @t89 @t88 @t161)) % 0.44/0.69 (define @t163 () (@list @t1 @t4 @t155)) % 0.44/0.69 (define @t164 () (forall @t163 @t162)) % 0.44/0.69 (define @t165 () (@list @t155)) % 0.44/0.69 (define @t166 () (forall @t165 @t162)) % 0.44/0.69 (define @t167 () (forall @t165 @t161)) % 0.44/0.69 (define @t168 () (or @t89 @t88 @t167)) % 0.44/0.69 (define @t169 () (forall @t23 (= @t47 (and @t34 (forall @t43 (= @t41 @t157)))))) % 0.44/0.69 (define @t170 () (or @t89 @t88 @t169)) % 0.44/0.69 (define @t171 () (forall @t43 (= @t139 (and @t39 (or @t102 @t103))))) % 0.44/0.69 (define @t172 () (tptp.aSet0 @t67)) % 0.44/0.69 (define @t173 () (and @t172 @t171)) % 0.44/0.69 (define @t174 () (or @t102 @t108)) % 0.44/0.69 (define @t175 () (and @t39 @t174)) % 0.44/0.69 (define @t176 () (forall @t43 (= @t175 @t139))) % 0.44/0.69 (define @t177 () (and @t172 @t176)) % 0.44/0.69 (define @t178 () (= (= @t67 @t67) @t177)) % 0.44/0.69 (define @t179 () (not @t106)) % 0.44/0.69 (define @t180 () (or @t179 @t116 @t178)) % 0.44/0.69 (define @t181 () (forall @t163 (or @t89 @t88 (= (= @t46 @t155) (and @t159 (forall @t43 (= @t157 @t156))))))) % 0.44/0.69 (define @t182 () (or @t179 @t116 @t173)) % 0.44/0.69 (define @t183 () (@list @t181)) % 0.44/0.69 (define @t184 () (not @t173)) % 0.44/0.69 (define @t185 () (@list @t173)) % 0.44/0.69 (define @t186 () (or @t147 @t148)) % 0.44/0.69 (define @t187 () (and @t145 @t186)) % 0.44/0.69 (define @t188 () (tptp.aElementOf0 @t141 @t67)) % 0.44/0.69 (define @t189 () (= @t188 @t187)) % 0.44/0.69 (define @t190 () (or @t147 @t142)) % 0.44/0.69 (define @t191 () (and @t145 @t190)) % 0.44/0.69 (define @t192 () (= @t188 @t191)) % 0.44/0.69 (define @t193 () (@list @t171)) % 0.44/0.69 (define @t194 () (or @t104 (= @t75 @t35))) % 0.44/0.69 (define @t195 () (and @t39 @t194)) % 0.44/0.69 (define @t196 () (forall @t43 (= @t195 @t139))) % 0.44/0.69 (define @t197 () (and @t172 @t196)) % 0.44/0.69 (define @t198 () (tptp.sdtpldt0 tptp.xS @t75)) % 0.44/0.69 (define @t199 () (= (= @t198 @t67) @t197)) % 0.44/0.69 (define @t200 () (tptp.aElement0 @t75)) % 0.44/0.69 (define @t201 () (not @t200)) % 0.44/0.69 (define @t202 () (or @t117 @t201 @t199)) % 0.44/0.69 (define @t203 () (and @t172 @t140)) % 0.44/0.69 (define @t204 () (= @t67 @t198)) % 0.44/0.69 (define @t205 () (= @t204 @t203)) % 0.44/0.69 (define @t206 () (or @t117 @t201 @t205)) % 0.44/0.69 (define @t207 () (or @t117 @t77 @t200)) % 0.44/0.69 (define @t208 () (@var "BOUND_VARIABLE_7595" $$unsorted)) % 0.44/0.69 (define @t209 () (= (tptp.aSubsetOf0 @t208 @t1) (and (tptp.aSet0 @t208) (forall @t23 (or (not (tptp.aElementOf0 @t20 @t208)) @t21))))) % 0.44/0.69 (define @t210 () (or @t89 @t209)) % 0.44/0.69 (define @t211 () (@list @t208)) % 0.44/0.69 (define @t212 () (forall @t211 @t210)) % 0.44/0.69 (define @t213 () (forall @t211 @t209)) % 0.44/0.69 (define @t214 () (or @t89 @t213)) % 0.44/0.69 (define @t215 () (forall @t7 (= @t27 (and @t25 (forall @t23 (or (not @t22) @t21)))))) % 0.44/0.69 (define @t216 () (tptp.aElementOf0 @t20 @t67)) % 0.44/0.69 (define @t217 () (tptp.aElementOf0 @t20 tptp.xS)) % 0.44/0.69 (define @t218 () (forall @t23 (or (not @t217) @t216))) % 0.44/0.69 (define @t219 () (and @t64 @t218)) % 0.44/0.69 (define @t220 () (= @t69 @t219)) % 0.44/0.69 (define @t221 () (not @t172)) % 0.44/0.69 (define @t222 () (or @t221 @t220)) % 0.44/0.69 (define @t223 () (@list false false)) % 0.44/0.69 (define @t224 () (forall @t23 (or (not @t216) @t217))) % 0.44/0.69 (define @t225 () (and @t172 @t224)) % 0.44/0.69 (define @t226 () (= @t68 @t225)) % 0.44/0.69 (define @t227 () (or @t117 @t226)) % 0.44/0.69 (define @t228 () (@quantifiers_skolemize @t224 0)) % 0.44/0.69 (define @t229 () (tptp.aElementOf0 @t228 @t67)) % 0.44/0.69 (define @t230 () (tptp.aElementOf0 @t228 tptp.xS)) % 0.44/0.69 (define @t231 () (not @t229)) % 0.44/0.69 (define @t232 () (or @t231 @t230)) % 0.44/0.69 (define @t233 () (tptp.aElement0 @t228)) % 0.44/0.69 (define @t234 () (or @t221 @t231 @t233)) % 0.44/0.69 (define @t235 () (tptp.aElementOf0 @t228 @t66)) % 0.44/0.69 (define @t236 () (= @t228 tptp.xx)) % 0.44/0.69 (define @t237 () (or @t235 @t236)) % 0.44/0.69 (define @t238 () (and @t233 @t237)) % 0.44/0.69 (define @t239 () (= @t229 @t238)) % 0.44/0.69 (define @t240 () (@list @t228)) % 0.44/0.69 (define @t241 () (= tptp.xx @t228)) % 0.44/0.69 (define @t242 () (or @t235 @t241)) % 0.44/0.69 (define @t243 () (and @t233 @t242)) % 0.44/0.69 (define @t244 () (= @t229 @t243)) % 0.44/0.69 (define @t245 () (forall @t7 @t132)) % 0.44/0.69 (define @t246 () (forall @t7 (not (tptp.aElementOf0 @t4 tptp.slcrc0)))) % 0.44/0.69 (define @t247 () (and (tptp.aSet0 tptp.slcrc0) @t246)) % 0.44/0.69 (define @t248 () (= (= tptp.slcrc0 tptp.slcrc0) @t247)) % 0.44/0.69 (define @t249 () (forall @t3 (= @t15 (and @t2 @t245)))) % 0.44/0.69 (define @t250 () (tptp.aElementOf0 tptp.xx tptp.slcrc0)) % 0.44/0.69 (define @t251 () (= @t115 @t250)) % 0.44/0.69 (define @t252 () (not @t251)) % 0.44/0.69 (define @t253 () (@list false true)) % 0.44/0.69 (define @t254 () (or @t250 (= tptp.xx tptp.xx))) % 0.44/0.69 (define @t255 () (and @t115 @t254)) % 0.44/0.69 (define @t256 () (= @t250 @t255)) % 0.44/0.69 (define @t257 () (tptp.aElementOf0 @t35 tptp.slcrc0)) % 0.44/0.69 (define @t258 () (forall @t43 (= @t257 (and @t39 (or @t257 @t103))))) % 0.44/0.69 (define @t259 () (not @t258)) % 0.44/0.69 (define @t260 () (@quantifiers_skolemize @t258 0)) % 0.44/0.69 (define @t261 () (= tptp.xx @t260)) % 0.44/0.69 (define @t262 () (tptp.aElementOf0 @t260 tptp.slcrc0)) % 0.44/0.69 (define @t263 () (or @t262 @t261)) % 0.44/0.69 (define @t264 () (tptp.aElement0 @t260)) % 0.44/0.69 (define @t265 () (and @t264 @t263)) % 0.44/0.69 (define @t266 () (= @t262 @t265)) % 0.44/0.69 (define @t267 () (not @t266)) % 0.44/0.69 (define @t268 () (or @t262 (= @t260 tptp.xx))) % 0.44/0.69 (define @t269 () (and @t264 @t268)) % 0.44/0.69 (define @t270 () (= @t262 @t269)) % 0.44/0.69 (define @t271 () (not @t270)) % 0.44/0.69 (define @t272 () (@list true false)) % 0.44/0.69 (define @t273 () (tptp.aElementOf0 @t260 tptp.xS)) % 0.44/0.69 (define @t274 () (and @t65 @t261)) % 0.44/0.69 (define @t275 () (forall @t43 (= @t104 (and @t39 (or @t104 @t103))))) % 0.44/0.69 (define @t276 () (@quantifiers_skolemize @t275 0)) % 0.44/0.69 (define @t277 () (= tptp.xx @t276)) % 0.44/0.69 (define @t278 () (tptp.aElementOf0 @t276 tptp.xS)) % 0.44/0.69 (define @t279 () (or @t278 @t277)) % 0.44/0.69 (define @t280 () (tptp.aElement0 @t276)) % 0.44/0.69 (define @t281 () (and @t280 @t279)) % 0.44/0.69 (define @t282 () (= @t278 @t281)) % 0.44/0.69 (define @t283 () (not @t278)) % 0.44/0.69 (define @t284 () (or @t117 @t283 @t280)) % 0.44/0.69 (define @t285 () (@list false false false false false)) % 0.44/0.69 (define @t286 () (not @t277)) % 0.44/0.69 (define @t287 () (not @t273)) % 0.44/0.69 (define @t288 () (not @t261)) % 0.44/0.69 (define @t289 () (= false true)) % 0.44/0.69 (define @t290 () (and @t273 @t261 @t277 @t283)) % 0.44/0.69 (define @t291 () (not @t282)) % 0.44/0.69 (define @t292 () (not @t275)) % 0.44/0.69 (define @t293 () (or @t278 (= @t276 tptp.xx))) % 0.44/0.69 (define @t294 () (and @t280 @t293)) % 0.44/0.69 (define @t295 () (= @t278 @t294)) % 0.44/0.69 (define @t296 () (not @t295)) % 0.44/0.69 (define @t297 () (or @t230 @t236)) % 0.44/0.69 (define @t298 () (and @t233 @t297)) % 0.44/0.69 (define @t299 () (= @t230 @t298)) % 0.44/0.69 (define @t300 () (or @t230 @t241)) % 0.44/0.69 (define @t301 () (and @t233 @t300)) % 0.44/0.69 (define @t302 () (= @t230 @t301)) % 0.44/0.69 (define @t303 () (and @t233 @t230 (not @t241))) % 0.44/0.69 (define @t304 () (not @t236)) % 0.44/0.69 (define @t305 () (and @t233 @t230 @t304)) % 0.44/0.69 (define @t306 () (= @t305 @t235)) % 0.44/0.69 (define @t307 () (= @t235 @t303)) % 0.44/0.69 (define @t308 () (not @t232)) % 0.44/0.69 (define @t309 () (not @t224)) % 0.44/0.69 (define @t310 () (not @t219)) % 0.44/0.69 (define @t311 () (not @t218)) % 0.44/0.69 (define @t312 () (@quantifiers_skolemize @t218 0)) % 0.44/0.69 (define @t313 () (tptp.aElementOf0 @t312 @t67)) % 0.44/0.69 (define @t314 () (tptp.aElementOf0 @t312 tptp.xS)) % 0.44/0.69 (define @t315 () (not @t314)) % 0.44/0.69 (define @t316 () (or @t315 @t313)) % 0.44/0.69 (define @t317 () (not @t316)) % 0.44/0.69 (define @t318 () (not @t313)) % 0.44/0.69 (define @t319 () (@list @t316)) % 0.44/0.69 (define @t320 () (forall @t43 (= @t195 @t104))) % 0.44/0.69 (define @t321 () (and @t64 @t320)) % 0.44/0.69 (define @t322 () (= (= @t198 tptp.xS) @t321)) % 0.44/0.69 (define @t323 () (or @t117 @t201 @t322)) % 0.44/0.69 (define @t324 () (forall @t43 (= @t104 @t138))) % 0.44/0.69 (define @t325 () (and @t64 @t324)) % 0.44/0.69 (define @t326 () (= tptp.xS @t198)) % 0.44/0.69 (define @t327 () (= @t326 @t325)) % 0.44/0.69 (define @t328 () (or @t117 @t201 @t327)) % 0.44/0.69 (define @t329 () (@quantifiers_skolemize @t324 0)) % 0.44/0.69 (define @t330 () (= @t75 @t329)) % 0.44/0.69 (define @t331 () (tptp.aElementOf0 @t329 tptp.xS)) % 0.44/0.69 (define @t332 () (or @t331 @t330)) % 0.44/0.69 (define @t333 () (tptp.aElement0 @t329)) % 0.44/0.69 (define @t334 () (and @t333 @t332)) % 0.44/0.69 (define @t335 () (= @t331 @t334)) % 0.44/0.69 (define @t336 () (not @t331)) % 0.44/0.69 (define @t337 () (or @t117 @t336 @t333)) % 0.44/0.69 (define @t338 () (not @t330)) % 0.44/0.69 (define @t339 () (not @t335)) % 0.44/0.69 (define @t340 () (not @t324)) % 0.44/0.69 (define @t341 () (or @t331 (= @t329 @t75))) % 0.44/0.69 (define @t342 () (and @t333 @t341)) % 0.44/0.69 (define @t343 () (= @t331 @t342)) % 0.44/0.69 (define @t344 () (not @t343)) % 0.44/0.69 (define @t345 () (not @t204)) % 0.44/0.69 (define @t346 () (not @t326)) % 0.44/0.69 (define @t347 () (and @t314 @t326 @t204 @t318)) % 0.44/0.69 (define @t348 () (not @t203)) % 0.44/0.69 (define @t349 () (not @t140)) % 0.44/0.69 (define @t350 () (= @t75 @t141)) % 0.44/0.69 (define @t351 () (or @t144 @t350)) % 0.44/0.69 (define @t352 () (and @t145 @t351)) % 0.44/0.69 (define @t353 () (= @t188 @t352)) % 0.44/0.69 (define @t354 () (not @t353)) % 0.44/0.69 (define @t355 () (or @t144 (= @t141 @t75))) % 0.44/0.69 (define @t356 () (and @t145 @t355)) % 0.44/0.69 (define @t357 () (= @t188 @t356)) % 0.44/0.69 (define @t358 () (not @t357)) % 0.44/0.69 (define @t359 () (not @t188)) % 0.44/0.69 (define @t360 () (or @t221 @t359 @t145)) % 0.44/0.69 (define @t361 () (not @t192)) % 0.44/0.69 (define @t362 () (not @t191)) % 0.44/0.69 (define @t363 () (not @t146)) % 0.44/0.69 (define @t364 () (not @t153)) % 0.44/0.69 (define @t365 () (not @t147)) % 0.44/0.69 (define @t366 () (not @t190)) % 0.44/0.69 (define @t367 () (not @t144)) % 0.44/0.69 (define @t368 () (not @t367)) % 0.44/0.69 (define @t369 () (and @t65 @t142 @t367)) % 0.44/0.69 (define @t370 () (not @t352)) % 0.44/0.69 (define @t371 () (@list @t352)) % 0.44/0.69 (define @t372 () (not @t145)) % 0.44/0.69 (define @t373 () (@list @t190)) % 0.44/0.69 (define @t374 () (not @t350)) % 0.44/0.69 (define @t375 () (and @t367 @t350 @t76)) % 0.44/0.69 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.69 (assume @p2 (forall @t3 (=> (tptp.aElement0 @t1) true))) % 0.44/0.69 (assume @p3 @t10) % 0.44/0.69 (assume @p4 (forall @t3 (=> @t2 (=> @t11 true)))) % 0.44/0.69 (assume @p5 @t17) % 0.44/0.69 (assume @p6 (tptp.isFinite0 tptp.slcrc0)) % 0.44/0.69 (assume @p7 (forall @t3 (=> @t2 (=> @t18 true)))) % 0.44/0.69 (assume @p8 (forall @t3 (=> @t19 (not @t11)))) % 0.44/0.69 (assume @p9 (forall @t3 (=> @t19 (not @t15)))) % 0.44/0.69 (assume @p10 @t31) % 0.44/0.69 (assume @p11 (forall @t3 (=> (and @t2 @t11) (forall @t7 (=> @t27 (tptp.isFinite0 @t4)))))) % 0.44/0.69 (assume @p12 (forall @t3 (=> @t2 (tptp.aSubsetOf0 @t1 @t1)))) % 0.44/0.69 (assume @p13 (forall @t33 (=> (and @t2 @t25) (=> (and @t32 @t27) (= @t1 @t4))))) % 0.44/0.69 (assume @p14 (forall (@list @t1 @t4 @t20) (=> (and @t2 @t25 @t34) (=> (and @t32 (tptp.aSubsetOf0 @t4 @t20)) (tptp.aSubsetOf0 @t1 @t20))))) % 0.44/0.69 (assume @p15 @t52) % 0.44/0.69 (assume @p16 @t63) % 0.44/0.69 (assume @p17 @t64) % 0.44/0.69 (assume @p18 @t65) % 0.44/0.69 (assume @p19 (not (and @t69 @t68))) % 0.44/0.69 (assume @p20 true) % 0.44/0.69 (assume-push @p854 @t70) % 0.44/0.69 (step @p22 :rule instantiate :premises (@p854) :args (@t71)) % 0.44/0.69 (step-pop @p855 :rule scope :premises (@p22)) % 0.44/0.69 (step @p23 :rule process_scope :premises (@p855) :args (@t72)) % 0.44/0.69 (step @p25 :rule implies_elim :premises (@p23)) % 0.44/0.69 (step @p26 :rule reordering :premises (@p25) :args ((or @t72 @t73))) % 0.44/0.69 (step @p27 :rule chain_m_resolution :premises (@p26 @p18) :args (@t73 @t74 (@list @t65))) % 0.44/0.69 (step @p28 :rule refl :args (@t76)) % 0.44/0.69 (step @p29 :rule bool-double-not-elim :args (@t70)) % 0.44/0.69 (step @p30 :rule nary_cong :premises (@p29 @p28) :args ((or (not @t73) @t76))) % 0.44/0.69 (step @p31 :rule bool-double-not-elim :args (@t76)) % 0.44/0.69 (step @p32 :rule refl :args (@t73)) % 0.44/0.69 (step @p33 :rule cong :premises (@p32 @p31) :args ((=> @t73 @t78))) % 0.44/0.69 (assume-push @p856 @t73) % 0.44/0.69 (step @p35 :rule skolemize :premises (@p856)) % 0.44/0.69 (step-pop @p857 :rule scope :premises (@p35)) % 0.44/0.69 (step @p36 :rule process_scope :premises (@p857) :args (@t78)) % 0.44/0.69 (step @p38 :rule eq_resolve :premises (@p36 @p33)) % 0.44/0.69 (step @p39 :rule implies_elim :premises (@p38)) % 0.44/0.69 (step @p40 :rule eq_resolve :premises (@p39 @p30)) % 0.44/0.69 (step @p41 :rule chain_m_resolution :premises (@p40 @p27) :args (@t76 @t79 (@list @t70))) % 0.44/0.69 (step @p42 :rule eq-symm :args (@t81 @t83)) % 0.44/0.69 (step @p43 :rule cong :premises (@p42) :args (@t84)) % 0.44/0.69 (step @p44 :rule refl :args (@t85)) % 0.44/0.69 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t86)) % 0.44/0.69 (step @p46 :rule eq-symm :args (@t80 @t58)) % 0.44/0.69 (step @p47 :rule cong :premises (@p46 @p45) :args (@t87)) % 0.44/0.69 (step @p48 :rule refl :args (@t88)) % 0.44/0.69 (step @p49 :rule refl :args (@t89)) % 0.44/0.69 (step @p50 :rule nary_cong :premises (@p49 @p48 @p47) :args (@t90)) % 0.44/0.69 (step @p51 :rule cong :premises (@p50) :args (@t92)) % 0.44/0.69 (step @p52 :rule quant-merge-prenex :args ((= (forall @t33 @t94) @t92))) % 0.44/0.69 (step @p53 :rule alpha_equiv :args (@t95 (@list @t80) @t96)) % 0.44/0.69 (step @p54 :rule refl :args (@t88)) % 0.44/0.69 (step @p55 :rule refl :args (@t89)) % 0.44/0.69 (step @p56 :rule nary_cong :premises (@p55 @p54 @p53) :args (@t97)) % 0.44/0.69 (step @p57 :rule quant-miniscope-or :args ((= @t94 @t97))) % 0.44/0.69 (step @p58 :rule trans :premises (@p57 @p56)) % 0.44/0.69 (step @p59 :rule symm :premises (@p58)) % 0.44/0.69 (step @p60 :rule cong :premises (@p59) :args ((forall @t33 @t99))) % 0.44/0.69 (step @p61 :rule trans :premises (@p60 @p52)) % 0.44/0.69 (step @p62 :rule trans :premises (@p61 @p51)) % 0.44/0.69 (step @p63 :rule aci_norm :args ((= (or @t100 @t98) @t99))) % 0.44/0.69 (step @p64 :rule refl :args (@t98)) % 0.44/0.69 (step @p65 :rule bool-and-de-morgan :args (@t2 @t5 true)) % 0.44/0.69 (step @p66 :rule nary_cong :premises (@p65 @p64) :args ((or @t101 @t98))) % 0.44/0.69 (step @p67 :rule trans :premises (@p66 @p63)) % 0.44/0.69 (step @p68 :rule bool-impl-elim :args (@t50 @t98)) % 0.44/0.69 (step @p69 :rule trans :premises (@p68 @p67)) % 0.44/0.69 (step @p70 :rule cong :premises (@p69) :args ((forall @t33 (=> @t50 @t98)))) % 0.44/0.69 (step @p71 :rule trans :premises (@p70 @p62)) % 0.44/0.69 (step @p72 :rule eq-symm :args (@t35 @t4)) % 0.44/0.69 (step @p73 :rule cong :premises (@p72) :args (@t53)) % 0.44/0.69 (step @p74 :rule refl :args (@t37)) % 0.44/0.69 (step @p75 :rule refl :args (@t39)) % 0.44/0.69 (step @p76 :rule nary_cong :premises (@p75 @p74 @p73) :args (@t54)) % 0.44/0.69 (step @p77 :rule refl :args (@t41)) % 0.44/0.69 (step @p78 :rule cong :premises (@p77 @p76) :args (@t55)) % 0.44/0.69 (step @p79 :rule cong :premises (@p78) :args (@t56)) % 0.44/0.69 (step @p80 :rule refl :args (@t34)) % 0.44/0.69 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t57)) % 0.44/0.69 (step @p82 :rule refl :args (@t59)) % 0.44/0.69 (step @p83 :rule cong :premises (@p82 @p81) :args (@t60)) % 0.44/0.69 (step @p84 :rule cong :premises (@p83) :args (@t61)) % 0.44/0.69 (step @p85 :rule refl :args (@t50)) % 0.44/0.69 (step @p86 :rule cong :premises (@p85 @p84) :args (@t62)) % 0.44/0.69 (step @p87 :rule cong :premises (@p86) :args (@t63)) % 0.44/0.69 (step @p88 :rule trans :premises (@p87 @p71)) % 0.44/0.69 (step @p89 :rule eq_resolve :premises (@p16 @p88)) % 0.44/0.69 (step @p90 :rule bool-eq-true :args (@t107)) % 0.44/0.69 (step @p91 :rule eq-symm :args (true @t107)) % 0.44/0.69 (step @p92 :rule trans :premises (@p91 @p90)) % 0.44/0.69 (step @p93 :rule refl :args (@t102)) % 0.44/0.69 (step @p94 :rule eq-symm :args (tptp.xx @t35)) % 0.44/0.69 (step @p95 :rule cong :premises (@p94) :args (@t109)) % 0.44/0.69 (step @p96 :rule refl :args (@t104)) % 0.44/0.69 (step @p97 :rule nary_cong :premises (@p75 @p96 @p95) :args (@t110)) % 0.44/0.69 (step @p98 :rule cong :premises (@p97 @p93) :args (@t111)) % 0.44/0.69 (step @p99 :rule cong :premises (@p98) :args (@t112)) % 0.44/0.69 (step @p100 :rule refl :args (@t106)) % 0.44/0.69 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t113)) % 0.44/0.69 (step @p102 :rule eq-refl :args (@t66)) % 0.44/0.69 (step @p103 :rule cong :premises (@p102 @p101) :args (@t114)) % 0.44/0.69 (step @p104 :rule trans :premises (@p103 @p92)) % 0.44/0.69 (step @p105 :rule refl :args (@t116)) % 0.44/0.69 (step @p106 :rule refl :args (@t117)) % 0.44/0.69 (step @p107 :rule nary_cong :premises (@p106 @p105 @p104) :args (@t118)) % 0.44/0.69 (step @p108 :rule refl :args (@t119)) % 0.44/0.69 (step @p109 :rule cong :premises (@p108 @p107) :args ((=> @t119 @t118))) % 0.44/0.69 (assume-push @p858 @t119) % 0.44/0.69 (step @p111 :rule instantiate :premises (@p89) :args ((@list tptp.xS tptp.xx @t66))) % 0.44/0.69 (step-pop @p859 :rule scope :premises (@p111)) % 0.44/0.69 (step @p112 :rule process_scope :premises (@p859) :args (@t118)) % 0.44/0.69 (step @p114 :rule eq_resolve :premises (@p112 @p109)) % 0.44/0.69 (step @p115 :rule implies_elim :premises (@p114)) % 0.44/0.69 (step @p116 :rule chain_m_resolution :premises (@p115 @p89) :args (@t120 @t74 (@list @t119))) % 0.44/0.69 (step @p117 :rule aci_norm :args ((= @t125 (or @t89 @t123 @t122)))) % 0.44/0.69 (step @p118 :rule cong :premises (@p117) :args (@t126)) % 0.44/0.69 (step @p119 :rule quant-merge-prenex :args ((= (forall @t3 @t128) @t126))) % 0.44/0.69 (step @p120 :rule alpha_equiv :args (@t129 (@list @t121) @t130)) % 0.44/0.69 (step @p121 :rule nary_cong :premises (@p55 @p120) :args (@t131)) % 0.44/0.69 (step @p122 :rule quant-miniscope-or :args ((= @t128 @t131))) % 0.44/0.69 (step @p123 :rule trans :premises (@p122 @p121)) % 0.44/0.69 (step @p124 :rule symm :premises (@p123)) % 0.44/0.69 (step @p125 :rule cong :premises (@p124) :args ((forall @t3 (or @t89 @t133)))) % 0.44/0.69 (step @p126 :rule trans :premises (@p125 @p119)) % 0.44/0.69 (step @p127 :rule trans :premises (@p126 @p118)) % 0.44/0.69 (step @p128 :rule bool-impl-elim :args (@t2 @t133)) % 0.44/0.69 (step @p129 :rule cong :premises (@p128) :args ((forall @t3 (=> @t2 @t133)))) % 0.44/0.69 (step @p130 :rule trans :premises (@p129 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@t370))) % 0.44/0.69 (step @p820 :rule chain_m_resolution :premises (@p819 @p788) :args (@t351 @t74 @t371)) % 0.44/0.69 (step @p821 :rule cnf_or_pos :args (@t351)) % 0.44/0.69 (step @p822 :rule reordering :premises (@p821) :args ((or @t144 @t350 (not @t351)))) % 0.44/0.69 (step @p823 :rule chain_m_resolution :premises (@p822 @p817 @p820) :args (@t350 @t272 (@list @t144 @t351))) % 0.44/0.69 (step @p824 :rule refl :args (@t374)) % 0.44/0.69 (step @p825 :rule nary_cong :premises (@p633 @p824 @p759) :args ((or @t77 @t374 @t368))) % 0.44/0.69 (assume-push @p950 @t367) % 0.44/0.69 (assume-push @p951 @t350) % 0.44/0.69 (assume-push @p952 @t76) % 0.44/0.69 (step @p829 :rule evaluate :args ((= true false))) % 0.44/0.69 (step @p830 :rule false_intro :premises (@p950)) % 0.44/0.69 (step @p426 :rule refl :args (tptp.xS)) % 0.44/0.69 (step @p831 :rule cong :premises (@p951 @p426) :args (@t76)) % 0.44/0.69 (step @p832 :rule true_intro :premises (@p952)) % 0.44/0.69 (step @p833 :rule symm :premises (@p832)) % 0.44/0.69 (step @p834 :rule trans :premises (@p833 @p831 @p830)) % 0.44/0.69 (step @p835 false :rule eq_resolve :premises (@p834 @p829)) % 0.44/0.69 (step-pop @p953 :rule scope :premises (@p835)) % 0.44/0.69 (step-pop @p954 :rule scope :premises (@p953)) % 0.44/0.69 (step-pop @p955 :rule scope :premises (@p954)) % 0.44/0.69 (step @p836 :rule process_scope :premises (@p955) :args (false)) % 0.44/0.69 (assume-push @p956 @t76) % 0.44/0.69 (assume-push @p957 @t350) % 0.44/0.69 (assume-push @p958 @t367) % 0.44/0.69 (step @p843 :rule and_intro :premises (@p958 @p957 @p956)) % 0.44/0.69 (step-pop @p959 :rule scope :premises (@p843)) % 0.44/0.69 (step-pop @p960 :rule scope :premises (@p959)) % 0.44/0.69 (step-pop @p961 :rule scope :premises (@p960)) % 0.44/0.69 (step @p844 :rule process_scope :premises (@p961) :args (@t375)) % 0.44/0.69 (step @p848 :rule implies_elim :premises (@p844)) % 0.44/0.69 (step @p849 :rule resolution :premises (@p848 @p836) :args (true @t375)) % 0.44/0.69 (step @p850 :rule not_and :premises (@p849)) % 0.44/0.69 (step @p851 :rule eq_resolve :premises (@p850 @p825)) % 0.44/0.69 (step @p852 :rule reordering :premises (@p851) :args ((or @t77 @t144 @t374))) % 0.44/0.69 (step @p853 false :rule chain_m_resolution :premises (@p852 @p823 @p817 @p41) :args (false (@list false true false) (@list @t350 @t144 @t76))) % 0.44/0.69 ) % 0.44/0.69 % SZS output end Proof % 0.44/0.69 % cvc5 exiting %------------------------------------------------------------------------------