%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU630^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:52:29 AM UTC 2026 % Result : Theorem 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU630^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n022.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:43:53 EDT 2026 % 0.18/0.35 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.45/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.64 % SZS status Theorem % 0.45/0.64 % SZS output start Proof % 0.45/0.64 ( % 0.45/0.64 (declare-sort $$unsorted 0) % 0.45/0.64 (declare-const tptp.emptyset $$unsorted) % 0.45/0.64 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.45/0.64 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.45/0.64 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.45/0.64 (declare-const tptp.ubforcartprodlem3 Bool) % 0.45/0.64 (declare-const tptp.dsetconstrI Bool) % 0.45/0.64 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 0.45/0.64 (define tptp.cartprod () (let ((_let_1 (@var "Xz" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4) (_ (_ tptp.dsetconstr (_ tptp.powerset (_ tptp.powerset (_ (_ tptp.binunion _let_5) _let_4)))) (lambda (@list _let_3) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_4) (= _let_3 (_ (_ tptp.kpair _let_2) _let_1))))))))))))))) % 0.45/0.64 (define @t1 () (@var "Xy" $$unsorted)) % 0.45/0.64 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.45/0.64 (define @t3 () (_ @t2 @t1)) % 0.45/0.64 (define @t4 () (@list @t1)) % 0.45/0.64 (define @t5 () (lambda @t4 @t3)) % 0.45/0.64 (define @t6 () (@var "A" $$unsorted)) % 0.45/0.64 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.45/0.64 (define @t8 () (_ @t7 @t5)) % 0.45/0.64 (define @t9 () (@var "Xx" $$unsorted)) % 0.45/0.64 (define @t10 () (_ tptp.in @t9)) % 0.45/0.64 (define @t11 () (_ @t10 @t8)) % 0.45/0.64 (define @t12 () (_ @t2 @t9)) % 0.45/0.64 (define @t13 () (=> @t12 @t11)) % 0.45/0.64 (define @t14 () (_ @t10 @t6)) % 0.45/0.64 (define @t15 () (@list @t6 @t2 @t9)) % 0.45/0.64 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.45/0.64 (define @t17 () (= tptp.dsetconstrI @t16)) % 0.45/0.64 (define @t18 () (@var "B" $$unsorted)) % 0.45/0.64 (define @t19 () (_ (_ tptp.binunion @t6) @t18)) % 0.45/0.64 (define @t20 () (_ tptp.powerset @t19)) % 0.45/0.64 (define @t21 () (_ tptp.powerset @t20)) % 0.45/0.64 (define @t22 () (_ tptp.in (_ (_ tptp.kpair @t9) @t1))) % 0.45/0.64 (define @t23 () (_ tptp.in @t1)) % 0.45/0.64 (define @t24 () (_ @t23 @t18)) % 0.45/0.64 (define @t25 () (=> @t24 (_ @t22 @t21))) % 0.45/0.64 (define @t26 () (forall @t4 @t25)) % 0.45/0.64 (define @t27 () (=> @t14 @t26)) % 0.45/0.64 (define @t28 () (@list @t6 @t18 @t9)) % 0.45/0.64 (define @t29 () (forall @t28 @t27)) % 0.45/0.64 (define @t30 () (= tptp.ubforcartprodlem3 @t29)) % 0.45/0.64 (define @t31 () (=> @t24 (_ @t22 (_ (_ tptp.cartprod @t6) @t18)))) % 0.45/0.64 (define @t32 () (forall @t4 @t31)) % 0.45/0.64 (define @t33 () (=> @t14 @t32)) % 0.45/0.64 (define @t34 () (forall @t28 @t33)) % 0.45/0.64 (define @t35 () (=> tptp.ubforcartprodlem3 @t34)) % 0.45/0.64 (define @t36 () (=> tptp.dsetconstrI @t35)) % 0.45/0.64 (define @t37 () (not @t36)) % 0.45/0.64 (define @t38 () (_ tptp.setadjoin @t1)) % 0.45/0.64 (define @t39 () (_ @t38 tptp.emptyset)) % 0.45/0.64 (define @t40 () (_ tptp.setadjoin @t9)) % 0.45/0.64 (define @t41 () (_ @t40 @t39)) % 0.45/0.64 (define @t42 () (_ (_ tptp.setadjoin @t41) tptp.emptyset)) % 0.45/0.64 (define @t43 () (_ @t40 tptp.emptyset)) % 0.45/0.64 (define @t44 () (_ tptp.setadjoin @t43)) % 0.45/0.64 (define @t45 () (_ @t44 @t42)) % 0.45/0.64 (define @t46 () (lambda (@list @t9 @t1) @t45)) % 0.45/0.64 (define @t47 () (@var "Xz" $$unsorted)) % 0.45/0.64 (define @t48 () (= @t9 (_ (_ tptp.kpair @t1) @t47))) % 0.45/0.64 (define @t49 () (_ (_ tptp.in @t47) @t18)) % 0.45/0.64 (define @t50 () (and @t49 @t48)) % 0.45/0.64 (define @t51 () (@list @t47)) % 0.45/0.64 (define @t52 () (exists @t51 @t50)) % 0.45/0.64 (define @t53 () (_ @t23 @t6)) % 0.45/0.64 (define @t54 () (and @t53 @t52)) % 0.45/0.64 (define @t55 () (exists @t4 @t54)) % 0.45/0.64 (define @t56 () (@list @t9)) % 0.45/0.64 (define @t57 () (lambda @t56 @t55)) % 0.45/0.64 (define @t58 () (_ tptp.dsetconstr @t21)) % 0.45/0.64 (define @t59 () (@list @t6 @t18)) % 0.45/0.64 (define @t60 () (lambda @t59 (_ @t58 @t57))) % 0.45/0.64 (define @t61 () (@var "BOUND_VARIABLE_7737" $$unsorted)) % 0.45/0.64 (define @t62 () (@var "BOUND_VARIABLE_7551" $$unsorted)) % 0.45/0.64 (define @t63 () (tptp.setadjoin @t62 tptp.emptyset)) % 0.45/0.64 (define @t64 () (@var "BOUND_VARIABLE_7707" $$unsorted)) % 0.45/0.64 (define @t65 () (tptp.setadjoin @t64 @t63)) % 0.45/0.64 (define @t66 () (tptp.setadjoin @t65 tptp.emptyset)) % 0.45/0.64 (define @t67 () (tptp.setadjoin @t64 tptp.emptyset)) % 0.45/0.64 (define @t68 () (tptp.setadjoin @t67 @t66)) % 0.45/0.64 (define @t69 () (not (= @t68 @t61))) % 0.45/0.64 (define @t70 () (tptp.in @t62 @t18)) % 0.45/0.64 (define @t71 () (not @t70)) % 0.45/0.64 (define @t72 () (tptp.in @t64 @t6)) % 0.45/0.64 (define @t73 () (not @t72)) % 0.45/0.64 (define @t74 () (@list @t64 @t62)) % 0.45/0.64 (define @t75 () (@list @t61)) % 0.45/0.64 (define @t76 () (tptp.binunion @t6 @t18)) % 0.45/0.64 (define @t77 () (tptp.powerset @t76)) % 0.45/0.64 (define @t78 () (tptp.powerset @t77)) % 0.45/0.64 (define @t79 () (tptp.dsetconstr @t78 (lambda @t75 (not (forall @t74 (or @t73 @t71 @t69)))))) % 0.45/0.64 (define @t80 () (@var "BOUND_VARIABLE_7768" $$unsorted)) % 0.45/0.64 (define @t81 () (tptp.setadjoin @t9 tptp.emptyset)) % 0.45/0.64 (define @t82 () (tptp.in (tptp.setadjoin @t81 (tptp.setadjoin (tptp.setadjoin @t9 (tptp.setadjoin @t80 tptp.emptyset)) tptp.emptyset)) @t79)) % 0.45/0.64 (define @t83 () (not (tptp.in @t80 @t18))) % 0.45/0.64 (define @t84 () (tptp.in @t9 @t6)) % 0.45/0.64 (define @t85 () (not @t84)) % 0.45/0.64 (define @t86 () (or @t85 @t83 @t82)) % 0.45/0.64 (define @t87 () (@list @t6 @t18 @t9 @t80)) % 0.45/0.64 (define @t88 () (forall @t87 @t86)) % 0.45/0.64 (define @t89 () (@quantifiers_skolemize @t88 1)) % 0.45/0.64 (define @t90 () (not (tptp.in @t62 @t89))) % 0.45/0.64 (define @t91 () (@quantifiers_skolemize @t88 0)) % 0.45/0.64 (define @t92 () (not (tptp.in @t64 @t91))) % 0.45/0.64 (define @t93 () (not (forall @t74 (or @t92 @t90 @t69)))) % 0.45/0.64 (define @t94 () (lambda @t75 @t93)) % 0.45/0.64 (define @t95 () (@purify @t94)) % 0.45/0.64 (define @t96 () (_ @t95 @t61)) % 0.45/0.64 (define @t97 () (_ @t94 @t61)) % 0.45/0.64 (define @t98 () (= @t96 @t97)) % 0.45/0.64 (define @t99 () (forall @t75 @t98)) % 0.45/0.64 (define @t100 () (@quantifiers_skolemize @t88 3)) % 0.45/0.64 (define @t101 () (@quantifiers_skolemize @t88 2)) % 0.45/0.64 (define @t102 () (tptp.setadjoin (tptp.setadjoin @t101 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t101 (tptp.setadjoin @t100 tptp.emptyset)) tptp.emptyset))) % 0.45/0.64 (define @t103 () (forall @t74 (or @t92 @t90 (not (= @t68 @t102))))) % 0.45/0.64 (define @t104 () (not @t103)) % 0.45/0.64 (define @t105 () (_ @t95 @t102)) % 0.45/0.64 (define @t106 () (forall @t75 (= @t93 @t96))) % 0.45/0.64 (define @t107 () (= @t104 @t105)) % 0.45/0.64 (define @t108 () (= @t105 @t104)) % 0.45/0.64 (define @t109 () (@var "BOUND_VARIABLE_7676" $$unsorted)) % 0.45/0.64 (define @t110 () (tptp.in (tptp.setadjoin @t81 (tptp.setadjoin (tptp.setadjoin @t9 (tptp.setadjoin @t109 tptp.emptyset)) tptp.emptyset)) @t78)) % 0.45/0.64 (define @t111 () (not (tptp.in @t109 @t18))) % 0.45/0.64 (define @t112 () (or @t111 @t110)) % 0.45/0.64 (define @t113 () (or @t85 @t112)) % 0.45/0.64 (define @t114 () (forall (@list @t6 @t18 @t9 @t109) @t113)) % 0.45/0.64 (define @t115 () (@list @t109)) % 0.45/0.64 (define @t116 () (forall @t115 @t113)) % 0.45/0.64 (define @t117 () (forall @t115 @t112)) % 0.45/0.64 (define @t118 () (@list @t1)) % 0.45/0.64 (define @t119 () (or @t85 @t117)) % 0.45/0.64 (define @t120 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.45/0.64 (define @t121 () (tptp.setadjoin @t9 @t120)) % 0.45/0.64 (define @t122 () (tptp.setadjoin @t121 tptp.emptyset)) % 0.45/0.64 (define @t123 () (tptp.setadjoin @t81 @t122)) % 0.45/0.64 (define @t124 () (tptp.in @t123 @t78)) % 0.45/0.64 (define @t125 () (tptp.in @t1 @t18)) % 0.45/0.64 (define @t126 () (not @t125)) % 0.45/0.64 (define @t127 () (forall @t4 (or @t126 @t124))) % 0.45/0.64 (define @t128 () (not @t14)) % 0.45/0.64 (define @t129 () (or @t128 @t127)) % 0.45/0.64 (define @t130 () (_ tptp.in @t123)) % 0.45/0.64 (define @t131 () (_ tptp.in @t45)) % 0.45/0.64 (define @t132 () (_ @t131 @t21)) % 0.45/0.64 (define @t133 () (not @t24)) % 0.45/0.64 (define @t134 () (or @t133 @t132)) % 0.45/0.64 (define @t135 () (lambda @t4 @t45)) % 0.45/0.64 (define @t136 () (_ @t46 @t9)) % 0.45/0.64 (define @t137 () (_ tptp.in (_ @t136 @t1))) % 0.45/0.64 (define @t138 () (=> @t24 (_ @t137 @t21))) % 0.45/0.64 (define @t139 () (forall @t4 @t138)) % 0.45/0.64 (define @t140 () (=> @t14 @t139)) % 0.45/0.64 (define @t141 () (forall @t28 @t140)) % 0.45/0.64 (define @t142 () (=> tptp.ubforcartprodlem3 @t88)) % 0.45/0.64 (define @t143 () (_ @t2 @t1)) % 0.45/0.64 (define @t144 () (lambda @t4 @t143)) % 0.45/0.64 (define @t145 () (tptp.dsetconstr @t6 @t144)) % 0.45/0.64 (define @t146 () (tptp.in @t9 @t145)) % 0.45/0.64 (define @t147 () (_ @t2 @t9)) % 0.45/0.64 (define @t148 () (not @t147)) % 0.45/0.64 (define @t149 () (or @t85 @t148 @t146)) % 0.45/0.64 (define @t150 () (not @t12)) % 0.45/0.64 (define @t151 () (or @t128 @t150 @t11)) % 0.45/0.64 (define @t152 () (=> tptp.dsetconstrI @t142)) % 0.45/0.64 (define @t153 () (or @t83 @t82)) % 0.45/0.64 (define @t154 () (or @t85 @t153)) % 0.45/0.64 (define @t155 () (forall @t87 @t154)) % 0.45/0.64 (define @t156 () (@list @t80)) % 0.45/0.64 (define @t157 () (forall @t156 @t154)) % 0.45/0.64 (define @t158 () (forall @t156 @t153)) % 0.45/0.64 (define @t159 () (or @t85 @t158)) % 0.45/0.64 (define @t160 () (forall @t4 (or @t126 (tptp.in @t123 @t79)))) % 0.45/0.64 (define @t161 () (or @t128 @t160)) % 0.45/0.64 (define @t162 () (not (= @t61 @t68))) % 0.45/0.64 (define @t163 () (or @t73 @t71 @t162)) % 0.45/0.64 (define @t164 () (forall @t74 @t163)) % 0.45/0.64 (define @t165 () (not @t164)) % 0.45/0.64 (define @t166 () (lambda @t75 @t165)) % 0.45/0.64 (define @t167 () (tptp.dsetconstr @t78 @t166)) % 0.45/0.64 (define @t168 () (tptp.in @t123 @t167)) % 0.45/0.64 (define @t169 () (or @t126 @t168)) % 0.45/0.64 (define @t170 () (forall @t4 @t169)) % 0.45/0.64 (define @t171 () (=> @t14 @t170)) % 0.45/0.64 (define @t172 () (= @t9 @t68)) % 0.45/0.64 (define @t173 () (not @t172)) % 0.45/0.64 (define @t174 () (or @t73 @t71 @t173)) % 0.45/0.64 (define @t175 () (forall @t74 @t174)) % 0.45/0.64 (define @t176 () (not @t175)) % 0.45/0.64 (define @t177 () (lambda @t56 @t176)) % 0.45/0.64 (define @t178 () (tptp.dsetconstr @t78 @t177)) % 0.45/0.64 (define @t179 () (tptp.in @t123 @t178)) % 0.45/0.64 (define @t180 () (or @t126 @t179)) % 0.45/0.64 (define @t181 () (forall @t4 @t180)) % 0.45/0.64 (define @t182 () (=> @t14 @t181)) % 0.45/0.64 (define @t183 () (_ (_ tptp.setadjoin @t62) tptp.emptyset)) % 0.45/0.64 (define @t184 () (_ tptp.setadjoin @t64)) % 0.45/0.64 (define @t185 () (_ @t184 @t183)) % 0.45/0.64 (define @t186 () (_ (_ tptp.setadjoin @t185) tptp.emptyset)) % 0.45/0.64 (define @t187 () (_ @t184 tptp.emptyset)) % 0.45/0.64 (define @t188 () (lambda @t56 (not (forall @t74 (or (not (_ (_ tptp.in @t64) @t6)) (not (_ (_ tptp.in @t62) @t18)) (not (= @t9 (_ (_ tptp.setadjoin @t187) @t186)))))))) % 0.45/0.64 (define @t189 () (_ @t58 @t188)) % 0.45/0.64 (define @t190 () (_ @t131 (_ @t58 @t177))) % 0.45/0.64 (define @t191 () (or @t133 @t190)) % 0.45/0.64 (define @t192 () (not (= @t9 (tptp.setadjoin @t120 (tptp.setadjoin (tptp.setadjoin @t1 @t63) tptp.emptyset))))) % 0.45/0.64 (define @t193 () (tptp.in @t1 @t6)) % 0.45/0.64 (define @t194 () (not @t193)) % 0.45/0.64 (define @t195 () (or @t194 @t71 @t192)) % 0.45/0.64 (define @t196 () (@list @t1 @t62)) % 0.45/0.64 (define @t197 () (forall @t196 @t195)) % 0.45/0.64 (define @t198 () (not @t197)) % 0.45/0.64 (define @t199 () (lambda @t56 @t198)) % 0.45/0.64 (define @t200 () (_ @t58 @t199)) % 0.45/0.64 (define @t201 () (=> @t24 (_ @t131 @t200))) % 0.45/0.64 (define @t202 () (lambda (@list @t18) @t200)) % 0.45/0.64 (define @t203 () (_ (lambda @t59 @t200) @t6)) % 0.45/0.64 (define @t204 () (=> @t24 (_ @t137 (_ @t203 @t18)))) % 0.45/0.64 (define @t205 () (forall @t4 @t204)) % 0.45/0.64 (define @t206 () (=> @t14 @t205)) % 0.45/0.64 (define @t207 () (forall @t28 @t206)) % 0.45/0.64 (define @t208 () (=> tptp.ubforcartprodlem3 @t207)) % 0.45/0.64 (define @t209 () (=> tptp.dsetconstrI @t208)) % 0.45/0.64 (define @t210 () (or @t71 @t192)) % 0.45/0.64 (define @t211 () (or @t194 @t210)) % 0.45/0.64 (define @t212 () (forall @t196 @t211)) % 0.45/0.64 (define @t213 () (@list @t62)) % 0.45/0.64 (define @t214 () (forall @t213 @t211)) % 0.45/0.64 (define @t215 () (forall @t213 @t210)) % 0.45/0.64 (define @t216 () (or @t194 @t215)) % 0.45/0.64 (define @t217 () (tptp.setadjoin @t47 tptp.emptyset)) % 0.45/0.64 (define @t218 () (tptp.setadjoin @t1 @t217)) % 0.45/0.64 (define @t219 () (tptp.setadjoin @t218 tptp.emptyset)) % 0.45/0.64 (define @t220 () (tptp.setadjoin @t120 @t219)) % 0.45/0.64 (define @t221 () (tptp.in @t47 @t18)) % 0.45/0.64 (define @t222 () (forall @t51 (or (not @t221) (not (= @t9 @t220))))) % 0.45/0.64 (define @t223 () (not @t53)) % 0.45/0.64 (define @t224 () (or @t223 @t222)) % 0.45/0.64 (define @t225 () (not @t222)) % 0.45/0.64 (define @t226 () (and @t53 @t225)) % 0.45/0.64 (define @t227 () (forall @t4 (not @t226))) % 0.45/0.64 (define @t228 () (not @t227)) % 0.45/0.64 (define @t229 () (_ (_ tptp.setadjoin @t47) tptp.emptyset)) % 0.45/0.64 (define @t230 () (_ @t38 @t229)) % 0.45/0.64 (define @t231 () (_ (_ tptp.setadjoin @t230) tptp.emptyset)) % 0.45/0.64 (define @t232 () (_ tptp.setadjoin @t39)) % 0.45/0.64 (define @t233 () (_ @t232 @t231)) % 0.45/0.64 (define @t234 () (= @t9 @t233)) % 0.45/0.64 (define @t235 () (not @t234)) % 0.45/0.64 (define @t236 () (not @t49)) % 0.45/0.64 (define @t237 () (or @t236 @t235)) % 0.45/0.64 (define @t238 () (and @t49 @t234)) % 0.45/0.64 (define @t239 () (forall @t51 (not @t238))) % 0.45/0.64 (define @t240 () (not @t239)) % 0.45/0.64 (define @t241 () (@var "BOUND_VARIABLE_7486" $$unsorted)) % 0.45/0.64 (define @t242 () (_ (_ tptp.setadjoin @t241) tptp.emptyset)) % 0.45/0.64 (define @t243 () (lambda (@list @t241) (_ @t232 (_ (_ tptp.setadjoin (_ @t38 @t242)) tptp.emptyset)))) % 0.45/0.64 (define @t244 () (= @t9 (_ (_ @t46 @t1) @t47))) % 0.45/0.64 (define @t245 () (and @t49 @t244)) % 0.45/0.64 (define @t246 () (exists @t51 @t245)) % 0.45/0.64 (define @t247 () (and @t53 @t246)) % 0.45/0.64 (define @t248 () (exists @t4 @t247)) % 0.45/0.64 (define @t249 () (tptp.powerset (tptp.powerset (tptp.binunion @t91 @t89)))) % 0.45/0.64 (define @t250 () (tptp.in @t102 (tptp.dsetconstr @t249 @t95))) % 0.45/0.64 (define @t251 () (tptp.in @t100 @t89)) % 0.45/0.64 (define @t252 () (not @t251)) % 0.45/0.64 (define @t253 () (tptp.in @t101 @t91)) % 0.45/0.64 (define @t254 () (not @t253)) % 0.45/0.64 (define @t255 () (or @t254 @t252 @t250)) % 0.45/0.64 (define @t256 () (not @t255)) % 0.45/0.64 (define @t257 () (not @t88)) % 0.45/0.64 (define @t258 () (tptp.dsetconstr @t249 @t94)) % 0.45/0.64 (define @t259 () (tptp.in @t102 @t258)) % 0.45/0.64 (define @t260 () (or @t254 @t252 @t259)) % 0.45/0.64 (define @t261 () (not @t260)) % 0.45/0.64 (define @t262 () (@list true)) % 0.45/0.64 (define @t263 () (@list @t255)) % 0.45/0.64 (define @t264 () (tptp.in @t102 @t249)) % 0.45/0.64 (define @t265 () (or @t254 @t252 @t264)) % 0.45/0.64 (define @t266 () (not @t105)) % 0.45/0.64 (define @t267 () (not @t264)) % 0.45/0.64 (define @t268 () (or @t267 @t266 @t250)) % 0.45/0.64 (define @t269 () (not @t108)) % 0.45/0.64 (define @t270 () (@list true false)) % 0.45/0.64 (define @t271 () (or @t254 @t252)) % 0.45/0.64 (define @t272 () (not @t271)) % 0.45/0.64 (define @t273 () (not (= @t102 @t102))) % 0.45/0.64 (define @t274 () (or @t254 @t252 @t273)) % 0.45/0.64 (assume @p1 @t17) % 0.45/0.64 (assume @p2 @t30) % 0.45/0.64 (assume @p3 @t37) % 0.45/0.64 (assume @p4 true) % 0.45/0.64 (step @p5 (= tptp.kpair @t46) :rule refl :args (@t46)) % 0.45/0.64 (step @p6 (= tptp.cartprod @t60) :rule refl :args (@t60)) % 0.45/0.64 (step @p7 :rule eq-symm :args (@t96 @t93)) % 0.45/0.64 (step @p8 :rule beta-reduce :args ((= @t97 @t93))) % 0.45/0.64 (step @p9 :rule refl :args (@t96)) % 0.45/0.64 (step @p10 :rule cong :premises (@p9 @p8) :args (@t98)) % 0.45/0.64 (step @p11 :rule trans :premises (@p10 @p7)) % 0.45/0.64 (step @p12 :rule cong :premises (@p11) :args (@t99)) % 0.45/0.64 (step @p13 :rule quant-unused-vars :args ((= (forall @t75 true) true))) % 0.45/0.64 (step @p14 :rule eq-refl :args (@t97)) % 0.45/0.64 (step @p15 :rule cong :premises (@p14) :args ((forall @t75 (= @t97 @t97)))) % 0.45/0.64 (step @p16 :rule trans :premises (@p15 @p13)) % 0.45/0.64 (step @p17 :rule refl :args (@t97)) % 0.45/0.64 (step @p18 :rule refl :args (@t61)) % 0.45/0.64 (step @p19 :rule skolem_intro :args (@t95)) % 0.45/0.64 (step @p20 :rule ho_cong :premises (@p19 @p18)) % 0.45/0.64 (step @p21 :rule cong :premises (@p20 @p17) :args (@t98)) % 0.45/0.64 (step @p22 :rule cong :premises (@p21) :args (@t99)) % 0.45/0.64 (step @p23 :rule trans :premises (@p22 @p16)) % 0.45/0.64 (step @p24 :rule true_elim :premises (@p23)) % 0.45/0.64 (step @p25 :rule eq_resolve :premises (@p24 @p12)) % 0.45/0.64 (step @p26 :rule eq-symm :args (@t104 @t105)) % 0.45/0.64 (step @p27 :rule refl :args (@t106)) % 0.45/0.64 (step @p28 :rule cong :premises (@p27 @p26) :args ((=> @t106 @t107))) % 0.45/0.64 (assume-push @p590 @t106) % 0.45/0.64 (step @p30 :rule instantiate :premises (@p25) :args ((@list @t102))) % 0.45/0.64 (step-pop @p591 :rule scope :premises (@p30)) % 0.45/0.64 (step @p31 :rule process_scope :premises (@p591) :args (@t107)) % 0.45/0.64 (step @p33 :rule eq_resolve :premises (@p31 @p28)) % 0.45/0.64 (step 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@p127 :rule symm :premises (@p126)) % 0.45/0.64 (step @p128 :rule refl :args (@t41)) % 0.45/0.64 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.45/0.64 (step @p130 :rule refl :args (@t39)) % 0.45/0.64 (step @p131 :rule cong :premises (@p130 @p74) :args ((= @t39 @t120))) % 0.45/0.64 (step @p132 :rule symm :premises (@p131)) % 0.45/0.64 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.45/0.64 (step @p134 :rule ho_cong :premises (@p124 @p133)) % 0.45/0.64 (step @p135 :rule trans :premises (@p134 @p129)) % 0.45/0.64 (step @p136 :rule ho_cong :premises (@p111 @p135)) % 0.45/0.64 (step @p137 :rule ho_cong :premises (@p136 @p72)) % 0.45/0.64 (step @p138 :rule trans :premises (@p137 @p123)) % 0.45/0.64 (step @p139 :rule refl :args (@t43)) % 0.45/0.64 (step @p140 :rule cong :premises (@p139 @p80) :args ((= @t43 @t81))) % 0.45/0.64 (step @p141 :rule symm :premises (@p140)) % 0.45/0.64 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.45/0.64 (step @p143 :rule ho_cong 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0.45/0.64 (step @p175 :rule cong :premises (@p174) :args (@t141)) % 0.45/0.64 (step @p176 :rule trans :premises (@p175 @p61)) % 0.45/0.64 (step @p177 :rule refl :args (tptp.ubforcartprodlem3)) % 0.45/0.64 (step @p178 :rule cong :premises (@p177 @p176) :args ((= tptp.ubforcartprodlem3 @t141))) % 0.45/0.64 (step @p179 :rule refl :args (@t9)) % 0.45/0.64 (step @p180 :rule ho_cong :premises (@p5 @p179)) % 0.45/0.64 (step @p181 :rule ho_cong :premises (@p180 @p162)) % 0.45/0.64 (step @p182 :rule ho_cong :premises (@p166 @p181)) % 0.45/0.64 (step @p183 :rule ho_cong :premises (@p182 @p160)) % 0.45/0.64 (step @p184 :rule cong :premises (@p169 @p183) :args (@t25)) % 0.45/0.64 (step @p185 :rule cong :premises (@p184) :args (@t26)) % 0.45/0.64 (step @p186 :rule cong :premises (@p173 @p185) :args (@t27)) % 0.45/0.64 (step @p187 :rule cong :premises (@p186) :args (@t29)) % 0.45/0.64 (step @p188 :rule cong :premises (@p177 @p187) :args (@t30)) % 0.45/0.64 (step @p189 :rule trans :premises (@p188 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(@t239)) % 0.45/0.64 (step @p461 :rule trans :premises (@p460 @p458)) % 0.45/0.64 (step @p462 :rule cong :premises (@p461) :args (@t240)) % 0.45/0.64 (step @p463 :rule exists-elim :args ((= (exists @t51 @t238) @t240))) % 0.45/0.64 (step @p464 :rule trans :premises (@p463 @p462)) % 0.45/0.64 (step @p465 :rule beta-reduce :args ((= (_ @t243 @t47) @t233))) % 0.45/0.64 (step @p466 :rule refl :args (@t47)) % 0.45/0.64 (step @p467 :rule beta-reduce :args ((= (_ (lambda (@list @t9 @t241) (_ @t44 (_ (_ tptp.setadjoin (_ @t40 @t242)) tptp.emptyset))) @t1) @t243))) % 0.45/0.64 (step @p468 :rule alpha_equiv :args (@t46 @t118 (@list @t241))) % 0.45/0.64 (step @p469 :rule ho_cong :premises (@p468 @p412)) % 0.45/0.64 (step @p470 :rule trans :premises (@p469 @p467)) % 0.45/0.64 (step @p471 :rule ho_cong :premises (@p470 @p466)) % 0.45/0.64 (step @p472 :rule trans :premises (@p471 @p465)) % 0.45/0.64 (step @p473 :rule cong :premises (@p179 @p472) :args (@t244)) % 0.45/0.64 (step @p474 :rule refl :args 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(@t52)) % 0.45/0.64 (step @p490 :rule nary_cong :premises (@p478 @p489) :args (@t54)) % 0.45/0.64 (step @p491 :rule cong :premises (@p490) :args (@t55)) % 0.45/0.64 (step @p492 :rule cong :premises (@p491) :args (@t57)) % 0.45/0.64 (step @p493 :rule ho_cong :premises (@p483 @p492)) % 0.45/0.64 (step @p494 :rule trans :premises (@p493 @p484)) % 0.45/0.64 (step @p495 :rule cong :premises (@p494) :args (@t60)) % 0.45/0.64 (step @p496 :rule trans :premises (@p6 @p495)) % 0.45/0.64 (step @p497 :rule ho_cong :premises (@p496 @p193)) % 0.45/0.64 (step @p498 :rule ho_cong :premises (@p497 @p362)) % 0.45/0.64 (step @p499 :rule ho_cong :premises (@p182 @p498)) % 0.45/0.64 (step @p500 :rule cong :premises (@p169 @p499) :args (@t31)) % 0.45/0.64 (step @p501 :rule cong :premises (@p500) :args (@t32)) % 0.45/0.64 (step @p502 :rule cong :premises (@p173 @p501) :args (@t33)) % 0.45/0.64 (step @p503 :rule cong :premises (@p502) :args (@t34)) % 0.45/0.64 (step @p504 :rule cong :premises (@p177 @p503) :args (@t35)) % 0.45/0.64 (step @p505 :rule cong :premises (@p248 @p504) :args (@t36)) % 0.45/0.64 (step @p506 :rule cong :premises (@p505) :args (@t37)) % 0.45/0.64 (step @p507 :rule trans :premises (@p506 @p375)) % 0.45/0.64 (step @p508 :rule trans :premises (@p507 @p252)) % 0.45/0.64 (step @p509 :rule eq_resolve :premises (@p3 @p508)) % 0.45/0.64 (step @p510 :rule not_implies_elim1 :premises (@p509)) % 0.45/0.64 (step @p511 :rule instantiate :premises (@p510) :args ((@list @t249 @t95 @t102))) % 0.45/0.64 (step @p512 :rule not_implies_elim2 :premises (@p509)) % 0.45/0.64 (step @p513 :rule not_implies_elim1 :premises (@p512)) % 0.45/0.64 (step @p514 :rule instantiate :premises (@p513) :args ((@list @t91 @t89 @t101 @t100))) % 0.45/0.64 (step @p515 :rule not_implies_elim2 :premises (@p512)) % 0.45/0.64 (step @p516 :rule refl :args (@t256)) % 0.45/0.64 (step @p517 :rule bool-double-not-elim :args (@t88)) % 0.45/0.64 (step @p518 :rule nary_cong :premises (@p517 @p516) :args ((or (not @t257) @t256))) % 0.45/0.64 (step @p519 :rule eq-refl :args (@t94)) % 0.45/0.64 (step @p520 :rule refl :args (@t94)) % 0.45/0.64 (step @p521 :rule cong :premises (@p520 @p19) :args ((= @t94 @t95))) % 0.45/0.64 (step @p522 :rule trans :premises (@p521 @p519)) % 0.45/0.64 (step @p523 :rule true_elim :premises (@p522)) % 0.45/0.64 (step @p524 :rule refl :args (@t249)) % 0.45/0.64 (step @p525 :rule cong :premises (@p524 @p523) :args (@t258)) % 0.45/0.64 (step @p526 :rule refl :args (@t102)) % 0.45/0.64 (step @p527 :rule cong :premises (@p526 @p525) :args (@t259)) % 0.45/0.64 (step @p528 :rule refl :args (@t252)) % 0.45/0.64 (step @p529 :rule refl :args (@t254)) % 0.45/0.64 (step @p530 :rule nary_cong :premises (@p529 @p528 @p527) :args (@t260)) % 0.45/0.64 (step @p531 :rule cong :premises (@p530) :args (@t261)) % 0.45/0.64 (step @p532 :rule refl :args (@t257)) % 0.45/0.64 (step @p533 :rule cong :premises (@p532 @p531) :args ((=> @t257 @t261))) % 0.45/0.64 (assume-push @p592 @t257) % 0.45/0.64 (step @p535 :rule skolemize :premises (@p515)) % 0.45/0.64 (step-pop @p593 :rule scope :premises (@p535)) % 0.45/0.64 (step @p536 :rule process_scope :premises (@p593) :args (@t261)) % 0.45/0.64 (step @p538 :rule eq_resolve :premises (@p536 @p533)) % 0.45/0.64 (step @p539 :rule implies_elim :premises (@p538)) % 0.45/0.64 (step @p540 :rule eq_resolve :premises (@p539 @p518)) % 0.45/0.64 (step @p541 :rule chain_m_resolution :premises (@p540 @p515) :args (@t256 @t262 (@list @t88))) % 0.45/0.64 (step @p542 :rule bool-double-not-elim :args (@t251)) % 0.45/0.64 (step @p543 :rule refl :args (@t255)) % 0.45/0.64 (step @p544 :rule nary_cong :premises (@p543 @p542) :args ((or @t255 (not @t252)))) % 0.45/0.64 (step @p545 :rule cnf_or_neg :args (@t255 1)) % 0.45/0.64 (step @p546 :rule eq_resolve :premises (@p545 @p544)) % 0.45/0.64 (step @p547 :rule reordering :premises (@p546) :args ((or @t251 @t255))) % 0.45/0.64 (step @p548 :rule chain_m_resolution :premises (@p547 @p541) :args (@t251 @t262 @t263)) % 0.45/0.64 (step @p549 :rule bool-double-not-elim :args (@t253)) % 0.45/0.64 (step @p550 :rule nary_cong :premises (@p543 @p549) :args ((or @t255 (not @t254)))) % 0.45/0.64 (step @p551 :rule cnf_or_neg :args (@t255 0)) % 0.45/0.64 (step @p552 :rule eq_resolve :premises (@p551 @p550)) % 0.45/0.64 (step @p553 :rule reordering :premises (@p552) :args ((or @t253 @t255))) % 0.45/0.64 (step @p554 :rule chain_m_resolution :premises (@p553 @p541) :args (@t253 @t262 @t263)) % 0.45/0.64 (step @p555 :rule cnf_or_pos :args (@t265)) % 0.45/0.64 (step @p556 :rule reordering :premises (@p555) :args ((or @t254 @t252 @t264 (not @t265)))) % 0.45/0.64 (step @p557 :rule chain_m_resolution :premises (@p556 @p554 @p548 @p514) :args (@t264 (@list false false false) (@list @t253 @t251 @t265))) % 0.45/0.64 (step @p558 :rule cnf_or_neg :args (@t255 2)) % 0.45/0.64 (step @p559 :rule chain_m_resolution :premises (@p558 @p541) :args ((not @t250) @t262 @t263)) % 0.45/0.64 (step @p560 :rule cnf_or_pos :args (@t268)) % 0.45/0.64 (step @p561 :rule reordering :premises (@p560) :args ((or @t250 @t267 @t266 (not @t268)))) % 0.45/0.64 (step @p562 :rule chain_m_resolution :premises (@p561 @p559 @p557 @p511) :args (@t266 (@list true false false) (@list @t250 @t264 @t268))) % 0.45/0.64 (step @p563 :rule bool-double-not-elim :args (@t103)) % 0.45/0.64 (step @p564 :rule refl :args (@t105)) % 0.45/0.64 (step @p565 :rule refl :args (@t269)) % 0.45/0.64 (step @p566 :rule nary_cong :premises (@p565 @p564 @p563) :args ((or @t269 @t105 (not @t104)))) % 0.45/0.64 (step @p567 :rule cnf_equiv_pos2 :args (@t108)) % 0.45/0.64 (step @p568 :rule eq_resolve :premises (@p567 @p566)) % 0.45/0.64 (step @p569 :rule reordering :premises (@p568) :args ((or @t105 @t103 @t269))) % 0.45/0.64 (step @p570 :rule chain_m_resolution :premises (@p569 @p562 @p35) :args (@t103 @t270 (@list @t105 @t108))) % 0.45/0.64 (step @p571 :rule cnf_or_pos :args (@t271)) % 0.45/0.64 (step @p572 :rule reordering :premises (@p571) :args ((or @t254 @t252 @t272))) % 0.45/0.64 (step @p573 :rule chain_m_resolution :premises (@p572 @p554 @p548) :args (@t272 (@list false false) (@list @t253 @t251))) % 0.45/0.64 (step @p574 :rule aci_norm :args ((= (or @t254 @t252 false) @t271))) % 0.45/0.64 (step @p575 :rule evaluate :args ((not true))) % 0.45/0.64 (step @p576 :rule eq-refl :args (@t102)) % 0.45/0.64 (step @p577 :rule cong :premises (@p576) :args (@t273)) % 0.45/0.64 (step @p578 :rule trans :premises (@p577 @p575)) % 0.45/0.64 (step @p579 :rule nary_cong :premises (@p529 @p528 @p578) :args (@t274)) % 0.45/0.64 (step @p580 :rule trans :premises (@p579 @p574)) % 0.45/0.64 (step @p581 :rule refl :args (@t103)) % 0.45/0.64 (step @p582 :rule cong :premises (@p581 @p580) :args ((=> @t103 @t274))) % 0.45/0.64 (assume-push @p594 @t103) % 0.45/0.64 (step @p584 :rule instantiate :premises (@p570) :args ((@list @t101 @t100))) % 0.45/0.64 (step-pop @p595 :rule scope :premises (@p584)) % 0.45/0.64 (step @p585 :rule process_scope :premises (@p595) :args (@t274)) % 0.45/0.64 (step @p587 :rule eq_resolve :premises (@p585 @p582)) % 0.45/0.64 (step @p588 :rule implies_elim :premises (@p587)) % 0.45/0.64 (step @p589 false :rule chain_m_resolution :premises (@p588 @p573 @p570) :args (false @t270 (@list @t271 @t103))) % 0.45/0.64 ) % 0.45/0.64 % SZS output end Proof % 0.45/0.64 % cvc5 exiting %------------------------------------------------------------------------------