%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ITP004^2 : TPTP v9.2.1. Bugfixed v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n015.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 08:24:23 AM UTC 2026 % Result : Theorem 0.46s 0.66s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : ITP004^2 : TPTP v9.2.1. Bugfixed v7.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.33 % Computer : n015.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue Jun 2 03:37:19 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.46/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.66 % SZS status Theorem % 0.46/0.66 % SZS output start Proof % 0.46/0.66 ( % 0.46/0.66 (declare-sort tptp.del 0) % 0.46/0.66 (declare-sort $$unsorted 0) % 0.46/0.66 (declare-const tptp.c_2Ebool_2E_21 (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.c_2Emin_2E_3D (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.c_2Epred__set_2EREST (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.c_2Epred__set_2EDELETE (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.inj__o (-> Bool $$unsorted)) % 0.46/0.66 (declare-const tptp.c_2Ebool_2E_2F_5C $$unsorted) % 0.46/0.66 (declare-const tptp.p (-> $$unsorted Bool)) % 0.46/0.66 (declare-const tptp.bool tptp.del) % 0.46/0.66 (declare-const tptp.c_2Epred__set_2ESUBSET (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.66 (declare-const tptp.arr (-> tptp.del tptp.del tptp.del)) % 0.46/0.66 (declare-const tptp.c_2Emin_2E_3D_3D_3E $$unsorted) % 0.46/0.66 (declare-const tptp.lam (-> tptp.del (-> $$unsorted $$unsorted) $$unsorted)) % 0.46/0.66 (declare-const tptp.c_2Ebool_2E_7E $$unsorted) % 0.46/0.66 (declare-const tptp.c_2Ebool_2EIN (-> tptp.del $$unsorted)) % 0.46/0.66 (declare-const tptp.mem (-> $$unsorted tptp.del Bool)) % 0.46/0.66 (declare-const tptp.c_2Epred__set_2ECHOICE (-> tptp.del $$unsorted)) % 0.46/0.66 (define @t1 () (@var "X" Bool)) % 0.46/0.66 (define @t2 () (_ tptp.inj__o @t1)) % 0.46/0.66 (define @t3 () (@list @t1)) % 0.46/0.66 (define @t4 () (@var "X" $$unsorted)) % 0.46/0.66 (define @t5 () (_ tptp.mem @t4)) % 0.46/0.66 (define @t6 () (@list @t4)) % 0.46/0.66 (define @t7 () (@var "B" tptp.del)) % 0.46/0.66 (define @t8 () (@var "F" $$unsorted)) % 0.46/0.66 (define @t9 () (_ (_ tptp.ap @t8) @t4)) % 0.46/0.66 (define @t10 () (_ (_ tptp.mem @t9) @t7)) % 0.46/0.66 (define @t11 () (@var "A" tptp.del)) % 0.46/0.66 (define @t12 () (_ @t5 @t11)) % 0.46/0.66 (define @t13 () (forall @t6 (=> @t12 @t10))) % 0.46/0.66 (define @t14 () (_ tptp.arr @t11)) % 0.46/0.66 (define @t15 () (_ @t14 @t7)) % 0.46/0.66 (define @t16 () (_ tptp.mem @t8)) % 0.46/0.66 (define @t17 () (_ @t16 @t15)) % 0.46/0.66 (define @t18 () (=> @t17 @t13)) % 0.46/0.66 (define @t19 () (@list @t11 @t7 @t8)) % 0.46/0.66 (define @t20 () (forall @t19 @t18)) % 0.46/0.66 (define @t21 () (@var "F" (-> $$unsorted $$unsorted))) % 0.46/0.66 (define @t22 () (_ (_ tptp.lam @t11) @t21)) % 0.46/0.66 (define @t23 () (_ @t21 @t4)) % 0.46/0.66 (define @t24 () (@var "G" $$unsorted)) % 0.46/0.66 (define @t25 () (_ tptp.arr tptp.bool)) % 0.46/0.66 (define @t26 () (_ @t25 tptp.bool)) % 0.46/0.66 (define @t27 () (_ @t25 @t26)) % 0.46/0.66 (define @t28 () (@var "R" $$unsorted)) % 0.46/0.66 (define @t29 () (_ tptp.p @t28)) % 0.46/0.66 (define @t30 () (@var "Q" $$unsorted)) % 0.46/0.66 (define @t31 () (_ tptp.p @t30)) % 0.46/0.66 (define @t32 () (_ (_ tptp.mem @t28) tptp.bool)) % 0.46/0.66 (define @t33 () (@list @t28)) % 0.46/0.66 (define @t34 () (_ tptp.mem @t30)) % 0.46/0.66 (define @t35 () (_ @t34 tptp.bool)) % 0.46/0.66 (define @t36 () (@list @t30)) % 0.46/0.66 (define @t37 () (@var "A_27a" tptp.del)) % 0.46/0.66 (define @t38 () (_ tptp.arr @t37)) % 0.46/0.66 (define @t39 () (_ @t38 tptp.bool)) % 0.46/0.66 (define @t40 () (_ tptp.arr @t39)) % 0.46/0.66 (define @t41 () (_ @t40 tptp.bool)) % 0.46/0.66 (define @t42 () (_ tptp.c_2Epred__set_2ESUBSET @t37)) % 0.46/0.66 (define @t43 () (@list @t37)) % 0.46/0.66 (define @t44 () (_ tptp.c_2Ebool_2EIN @t37)) % 0.46/0.66 (define @t45 () (_ @t40 @t37)) % 0.46/0.66 (define @t46 () (_ tptp.c_2Epred__set_2ECHOICE @t37)) % 0.46/0.66 (define @t47 () (_ (_ tptp.mem @t46) @t45)) % 0.46/0.66 (define @t48 () (forall @t43 @t47)) % 0.46/0.66 (define @t49 () (_ @t38 @t39)) % 0.46/0.66 (define @t50 () (_ tptp.c_2Epred__set_2EDELETE @t37)) % 0.46/0.66 (define @t51 () (_ @t40 @t39)) % 0.46/0.66 (define @t52 () (_ tptp.c_2Epred__set_2EREST @t37)) % 0.46/0.66 (define @t53 () (_ (_ tptp.mem @t52) @t51)) % 0.46/0.66 (define @t54 () (forall @t43 @t53)) % 0.46/0.66 (define @t55 () (@var "Y" $$unsorted)) % 0.46/0.66 (define @t56 () (@var "V1t" $$unsorted)) % 0.46/0.66 (define @t57 () (@var "V2x" $$unsorted)) % 0.46/0.66 (define @t58 () (_ tptp.ap @t44)) % 0.46/0.66 (define @t59 () (_ @t58 @t57)) % 0.46/0.66 (define @t60 () (_ tptp.ap @t59)) % 0.46/0.66 (define @t61 () (_ @t60 @t56)) % 0.46/0.66 (define @t62 () (_ tptp.p @t61)) % 0.46/0.66 (define @t63 () (@var "V0s" $$unsorted)) % 0.46/0.66 (define @t64 () (_ @t60 @t63)) % 0.46/0.66 (define @t65 () (_ tptp.p @t64)) % 0.46/0.66 (define @t66 () (=> @t65 @t62)) % 0.46/0.66 (define @t67 () (_ (_ tptp.mem @t57) @t37)) % 0.46/0.66 (define @t68 () (@list @t57)) % 0.46/0.66 (define @t69 () (forall @t68 (=> @t67 @t66))) % 0.46/0.66 (define @t70 () (_ tptp.ap @t42)) % 0.46/0.66 (define @t71 () (_ @t70 @t63)) % 0.46/0.66 (define @t72 () (_ (_ tptp.ap @t71) @t56)) % 0.46/0.66 (define @t73 () (_ tptp.p @t72)) % 0.46/0.66 (define @t74 () (= @t73 @t69)) % 0.46/0.66 (define @t75 () (_ tptp.mem @t56)) % 0.46/0.66 (define @t76 () (_ @t75 @t39)) % 0.46/0.66 (define @t77 () (=> @t76 @t74)) % 0.46/0.66 (define @t78 () (@list @t56)) % 0.46/0.66 (define @t79 () (forall @t78 @t77)) % 0.46/0.66 (define @t80 () (_ tptp.mem @t63)) % 0.46/0.66 (define @t81 () (_ @t80 @t39)) % 0.46/0.66 (define @t82 () (=> @t81 @t79)) % 0.46/0.66 (define @t83 () (@list @t37 @t63)) % 0.46/0.66 (define @t84 () (forall @t83 @t82)) % 0.46/0.66 (define @t85 () (@var "V2y" $$unsorted)) % 0.46/0.66 (define @t86 () (@var "V1x" $$unsorted)) % 0.46/0.66 (define @t87 () (not (= @t86 @t85))) % 0.46/0.66 (define @t88 () (_ @t58 @t86)) % 0.46/0.66 (define @t89 () (_ tptp.ap @t88)) % 0.46/0.66 (define @t90 () (_ @t89 @t63)) % 0.46/0.66 (define @t91 () (_ tptp.p @t90)) % 0.46/0.66 (define @t92 () (and @t91 @t87)) % 0.46/0.66 (define @t93 () (_ (_ tptp.ap @t50) @t63)) % 0.46/0.66 (define @t94 () (_ tptp.ap @t93)) % 0.46/0.66 (define @t95 () (_ @t94 @t85)) % 0.46/0.66 (define @t96 () (_ @t89 @t95)) % 0.46/0.66 (define @t97 () (_ tptp.p @t96)) % 0.46/0.66 (define @t98 () (= @t97 @t92)) % 0.46/0.66 (define @t99 () (_ (_ tptp.mem @t85) @t37)) % 0.46/0.66 (define @t100 () (@list @t85)) % 0.46/0.66 (define @t101 () (forall @t100 (=> @t99 @t98))) % 0.46/0.66 (define @t102 () (_ (_ tptp.mem @t86) @t37)) % 0.46/0.66 (define @t103 () (=> @t102 @t101)) % 0.46/0.66 (define @t104 () (@list @t86)) % 0.46/0.66 (define @t105 () (forall @t104 @t103)) % 0.46/0.66 (define @t106 () (=> @t81 @t105)) % 0.46/0.66 (define @t107 () (forall @t83 @t106)) % 0.46/0.66 (define @t108 () (_ (_ tptp.ap @t46) @t63)) % 0.46/0.66 (define @t109 () (_ @t94 @t108)) % 0.46/0.66 (define @t110 () (_ (_ tptp.ap @t52) @t63)) % 0.46/0.66 (define @t111 () (= @t110 @t109)) % 0.46/0.66 (define @t112 () (forall @t83 (=> @t81 @t111))) % 0.46/0.66 (define @t113 () (_ @t70 @t110)) % 0.46/0.66 (define @t114 () (_ (_ tptp.ap @t113) @t63)) % 0.46/0.66 (define @t115 () (_ tptp.p @t114)) % 0.46/0.66 (define @t116 () (forall @t83 (=> @t81 @t115))) % 0.46/0.66 (define @t117 () (not @t116)) % 0.46/0.66 (define @t118 () (@var "BOUND_VARIABLE_7747" $$unsorted)) % 0.46/0.66 (define @t119 () (tptp.mem (tptp.ap @t8 @t118) @t7)) % 0.46/0.66 (define @t120 () (not (tptp.mem @t118 @t11))) % 0.46/0.66 (define @t121 () (tptp.arr @t11 @t7)) % 0.46/0.66 (define @t122 () (tptp.mem @t8 @t121)) % 0.46/0.66 (define @t123 () (not @t122)) % 0.46/0.66 (define @t124 () (or @t123 @t120 @t119)) % 0.46/0.66 (define @t125 () (or @t120 @t119)) % 0.46/0.66 (define @t126 () (or @t123 @t125)) % 0.46/0.66 (define @t127 () (@list @t11 @t7 @t8 @t118)) % 0.46/0.66 (define @t128 () (forall @t127 @t126)) % 0.46/0.66 (define @t129 () (@list @t118)) % 0.46/0.66 (define @t130 () (forall @t129 @t126)) % 0.46/0.66 (define @t131 () (forall @t129 @t125)) % 0.46/0.66 (define @t132 () (or @t123 @t131)) % 0.46/0.66 (define @t133 () (tptp.ap @t8 @t4)) % 0.46/0.66 (define @t134 () (tptp.mem @t133 @t7)) % 0.46/0.66 (define @t135 () (tptp.mem @t4 @t11)) % 0.46/0.66 (define @t136 () (forall @t6 (or (not @t135) @t134))) % 0.46/0.66 (define @t137 () (not @t17)) % 0.46/0.66 (define @t138 () (or @t137 @t136)) % 0.46/0.66 (define @t139 () (not @t12)) % 0.46/0.66 (define @t140 () (or @t139 @t10)) % 0.46/0.66 (define @t141 () (@var "BOUND_VARIABLE_8187" $$unsorted)) % 0.46/0.66 (define @t142 () (@var "BOUND_VARIABLE_8185" $$unsorted)) % 0.46/0.66 (define @t143 () (tptp.c_2Ebool_2EIN @t37)) % 0.46/0.66 (define @t144 () (tptp.ap @t143 @t142)) % 0.46/0.66 (define @t145 () (tptp.c_2Epred__set_2EDELETE @t37)) % 0.46/0.66 (define @t146 () (tptp.ap @t145 @t63)) % 0.46/0.66 (define @t147 () (= (tptp.p (tptp.ap @t144 (tptp.ap @t146 @t141))) (and (tptp.p (tptp.ap @t144 @t63)) (not (= @t142 @t141))))) % 0.46/0.66 (define @t148 () (not (tptp.mem @t141 @t37))) % 0.46/0.66 (define @t149 () (not (tptp.mem @t142 @t37))) % 0.46/0.66 (define @t150 () (tptp.arr @t37 tptp.bool)) % 0.46/0.66 (define @t151 () (tptp.mem @t63 @t150)) % 0.46/0.66 (define @t152 () (not @t151)) % 0.46/0.66 (define @t153 () (or @t152 @t149 @t148 @t147)) % 0.46/0.66 (define @t154 () (or @t149 @t148 @t147)) % 0.46/0.66 (define @t155 () (or @t152 @t154)) % 0.46/0.66 (define @t156 () (@list @t37 @t63 @t142 @t141)) % 0.46/0.66 (define @t157 () (forall @t156 @t155)) % 0.46/0.66 (define @t158 () (@list @t142 @t141)) % 0.46/0.66 (define @t159 () (forall @t158 @t155)) % 0.46/0.66 (define @t160 () (forall @t158 @t154)) % 0.46/0.66 (define @t161 () (@var "BOUND_VARIABLE_8162" $$unsorted)) % 0.46/0.66 (define @t162 () (or @t152 @t160)) % 0.46/0.66 (define @t163 () (tptp.ap @t143 @t86)) % 0.46/0.66 (define @t164 () (tptp.ap @t163 @t63)) % 0.46/0.66 (define @t165 () (tptp.p @t164)) % 0.46/0.66 (define @t166 () (= (tptp.p (tptp.ap @t163 (tptp.ap @t146 @t161))) (and @t165 (not (= @t86 @t161))))) % 0.46/0.66 (define @t167 () (not (tptp.mem @t161 @t37))) % 0.46/0.66 (define @t168 () (tptp.mem @t86 @t37)) % 0.46/0.66 (define @t169 () (not @t168)) % 0.46/0.66 (define @t170 () (or @t169 @t167 @t166)) % 0.46/0.66 (define @t171 () (@list @t86 @t161)) % 0.46/0.66 (define @t172 () (forall @t171 @t170)) % 0.46/0.66 (define @t173 () (not @t81)) % 0.46/0.66 (define @t174 () (or @t173 @t172)) % 0.46/0.66 (define @t175 () (or @t167 @t166)) % 0.46/0.66 (define @t176 () (or @t169 @t175)) % 0.46/0.66 (define @t177 () (forall @t171 @t176)) % 0.46/0.66 (define @t178 () (@list @t161)) % 0.46/0.66 (define @t179 () (forall @t178 @t176)) % 0.46/0.66 (define @t180 () (forall @t178 @t175)) % 0.46/0.66 (define @t181 () (or @t169 @t180)) % 0.46/0.66 (define @t182 () (tptp.ap @t146 @t85)) % 0.46/0.66 (define @t183 () (tptp.ap @t163 @t182)) % 0.46/0.66 (define @t184 () (tptp.p @t183)) % 0.46/0.66 (define @t185 () (tptp.mem @t85 @t37)) % 0.46/0.66 (define @t186 () (forall @t100 (or (not @t185) (= @t184 (and @t165 @t87))))) % 0.46/0.66 (define @t187 () (not @t102)) % 0.46/0.66 (define @t188 () (or @t187 @t186)) % 0.46/0.66 (define @t189 () (_ tptp.ap @t163)) % 0.46/0.66 (define @t190 () (_ tptp.ap @t143)) % 0.46/0.66 (define @t191 () (_ tptp.ap @t146)) % 0.46/0.66 (define @t192 () (not @t99)) % 0.46/0.66 (define @t193 () (or @t192 @t98)) % 0.46/0.66 (define @t194 () (tptp.c_2Epred__set_2EREST @t37)) % 0.46/0.66 (define @t195 () (tptp.ap @t194 @t63)) % 0.46/0.66 (define @t196 () (tptp.c_2Epred__set_2ESUBSET @t37)) % 0.46/0.66 (define @t197 () (tptp.ap @t196 @t195)) % 0.46/0.66 (define @t198 () (tptp.ap @t197 @t63)) % 0.46/0.66 (define @t199 () (tptp.p @t198)) % 0.46/0.66 (define @t200 () (forall @t83 (or @t152 @t199))) % 0.46/0.66 (define @t201 () (@quantifiers_skolemize @t200 1)) % 0.46/0.66 (define @t202 () (@quantifiers_skolemize @t200 0)) % 0.46/0.66 (define @t203 () (tptp.c_2Ebool_2EIN @t202)) % 0.46/0.66 (define @t204 () (tptp.ap @t203 @t57)) % 0.46/0.66 (define @t205 () (tptp.c_2Epred__set_2EREST @t202)) % 0.46/0.66 (define @t206 () (tptp.ap @t205 @t201)) % 0.46/0.66 (define @t207 () (forall @t68 (or (not (tptp.mem @t57 @t202)) (not (tptp.p (tptp.ap @t204 @t206))) (tptp.p (tptp.ap @t204 @t201))))) % 0.46/0.66 (define @t208 () (@quantifiers_skolemize @t207 0)) % 0.46/0.66 (define @t209 () (tptp.c_2Epred__set_2ECHOICE @t202)) % 0.46/0.66 (define @t210 () (tptp.ap @t209 @t201)) % 0.46/0.66 (define @t211 () (not (= @t208 @t210))) % 0.46/0.66 (define @t212 () (tptp.ap @t203 @t208)) % 0.46/0.66 (define @t213 () (tptp.p (tptp.ap @t212 @t201))) % 0.46/0.66 (define @t214 () (and @t213 @t211)) % 0.46/0.66 (define @t215 () (tptp.ap (tptp.ap (tptp.c_2Epred__set_2EDELETE @t202) @t201) @t210)) % 0.46/0.66 (define @t216 () (tptp.ap @t212 @t215)) % 0.46/0.66 (define @t217 () (tptp.p @t216)) % 0.46/0.66 (define @t218 () (= @t217 @t214)) % 0.46/0.66 (define @t219 () (tptp.mem @t210 @t202)) % 0.46/0.66 (define @t220 () (not @t219)) % 0.46/0.66 (define @t221 () (tptp.mem @t208 @t202)) % 0.46/0.66 (define @t222 () (not @t221)) % 0.46/0.66 (define @t223 () (tptp.arr @t202 tptp.bool)) % 0.46/0.66 (define @t224 () (tptp.mem @t201 @t223)) % 0.46/0.66 (define @t225 () (not @t224)) % 0.46/0.66 (define @t226 () (or @t225 @t222 @t220 @t218)) % 0.46/0.66 (define @t227 () (forall @t156 @t153)) % 0.46/0.66 (define @t228 () (and @t213 (not (= @t210 @t208)))) % 0.46/0.66 (define @t229 () (= @t217 @t228)) % 0.46/0.66 (define @t230 () (or @t225 @t222 @t220 @t229)) % 0.46/0.66 (define @t231 () (@list false)) % 0.46/0.66 (define @t232 () (@var "BOUND_VARIABLE_8109" $$unsorted)) % 0.46/0.66 (define @t233 () (tptp.ap @t196 @t63)) % 0.46/0.66 (define @t234 () (tptp.ap @t143 @t57)) % 0.46/0.66 (define @t235 () (tptp.ap @t234 @t63)) % 0.46/0.66 (define @t236 () (tptp.p @t235)) % 0.46/0.66 (define @t237 () (not @t236)) % 0.46/0.66 (define @t238 () (tptp.mem @t57 @t37)) % 0.46/0.66 (define @t239 () (not @t238)) % 0.46/0.66 (define @t240 () (= (forall @t68 (or @t239 @t237 (tptp.p (tptp.ap @t234 @t232)))) (tptp.p (tptp.ap @t233 @t232)))) % 0.46/0.66 (define @t241 () (not (tptp.mem @t232 @t150))) % 0.46/0.66 (define @t242 () (or @t152 @t241 @t240)) % 0.46/0.66 (define @t243 () (or @t241 @t240)) % 0.46/0.66 (define @t244 () (or @t152 @t243)) % 0.46/0.66 (define @t245 () (@list @t37 @t63 @t232)) % 0.46/0.66 (define @t246 () (forall @t245 @t244)) % 0.46/0.66 (define @t247 () (@list @t232)) % 0.46/0.66 (define @t248 () (forall @t247 @t244)) % 0.46/0.66 (define @t249 () (forall @t247 @t243)) % 0.46/0.66 (define @t250 () (or @t152 @t249)) % 0.46/0.66 (define @t251 () (tptp.ap @t233 @t56)) % 0.46/0.66 (define @t252 () (tptp.p @t251)) % 0.46/0.66 (define @t253 () (tptp.ap @t234 @t56)) % 0.46/0.66 (define @t254 () (tptp.p @t253)) % 0.46/0.66 (define @t255 () (forall @t68 (or @t239 @t237 @t254))) % 0.46/0.66 (define @t256 () (tptp.mem @t56 @t150)) % 0.46/0.66 (define @t257 () (not @t256)) % 0.46/0.66 (define @t258 () (forall @t78 (or @t257 (= @t255 @t252)))) % 0.46/0.66 (define @t259 () (or @t173 @t258)) % 0.46/0.66 (define @t260 () (or @t257 (= @t252 @t255))) % 0.46/0.66 (define @t261 () (_ tptp.ap @t196)) % 0.46/0.66 (define @t262 () (= @t73 @t255)) % 0.46/0.66 (define @t263 () (not @t76)) % 0.46/0.66 (define @t264 () (or @t263 @t262)) % 0.46/0.66 (define @t265 () (_ tptp.ap @t234)) % 0.46/0.66 (define @t266 () (not @t65)) % 0.46/0.66 (define @t267 () (not @t67)) % 0.46/0.66 (define @t268 () (or @t267 @t266 @t62)) % 0.46/0.66 (define @t269 () (tptp.p (tptp.ap (tptp.ap (tptp.c_2Epred__set_2ESUBSET @t202) @t206) @t201))) % 0.46/0.66 (define @t270 () (tptp.mem @t206 @t223)) % 0.46/0.66 (define @t271 () (not @t270)) % 0.46/0.66 (define @t272 () (or @t271 @t225 (= @t207 @t269))) % 0.46/0.66 (define @t273 () (forall @t245 @t242)) % 0.46/0.66 (define @t274 () (= @t269 @t207)) % 0.46/0.66 (define @t275 () (or @t271 @t225 @t274)) % 0.46/0.66 (define @t276 () (tptp.arr @t150 @t150)) % 0.46/0.66 (define @t277 () (tptp.mem @t194 @t276)) % 0.46/0.66 (define @t278 () (_ tptp.arr @t150)) % 0.46/0.66 (define @t279 () (@list @t202)) % 0.46/0.66 (define @t280 () (or @t173 @t115)) % 0.46/0.66 (define @t281 () (or @t225 @t269)) % 0.46/0.66 (define @t282 () (@list true)) % 0.46/0.66 (define @t283 () (@list @t281)) % 0.46/0.66 (define @t284 () (tptp.mem @t205 (tptp.arr @t223 @t223))) % 0.46/0.66 (define @t285 () (not @t284)) % 0.46/0.66 (define @t286 () (or @t285 @t225 @t270)) % 0.46/0.66 (define @t287 () (@list false false false)) % 0.46/0.66 (define @t288 () (not @t207)) % 0.46/0.66 (define @t289 () (@list true false)) % 0.46/0.66 (define @t290 () (tptp.p (tptp.ap @t212 @t206))) % 0.46/0.66 (define @t291 () (not @t290)) % 0.46/0.66 (define @t292 () (or @t222 @t291 @t213)) % 0.46/0.66 (define @t293 () (@list @t292)) % 0.46/0.66 (define @t294 () (tptp.c_2Epred__set_2ECHOICE @t37)) % 0.46/0.66 (define @t295 () (tptp.ap @t294 @t63)) % 0.46/0.66 (define @t296 () (tptp.ap @t146 @t295)) % 0.46/0.66 (define @t297 () (or @t173 @t111)) % 0.46/0.66 (define @t298 () (= @t206 @t215)) % 0.46/0.66 (define @t299 () (or @t225 @t298)) % 0.46/0.66 (define @t300 () (not @t228)) % 0.46/0.66 (define @t301 () (not @t229)) % 0.46/0.66 (define @t302 () (tptp.arr @t150 @t37)) % 0.46/0.66 (define @t303 () (tptp.mem @t294 @t302)) % 0.46/0.66 (define @t304 () (tptp.mem @t209 (tptp.arr @t223 @t202))) % 0.46/0.66 (define @t305 () (not @t304)) % 0.46/0.66 (define @t306 () (or @t305 @t225 @t219)) % 0.46/0.66 (define @t307 () (not @t306)) % 0.46/0.66 (define @t308 () (forall @t127 @t124)) % 0.46/0.66 (assume @p1 (forall @t3 (= (_ tptp.p @t2) @t1))) % 0.46/0.66 (assume @p2 (forall @t3 (_ (_ tptp.mem @t2) tptp.bool))) % 0.46/0.66 (assume @p3 (forall @t6 (=> (_ @t5 tptp.bool) (= @t4 (_ tptp.inj__o (_ tptp.p @t4)))))) % 0.46/0.66 (assume @p4 @t20) % 0.46/0.66 (assume @p5 (forall (@list @t11 @t7 @t21) (=> (forall @t6 (=> @t12 (_ (_ tptp.mem @t23) @t7))) (_ (_ tptp.mem @t22) @t15)))) % 0.46/0.66 (assume @p6 (forall @t19 (=> @t17 (forall (@list @t24) (=> (_ (_ tptp.mem @t24) @t15) (=> (forall @t6 (=> @t12 (= @t9 (_ (_ tptp.ap @t24) @t4)))) (= @t8 @t24))))))) % 0.46/0.66 (assume @p7 (forall (@list @t11 @t21 @t4) (=> @t12 (= (_ (_ tptp.ap @t22) @t4) @t23)))) % 0.46/0.66 (assume @p8 (_ (_ tptp.mem tptp.c_2Emin_2E_3D_3D_3E) @t27)) % 0.46/0.66 (assume @p9 (forall @t36 (=> @t35 (forall @t33 (=> @t32 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Emin_2E_3D_3D_3E) @t30)) @t28)) (=> @t31 @t29))))))) % 0.46/0.66 (assume @p10 (forall @t43 (_ (_ tptp.mem @t42) (_ @t40 @t41)))) % 0.46/0.66 (assume @p11 (_ (_ tptp.mem tptp.c_2Ebool_2E_7E) @t26)) % 0.46/0.66 (assume @p12 (forall @t36 (=> @t35 (= (_ tptp.p (_ (_ tptp.ap tptp.c_2Ebool_2E_7E) @t30)) (not @t31))))) % 0.46/0.66 (assume @p13 (_ (_ tptp.mem tptp.c_2Ebool_2E_2F_5C) @t27)) % 0.46/0.66 (assume @p14 (forall @t36 (=> @t35 (forall @t33 (=> @t32 (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap tptp.c_2Ebool_2E_2F_5C) @t30)) @t28)) (and @t31 @t29))))))) % 0.46/0.66 (assume @p15 (forall @t43 (_ (_ tptp.mem @t44) (_ @t38 @t41)))) % 0.46/0.66 (assume @p16 @t48) % 0.46/0.66 (assume @p17 (forall @t43 (_ (_ tptp.mem @t50) (_ @t40 @t49)))) % 0.46/0.66 (assume @p18 @t54) % 0.46/0.66 (assume @p19 (forall @t43 (_ (_ tptp.mem (_ tptp.c_2Emin_2E_3D @t37)) @t49))) % 0.46/0.66 (assume @p20 (forall (@list @t11 @t4) (=> @t12 (forall (@list @t55) (=> (_ (_ tptp.mem @t55) @t11) (= (_ tptp.p (_ (_ tptp.ap (_ (_ tptp.ap (_ tptp.c_2Emin_2E_3D @t11)) @t4)) @t55)) (= @t4 @t55))))))) % 0.46/0.66 (assume @p21 (forall @t43 (_ (_ tptp.mem (_ tptp.c_2Ebool_2E_21 @t37)) @t41))) % 0.46/0.66 (assume @p22 (forall (@list @t11 @t30) (=> (_ @t34 (_ @t14 tptp.bool)) (= (_ tptp.p (_ (_ tptp.ap (_ tptp.c_2Ebool_2E_21 @t11)) @t30)) (forall @t6 (=> @t12 (_ tptp.p (_ (_ tptp.ap @t30) @t4)))))))) % 0.46/0.66 (assume @p23 @t84) % 0.46/0.66 (assume @p24 @t107) % 0.46/0.66 (assume @p25 @t112) % 0.46/0.66 (assume @p26 @t117) % 0.46/0.66 (assume @p27 true) % 0.46/0.66 (step @p28 :rule aci_norm :args ((= @t126 @t124))) % 0.46/0.66 (step @p29 :rule cong :premises (@p28) :args (@t128)) % 0.46/0.66 (step @p30 :rule quant-merge-prenex :args ((= (forall @t19 @t130) @t128))) % 0.46/0.66 (step @p31 :rule alpha_equiv :args (@t131 (@list @t118) (@list @t4))) % 0.46/0.66 (step @p32 :rule refl :args (@t123)) % 0.46/0.66 (step @p33 :rule nary_cong :premises (@p32 @p31) :args (@t132)) % 0.46/0.66 (step @p34 :rule quant-miniscope-or :args ((= @t130 @t132))) % 0.46/0.66 (step @p35 :rule trans :premises (@p34 @p33)) % 0.46/0.66 (step @p36 :rule symm :premises (@p35)) % 0.46/0.66 (step @p37 :rule cong :premises (@p36) :args ((forall @t19 (or @t123 @t136)))) % 0.46/0.66 (step @p38 :rule trans :premises (@p37 @p30)) % 0.46/0.66 (step @p39 :rule trans :premises (@p38 @p29)) % 0.46/0.66 (step @p40 :rule refl :args (@t136)) % 0.46/0.66 (step @p41 :rule refl :args ((tptp.mem @t8 @t15))) % 0.46/0.66 (step @p42 :rule refl :args (@t121)) % 0.46/0.66 (step @p43 :rule refl :args (@t8)) % 0.46/0.66 (step @p44 :rule cong :premises (@p43 @p42) :args (@t122)) % 0.46/0.66 (step @p45 :rule trans :premises (@p44 @p41)) % 0.46/0.66 (step @p46 :rule refl :args (@t16)) % 0.46/0.66 (step @p47 :rule ho_cong :premises (@p46 @p42)) % 0.46/0.66 (step @p48 :rule cong :premises (@p47 @p45) :args ((= (_ @t16 @t121) @t122))) % 0.46/0.66 (step @p49 :rule symm :premises (@p48)) % 0.46/0.66 (step @p50 :rule refl :args (@t17)) % 0.46/0.66 (step @p51 :rule eq_resolve :premises (@p50 @p49)) % 0.46/0.66 (step @p52 :rule refl :args (@t15)) % 0.46/0.66 (step @p53 :rule cong :premises (@p52 @p42) :args ((= @t15 @t121))) % 0.46/0.66 (step @p54 :rule symm :premises (@p53)) % 0.46/0.66 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.46/0.66 (step @p56 :rule ho_cong :premises (@p46 @p55)) % 0.46/0.66 (step @p57 :rule trans :premises (@p56 @p51)) % 0.46/0.66 (step @p58 :rule cong :premises (@p57) :args (@t137)) % 0.46/0.66 (step @p59 :rule nary_cong :premises (@p58 @p40) :args (@t138)) % 0.46/0.66 (step @p60 :rule cong :premises (@p59) :args ((forall @t19 @t138))) % 0.46/0.66 (step @p61 :rule trans :premises (@p60 @p39)) % 0.46/0.66 (step @p62 :rule bool-impl-elim :args (@t17 @t136)) % 0.46/0.66 (step @p63 :rule cong :premises (@p62) :args ((forall @t19 (=> @t17 @t136)))) % 0.46/0.66 (step @p64 :rule trans :premises (@p63 @p61)) % 0.46/0.66 (step @p65 :rule refl :args ((tptp.mem @t9 @t7))) % 0.46/0.66 (step @p66 :rule refl :args (@t7)) % 0.46/0.66 (step @p67 :rule refl :args (@t133)) % 0.46/0.66 (step @p68 :rule cong :premises (@p67 @p66) :args (@t134)) % 0.46/0.66 (step @p69 :rule trans :premises (@p68 @p65)) % 0.46/0.66 (step @p70 :rule refl :args (tptp.mem)) % 0.46/0.66 (step @p71 :rule ho_cong :premises (@p70 @p67)) % 0.46/0.66 (step @p72 :rule ho_cong :premises (@p71 @p66)) % 0.46/0.66 (step @p73 :rule cong :premises (@p72 @p69) :args ((= (_ (_ tptp.mem @t133) @t7) @t134))) % 0.46/0.66 (step @p74 :rule symm :premises (@p73)) % 0.46/0.66 (step @p75 :rule refl :args (@t10)) % 0.46/0.66 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.46/0.66 (step @p77 :rule refl :args (@t9)) % 0.46/0.66 (step @p78 :rule cong :premises (@p77 @p67) :args ((= @t9 @t133))) % 0.46/0.66 (step @p79 :rule symm :premises (@p78)) % 0.46/0.66 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.46/0.66 (step @p81 :rule ho_cong :premises (@p70 @p80)) % 0.46/0.66 (step @p82 :rule ho_cong :premises (@p81 @p66)) % 0.46/0.66 (step @p83 :rule trans :premises (@p82 @p76)) % 0.46/0.66 (step @p84 :rule refl :args (@t135)) % 0.46/0.66 (step @p85 :rule refl :args (@t12)) % 0.46/0.66 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t12 @t135))) % 0.46/0.66 (step @p87 :rule symm :premises (@p86)) % 0.46/0.66 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.46/0.66 (step @p89 :rule cong :premises (@p88) :args (@t139)) % 0.46/0.66 (step @p90 :rule nary_cong :premises (@p89 @p83) :args (@t140)) % 0.46/0.66 (step @p91 :rule cong :premises (@p90) :args ((forall @t6 @t140))) % 0.46/0.66 (step @p92 :rule bool-impl-elim :args (@t12 @t10)) % 0.46/0.66 (step @p93 :rule cong :premises (@p92) :args (@t13)) % 0.46/0.66 (step @p94 :rule trans :premises (@p93 @p91)) % 0.46/0.66 (step @p95 :rule refl :args (@t17)) % 0.46/0.66 (step @p96 :rule cong :premises (@p95 @p94) :args (@t18)) % 0.46/0.66 (step @p97 :rule cong :premises (@p96) :args (@t20)) % 0.46/0.66 (step @p98 :rule trans :premises (@p97 @p64)) % 0.46/0.66 (step @p99 :rule eq_resolve :premises (@p4 @p98)) % 0.46/0.66 (step @p100 :rule aci_norm :args ((= @t155 @t153))) % 0.46/0.66 (step @p101 :rule cong :premises (@p100) :args (@t157)) % 0.46/0.66 (step @p102 :rule quant-merge-prenex :args ((= (forall @t83 @t159) @t157))) % 0.46/0.66 (step @p103 :rule alpha_equiv :args (@t160 (@list @t142 @t141) (@list @t86 @t161))) % 0.46/0.66 (step @p104 :rule refl :args (@t152)) % 0.46/0.66 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t162)) % 0.46/0.66 (step @p106 :rule quant-miniscope-or :args ((= @t159 @t162))) % 0.46/0.66 (step @p107 :rule trans :premises (@p106 @p105)) % 0.46/0.66 (step @p108 :rule symm :premises (@p107)) % 0.46/0.66 (step @p109 :rule cong :premises (@p108) :args ((forall @t83 (or @t152 @t172)))) % 0.46/0.66 (step @p110 :rule trans :premises (@p109 @p102)) % 0.46/0.66 (step @p111 :rule trans :premises (@p110 @p101)) % 0.46/0.66 (step @p112 :rule refl :args (@t172)) % 0.46/0.66 (step @p113 :rule refl :args ((tptp.mem @t63 @t39))) % 0.46/0.66 (step @p114 :rule refl :args (@t150)) % 0.46/0.66 (step @p115 :rule refl :args (@t63)) % 0.46/0.66 (step @p116 :rule cong :premises (@p115 @p114) :args (@t151)) % 0.46/0.66 (step @p117 :rule trans :premises (@p116 @p113)) % 0.46/0.66 (step @p118 :rule refl :args (@t80)) % 0.46/0.66 (step @p119 :rule ho_cong :premises (@p118 @p114)) % 0.46/0.66 (step @p120 :rule cong :premises (@p119 @p117) :args ((= (_ @t80 @t150) @t151))) % 0.46/0.66 (step @p121 :rule symm :premises (@p120)) % 0.46/0.66 (step @p122 :rule refl :args (@t81)) % 0.46/0.66 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.46/0.66 (step @p124 :rule refl :args (@t39)) % 0.46/0.66 (step @p125 :rule cong :premises (@p124 @p114) :args ((= @t39 @t150))) % 0.46/0.66 (step @p126 :rule symm :premises (@p125)) % 0.46/0.66 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 0.46/0.66 (step @p128 :rule ho_cong :premises (@p118 @p127)) % 0.46/0.66 (step @p129 :rule trans :premises (@p128 @p123)) % 0.46/0.66 (step @p130 :rule cong :premises (@p129) :args (@t173)) % 0.46/0.66 (step @p131 :rule nary_cong :premises (@p130 @p112) :args (@t174)) % 0.46/0.66 (step @p132 :rule cong :premises (@p131) :args ((forall @t83 @t174))) % 0.46/0.66 (step @p133 :rule trans :premises (@p132 @p111)) % 0.46/0.66 (step @p134 :rule bool-impl-elim :args (@t81 @t172)) % 0.46/0.66 (step @p135 :rule cong :premises (@p134) :args ((forall @t83 (=> @t81 @t172)))) % 0.46/0.66 (step @p136 :rule trans :premises (@p135 @p133)) % 0.46/0.66 (step @p137 :rule aci_norm :args ((= @t176 @t170))) % 0.46/0.66 (step @p138 :rule cong :premises (@p137) :args (@t177)) % 0.46/0.66 (step @p139 :rule quant-merge-prenex :args ((= (forall @t104 @t179) @t177))) % 0.46/0.66 (step @p140 :rule alpha_equiv :args (@t180 (@list @t161) (@list @t85))) % 0.46/0.66 (step @p141 :rule refl :args (@t169)) % 0.46/0.66 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t181)) % 0.46/0.66 (step @p143 :rule quant-miniscope-or :args ((= @t179 @t181))) % 0.46/0.66 (step @p144 :rule trans :premises (@p143 @p142)) % 0.46/0.66 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(@t303)) % 0.46/0.66 (step @p651 :rule trans :premises (@p650 @p645)) % 0.46/0.66 (step @p652 :rule ho_cong :premises (@p70 @p586)) % 0.46/0.66 (step @p653 :rule ho_cong :premises (@p652 @p649)) % 0.46/0.66 (step @p654 :rule cong :premises (@p653 @p651) :args ((= (_ (_ tptp.mem @t294) @t302) @t303))) % 0.46/0.66 (step @p655 :rule symm :premises (@p654)) % 0.46/0.66 (step @p656 :rule refl :args (@t47)) % 0.46/0.66 (step @p657 :rule eq_resolve :premises (@p656 @p655)) % 0.46/0.66 (step @p658 :rule ho_cong :premises (@p486 @p647)) % 0.46/0.66 (step @p659 :rule cong :premises (@p658 @p649) :args ((= (_ @t278 @t37) @t302))) % 0.46/0.66 (step @p660 :rule symm :premises (@p659)) % 0.46/0.66 (step @p661 :rule refl :args (@t45)) % 0.46/0.66 (step @p662 :rule eq_resolve :premises (@p661 @p660)) % 0.46/0.66 (step @p663 :rule ho_cong :premises (@p492 @p647)) % 0.46/0.66 (step @p664 :rule trans :premises (@p663 @p662)) % 0.46/0.66 (step @p665 :rule ho_cong :premises (@p70 @p605)) % 0.46/0.66 (step @p666 :rule ho_cong :premises (@p665 @p664)) % 0.46/0.66 (step @p667 :rule trans :premises (@p666 @p657)) % 0.46/0.66 (step @p668 :rule cong :premises (@p667) :args (@t48)) % 0.46/0.66 (step @p669 :rule eq_resolve :premises (@p16 @p668)) % 0.46/0.66 (step @p670 :rule instantiate :premises (@p669) :args (@t279)) % 0.46/0.66 (step @p671 :rule cnf_or_pos :args (@t306)) % 0.46/0.66 (step @p672 :rule reordering :premises (@p671) :args ((or @t225 @t305 @t219 @t307))) % 0.46/0.66 (step @p673 :rule chain_m_resolution :premises (@p672 @p563 @p670 @p644) :args (@t307 (@list false false true) (@list @t224 @t304 @t219))) % 0.46/0.66 (assume-push @p684 @t308) % 0.46/0.66 (step @p675 :rule instantiate :premises (@p99) :args ((@list @t223 @t202 @t209 @t201))) % 0.46/0.66 (step-pop @p685 :rule scope :premises (@p675)) % 0.46/0.66 (step @p676 :rule process_scope :premises (@p685) :args (@t306)) % 0.46/0.66 (step @p678 :rule implies_elim :premises (@p676)) % 0.46/0.66 (step @p679 false :rule chain_m_resolution :premises (@p678 @p673 @p99) :args (false @t289 (@list @t306 @t308))) % 0.46/0.66 ) % 0.46/0.66 % SZS output end Proof % 0.46/0.66 % cvc5 exiting %------------------------------------------------------------------------------