%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU688^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.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 08:52:44 AM UTC 2026 % Result : Theorem 0.15s 0.39s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU688^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 17:46:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.33 %----Proving TH0 % 0.15/0.39 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.15/0.39 % SZS status Theorem % 0.15/0.39 % SZS output start Proof % 0.15/0.39 ( % 0.15/0.39 (declare-sort $$unsorted 0) % 0.15/0.39 (declare-const tptp.emptyset $$unsorted) % 0.15/0.39 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.39 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.15/0.39 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.15/0.39 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.39 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.15/0.39 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.39 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.15/0.39 (declare-const tptp.funcGraphProp2 Bool) % 0.15/0.39 (declare-const tptp.infuncsetfunc Bool) % 0.15/0.39 (declare-const tptp.funcSet (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.39 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.15/0.39 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.15/0.39 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.15/0.39 (define tptp.func () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.15/0.39 (define @t1 () (@var "Xf" $$unsorted)) % 0.15/0.39 (define @t2 () (@var "B" $$unsorted)) % 0.15/0.39 (define @t3 () (@var "A" $$unsorted)) % 0.15/0.39 (define @t4 () (_ (_ (_ tptp.func @t3) @t2) @t1)) % 0.15/0.39 (define @t5 () (_ (_ tptp.funcSet @t3) @t2)) % 0.15/0.39 (define @t6 () (_ tptp.in @t1)) % 0.15/0.39 (define @t7 () (_ @t6 @t5)) % 0.15/0.39 (define @t8 () (=> @t7 @t4)) % 0.15/0.39 (define @t9 () (@list @t3 @t2 @t1)) % 0.15/0.39 (define @t10 () (forall @t9 @t8)) % 0.15/0.39 (define @t11 () (= tptp.infuncsetfunc @t10)) % 0.15/0.39 (define @t12 () (@var "Xy" $$unsorted)) % 0.15/0.39 (define @t13 () (@var "Xx" $$unsorted)) % 0.15/0.39 (define @t14 () (_ (_ (_ (_ tptp.ap @t3) @t2) @t1) @t13)) % 0.15/0.39 (define @t15 () (_ (_ tptp.kpair @t13) @t12)) % 0.15/0.39 (define @t16 () (_ tptp.in @t15)) % 0.15/0.39 (define @t17 () (_ @t16 @t1)) % 0.15/0.39 (define @t18 () (=> @t17 (= @t14 @t12))) % 0.15/0.39 (define @t19 () (_ (_ tptp.in @t12) @t2)) % 0.15/0.39 (define @t20 () (=> @t19 @t18)) % 0.15/0.39 (define @t21 () (@list @t12)) % 0.15/0.39 (define @t22 () (forall @t21 @t20)) % 0.15/0.39 (define @t23 () (_ (_ tptp.in @t13) @t3)) % 0.15/0.39 (define @t24 () (=> @t23 @t22)) % 0.15/0.39 (define @t25 () (@list @t13)) % 0.15/0.39 (define @t26 () (forall @t25 @t24)) % 0.15/0.39 (define @t27 () (=> @t4 @t26)) % 0.15/0.39 (define @t28 () (forall @t9 @t27)) % 0.15/0.39 (define @t29 () (= tptp.funcGraphProp2 @t28)) % 0.15/0.39 (define @t30 () (=> @t7 @t26)) % 0.15/0.39 (define @t31 () (forall @t9 @t30)) % 0.15/0.39 (define @t32 () (=> tptp.funcGraphProp2 @t31)) % 0.15/0.39 (define @t33 () (=> tptp.infuncsetfunc @t32)) % 0.15/0.39 (define @t34 () (not @t33)) % 0.15/0.39 (define @t35 () (_ (_ tptp.setadjoin @t13) tptp.emptyset)) % 0.15/0.39 (define @t36 () (= @t3 @t35)) % 0.15/0.39 (define @t37 () (and @t23 @t36)) % 0.15/0.39 (define @t38 () (exists @t25 @t37)) % 0.15/0.39 (define @t39 () (@list @t3)) % 0.15/0.39 (define @t40 () (lambda @t39 @t38)) % 0.15/0.39 (define @t41 () (@var "Xphi" (-> $$unsorted Bool))) % 0.15/0.39 (define @t42 () (lambda @t25 (_ @t41 @t13))) % 0.15/0.39 (define @t43 () (_ tptp.dsetconstr @t3)) % 0.15/0.39 (define @t44 () (_ @t43 @t42)) % 0.15/0.39 (define @t45 () (@list @t3 @t41)) % 0.15/0.39 (define @t46 () (lambda @t45 (_ tptp.singleton @t44))) % 0.15/0.39 (define @t47 () (_ (_ tptp.cartprod @t3) @t2)) % 0.15/0.39 (define @t48 () (@var "C" $$unsorted)) % 0.15/0.39 (define @t49 () (_ (_ tptp.subset @t48) @t47)) % 0.15/0.39 (define @t50 () (lambda (@list @t3 @t2 @t48) @t49)) % 0.15/0.39 (define @t51 () (@var "R" $$unsorted)) % 0.15/0.39 (define @t52 () (_ @t16 @t51)) % 0.15/0.39 (define @t53 () (lambda @t21 @t52)) % 0.15/0.39 (define @t54 () (=> @t23 (_ (_ tptp.ex1 @t2) @t53))) % 0.15/0.39 (define @t55 () (forall @t25 @t54)) % 0.15/0.39 (define @t56 () (and (_ (_ (_ tptp.breln @t3) @t2) @t51) @t55)) % 0.15/0.39 (define @t57 () (@list @t3 @t2 @t51)) % 0.15/0.39 (define @t58 () (lambda @t57 @t56)) % 0.15/0.39 (define @t59 () (@var "BOUND_VARIABLE_7835" $$unsorted)) % 0.15/0.39 (define @t60 () (tptp.ap @t3 @t2 @t1 @t59)) % 0.15/0.39 (define @t61 () (@var "BOUND_VARIABLE_7837" $$unsorted)) % 0.15/0.39 (define @t62 () (not (tptp.in (tptp.kpair @t59 @t61) @t1))) % 0.15/0.39 (define @t63 () (not (tptp.in @t61 @t2))) % 0.15/0.39 (define @t64 () (not (tptp.in @t59 @t3))) % 0.15/0.39 (define @t65 () (tptp.funcSet @t3 @t2)) % 0.15/0.39 (define @t66 () (tptp.in @t1 @t65)) % 0.15/0.39 (define @t67 () (not @t66)) % 0.15/0.39 (define @t68 () (@list @t3 @t2 @t1 @t59 @t61)) % 0.15/0.39 (define @t69 () (forall @t68 (or @t67 @t64 @t63 @t62 (= @t61 @t60)))) % 0.15/0.39 (define @t70 () (@var "BOUND_VARIABLE_7806" $$unsorted)) % 0.15/0.39 (define @t71 () (tptp.ap @t3 @t2 @t1 @t70)) % 0.15/0.39 (define @t72 () (@var "BOUND_VARIABLE_7808" $$unsorted)) % 0.15/0.39 (define @t73 () (not (tptp.in (tptp.kpair @t70 @t72) @t1))) % 0.15/0.39 (define @t74 () (not (tptp.in @t72 @t2))) % 0.15/0.39 (define @t75 () (not (tptp.in @t70 @t3))) % 0.15/0.39 (define @t76 () (tptp.kpair @t13 @t12)) % 0.15/0.39 (define @t77 () (tptp.in @t76 @t1)) % 0.15/0.39 (define @t78 () (tptp.dsetconstr @t2 (lambda @t21 @t77))) % 0.15/0.39 (define @t79 () (@var "BOUND_VARIABLE_7577" $$unsorted)) % 0.15/0.39 (define @t80 () (tptp.setadjoin @t79 tptp.emptyset)) % 0.15/0.39 (define @t81 () (@list @t79)) % 0.15/0.39 (define @t82 () (tptp.in @t13 @t3)) % 0.15/0.39 (define @t83 () (not @t82)) % 0.15/0.39 (define @t84 () (forall @t25 (or @t83 (not (forall @t81 (or (not (tptp.in @t79 @t78)) (not (= @t80 @t78)))))))) % 0.15/0.39 (define @t85 () (not @t84)) % 0.15/0.39 (define @t86 () (tptp.cartprod @t3 @t2)) % 0.15/0.39 (define @t87 () (tptp.subset @t1 @t86)) % 0.15/0.39 (define @t88 () (not @t87)) % 0.15/0.39 (define @t89 () (= @t71 @t72)) % 0.15/0.39 (define @t90 () (or @t88 @t85 @t75 @t74 @t73 @t89)) % 0.15/0.39 (define @t91 () (or @t75 @t74 @t73 @t89)) % 0.15/0.39 (define @t92 () (or @t88 @t85 @t91)) % 0.15/0.39 (define @t93 () (forall (@list @t3 @t2 @t1 @t70 @t72) @t92)) % 0.15/0.39 (define @t94 () (@list @t70 @t72)) % 0.15/0.39 (define @t95 () (forall @t94 @t92)) % 0.15/0.39 (define @t96 () (forall @t94 @t91)) % 0.15/0.39 (define @t97 () (@var "BOUND_VARIABLE_7779" $$unsorted)) % 0.15/0.39 (define @t98 () (@list @t13 @t97)) % 0.15/0.39 (define @t99 () (or @t88 @t85 @t96)) % 0.15/0.39 (define @t100 () (tptp.ap @t3 @t2 @t1 @t13)) % 0.15/0.39 (define @t101 () (not (tptp.in (tptp.kpair @t13 @t97) @t1))) % 0.15/0.39 (define @t102 () (not (tptp.in @t97 @t2))) % 0.15/0.39 (define @t103 () (@list @t13 @t97)) % 0.15/0.39 (define @t104 () (forall @t103 (or @t83 @t102 @t101 (= @t100 @t97)))) % 0.15/0.39 (define @t105 () (_ tptp.subset @t1)) % 0.15/0.39 (define @t106 () (_ @t105 @t47)) % 0.15/0.39 (define @t107 () (not @t106)) % 0.15/0.39 (define @t108 () (or @t107 @t85 @t104)) % 0.15/0.39 (define @t109 () (and @t106 @t84)) % 0.15/0.39 (define @t110 () (= @t97 @t100)) % 0.15/0.39 (define @t111 () (or @t83 @t102 @t101 @t110)) % 0.15/0.39 (define @t112 () (or @t102 @t101 @t110)) % 0.15/0.39 (define @t113 () (or @t83 @t112)) % 0.15/0.39 (define @t114 () (forall @t103 @t113)) % 0.15/0.39 (define @t115 () (@list @t97)) % 0.15/0.39 (define @t116 () (forall @t115 @t113)) % 0.15/0.39 (define @t117 () (forall @t115 @t112)) % 0.15/0.39 (define @t118 () (or @t83 @t117)) % 0.15/0.39 (define @t119 () (tptp.in @t12 @t2)) % 0.15/0.39 (define @t120 () (forall @t21 (or (not @t119) (not @t77) (= @t12 @t100)))) % 0.15/0.39 (define @t121 () (not @t23)) % 0.15/0.39 (define @t122 () (or @t121 @t120)) % 0.15/0.39 (define @t123 () (= @t12 @t14)) % 0.15/0.39 (define @t124 () (_ tptp.in @t76)) % 0.15/0.39 (define @t125 () (not @t17)) % 0.15/0.39 (define @t126 () (not @t19)) % 0.15/0.39 (define @t127 () (or @t126 @t125 @t123)) % 0.15/0.39 (define @t128 () (=> @t17 @t123)) % 0.15/0.39 (define @t129 () (tptp.in @t76 @t51)) % 0.15/0.39 (define @t130 () (tptp.dsetconstr @t2 (lambda @t21 @t129))) % 0.15/0.39 (define @t131 () (not (forall @t81 (or (not (tptp.in @t79 @t130)) (not (= @t80 @t130)))))) % 0.15/0.39 (define @t132 () (_ (_ tptp.subset @t51) @t47)) % 0.15/0.39 (define @t133 () (and @t132 (forall @t25 (or @t83 @t131)))) % 0.15/0.39 (define @t134 () (lambda (@list @t51) @t133)) % 0.15/0.39 (define @t135 () (lambda (@list @t2 @t51) @t133)) % 0.15/0.39 (define @t136 () (_ (lambda @t57 @t133) @t3)) % 0.15/0.39 (define @t137 () (_ (_ @t136 @t2) @t1)) % 0.15/0.39 (define @t138 () (=> @t137 @t26)) % 0.15/0.39 (define @t139 () (forall @t9 @t138)) % 0.15/0.39 (define @t140 () (or @t121 @t131)) % 0.15/0.39 (define @t141 () (tptp.dsetconstr @t2 @t53)) % 0.15/0.39 (define @t142 () (= @t80 @t141)) % 0.15/0.39 (define @t143 () (not @t142)) % 0.15/0.39 (define @t144 () (tptp.in @t79 @t141)) % 0.15/0.39 (define @t145 () (not @t144)) % 0.15/0.39 (define @t146 () (or @t145 @t143)) % 0.15/0.39 (define @t147 () (not (= @t141 @t80))) % 0.15/0.39 (define @t148 () (or @t145 @t147)) % 0.15/0.39 (define @t149 () (forall @t81 @t148)) % 0.15/0.39 (define @t150 () (not @t149)) % 0.15/0.39 (define @t151 () (tptp.dsetconstr @t2 @t41)) % 0.15/0.39 (define @t152 () (not (tptp.in @t79 @t151))) % 0.15/0.39 (define @t153 () (@list @t41)) % 0.15/0.39 (define @t154 () (not (= @t80 @t151))) % 0.15/0.39 (define @t155 () (or @t152 @t154)) % 0.15/0.39 (define @t156 () (forall @t81 @t155)) % 0.15/0.39 (define @t157 () (not @t156)) % 0.15/0.39 (define @t158 () (tptp.setadjoin @t13 tptp.emptyset)) % 0.15/0.39 (define @t159 () (forall @t25 (or (not (tptp.in @t13 @t151)) (not (= @t158 @t151))))) % 0.15/0.39 (define @t160 () (@list @t13)) % 0.15/0.39 (define @t161 () (not @t159)) % 0.15/0.39 (define @t162 () (lambda @t153 @t161)) % 0.15/0.39 (define @t163 () (tptp.dsetconstr @t3 @t41)) % 0.15/0.39 (define @t164 () (_ (lambda @t45 (not (forall @t25 (or (not (tptp.in @t13 @t163)) (not (= @t158 @t163)))))) @t2)) % 0.15/0.39 (define @t165 () (=> @t23 (_ @t164 @t53))) % 0.15/0.39 (define @t166 () (forall @t25 @t165)) % 0.15/0.39 (define @t167 () (lambda (@list @t48) @t49)) % 0.15/0.39 (define @t168 () (lambda (@list @t2 @t48) @t49)) % 0.15/0.39 (define @t169 () (_ @t50 @t3)) % 0.15/0.39 (define @t170 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.15/0.39 (define @t171 () (_ @t41 @t170)) % 0.15/0.39 (define @t172 () (@list @t170)) % 0.15/0.39 (define @t173 () (lambda @t172 @t171)) % 0.15/0.39 (define @t174 () (tptp.dsetconstr @t3 @t173)) % 0.15/0.39 (define @t175 () (= @t158 @t174)) % 0.15/0.39 (define @t176 () (not @t175)) % 0.15/0.39 (define @t177 () (tptp.in @t13 @t174)) % 0.15/0.39 (define @t178 () (not @t177)) % 0.15/0.39 (define @t179 () (or @t178 @t176)) % 0.15/0.39 (define @t180 () (_ @t41 @t170)) % 0.15/0.39 (define @t181 () (lambda @t172 @t180)) % 0.15/0.39 (define @t182 () (_ @t43 @t181)) % 0.15/0.39 (define @t183 () (= @t158 @t182)) % 0.15/0.39 (define @t184 () (not @t183)) % 0.15/0.39 (define @t185 () (tptp.in @t13 @t182)) % 0.15/0.39 (define @t186 () (not @t185)) % 0.15/0.39 (define @t187 () (or @t186 @t184)) % 0.15/0.39 (define @t188 () (= @t158 @t44)) % 0.15/0.39 (define @t189 () (not @t188)) % 0.15/0.39 (define @t190 () (tptp.in @t13 @t44)) % 0.15/0.39 (define @t191 () (not @t190)) % 0.15/0.39 (define @t192 () (or @t191 @t189)) % 0.15/0.39 (define @t193 () (not (= @t44 @t158))) % 0.15/0.39 (define @t194 () (or @t191 @t193)) % 0.15/0.39 (define @t195 () (forall @t25 @t194)) % 0.15/0.39 (define @t196 () (not @t195)) % 0.15/0.39 (define @t197 () (not @t36)) % 0.15/0.39 (define @t198 () (or @t121 @t197)) % 0.15/0.39 (define @t199 () (forall @t25 (not @t37))) % 0.15/0.39 (define @t200 () (not @t199)) % 0.15/0.39 (define @t201 () (=> tptp.funcGraphProp2 @t69)) % 0.15/0.39 (define @t202 () (@var "BOUND_VARIABLE_7731" $$unsorted)) % 0.15/0.39 (define @t203 () (tptp.dsetconstr @t2 (lambda @t21 (tptp.in (tptp.kpair @t202 @t12) @t1)))) % 0.15/0.39 (define @t204 () (or (not (tptp.in @t202 @t3)) (not (forall @t81 (or (not (tptp.in @t79 @t203)) (not (= @t80 @t203))))))) % 0.15/0.39 (define @t205 () (and @t87 @t204)) % 0.15/0.39 (define @t206 () (or @t67 @t205)) % 0.15/0.39 (define @t207 () (@list @t202)) % 0.15/0.39 (define @t208 () (forall @t207 @t206)) % 0.15/0.39 (define @t209 () (forall @t207 @t204)) % 0.15/0.39 (define @t210 () (forall @t207 @t87)) % 0.15/0.39 (define @t211 () (and @t210 @t209)) % 0.15/0.39 (define @t212 () (forall @t207 @t205)) % 0.15/0.39 (define @t213 () (or @t67 @t212)) % 0.15/0.39 (define @t214 () (not @t7)) % 0.15/0.39 (define @t215 () (or @t214 @t109)) % 0.15/0.39 (define @t216 () (=> @t7 @t137)) % 0.15/0.39 (define @t217 () (forall @t9 @t216)) % 0.15/0.39 (define @t218 () (=> tptp.infuncsetfunc @t201)) % 0.15/0.39 (define @t219 () (= @t60 @t61)) % 0.15/0.39 (define @t220 () (or @t67 @t64 @t63 @t62 @t219)) % 0.15/0.39 (define @t221 () (or @t64 @t63 @t62 @t219)) % 0.15/0.39 (define @t222 () (or @t67 @t221)) % 0.15/0.39 (define @t223 () (forall @t68 @t222)) % 0.15/0.39 (define @t224 () (@list @t59 @t61)) % 0.15/0.39 (define @t225 () (forall @t224 @t222)) % 0.15/0.39 (define @t226 () (forall @t224 @t221)) % 0.15/0.39 (define @t227 () (or @t67 @t226)) % 0.15/0.39 (define @t228 () (or @t214 @t104)) % 0.15/0.39 (define @t229 () (@quantifiers_skolemize @t69 1)) % 0.15/0.39 (define @t230 () (@quantifiers_skolemize @t69 0)) % 0.15/0.39 (define @t231 () (@quantifiers_skolemize @t69 2)) % 0.15/0.39 (define @t232 () (tptp.in @t231 (tptp.funcSet @t230 @t229))) % 0.15/0.39 (define @t233 () (@quantifiers_skolemize @t69 3)) % 0.15/0.39 (define @t234 () (@quantifiers_skolemize @t69 4)) % 0.15/0.39 (define @t235 () (= @t234 (tptp.ap @t230 @t229 @t231 @t233))) % 0.15/0.39 (define @t236 () (tptp.in (tptp.kpair @t233 @t234) @t231)) % 0.15/0.39 (define @t237 () (not @t236)) % 0.15/0.39 (define @t238 () (tptp.in @t234 @t229)) % 0.15/0.39 (define @t239 () (not @t238)) % 0.15/0.39 (define @t240 () (tptp.in @t233 @t230)) % 0.15/0.39 (define @t241 () (not @t240)) % 0.15/0.39 (define @t242 () (not @t232)) % 0.15/0.39 (define @t243 () (or @t242 @t241 @t239 @t237 @t235)) % 0.15/0.39 (define @t244 () (@list true)) % 0.15/0.39 (define @t245 () (@list @t243)) % 0.15/0.39 (define @t246 () (tptp.dsetconstr @t229 (lambda @t21 (tptp.in (tptp.kpair @t233 @t12) @t231)))) % 0.15/0.39 (define @t247 () (tptp.subset @t231 (tptp.cartprod @t230 @t229))) % 0.15/0.39 (define @t248 () (and @t247 (or @t241 (not (forall @t81 (or (not (tptp.in @t79 @t246)) (not (= @t80 @t246)))))))) % 0.15/0.39 (define @t249 () (or @t242 @t248)) % 0.15/0.39 (define @t250 () (tptp.dsetconstr @t229 (lambda @t21 (tptp.in @t76 @t231)))) % 0.15/0.39 (define @t251 () (forall @t25 (or (not (tptp.in @t13 @t230)) (not (forall @t81 (or (not (tptp.in @t79 @t250)) (not (= @t80 @t250)))))))) % 0.15/0.39 (define @t252 () (not @t251)) % 0.15/0.39 (define @t253 () (not @t247)) % 0.15/0.39 (define @t254 () (or @t253 @t252 @t241 @t239 @t237 @t235)) % 0.15/0.39 (define @t255 () (@quantifiers_skolemize @t251 0)) % 0.15/0.39 (define @t256 () (tptp.dsetconstr @t229 (lambda @t21 (tptp.in (tptp.kpair @t255 @t12) @t231)))) % 0.15/0.39 (define @t257 () (or (not (tptp.in @t255 @t230)) (not (forall @t81 (or (not (tptp.in @t79 @t256)) (not (= @t80 @t256))))))) % 0.15/0.39 (define @t258 () (and @t247 @t257)) % 0.15/0.39 (define @t259 () (not @t258)) % 0.15/0.39 (define @t260 () (or @t242 @t258)) % 0.15/0.39 (assume @p1 @t11) % 0.15/0.39 (assume @p2 @t29) % 0.15/0.39 (assume @p3 @t34) % 0.15/0.39 (assume @p4 true) % 0.15/0.39 (step @p5 (= tptp.singleton @t40) :rule refl :args (@t40)) % 0.15/0.39 (step @p6 (= tptp.ex1 @t46) :rule refl :args (@t46)) % 0.15/0.39 (step @p7 (= tptp.breln @t50) :rule refl :args (@t50)) % 0.15/0.39 (step @p8 (= tptp.func @t58) :rule refl :args (@t58)) % 0.15/0.39 (step @p9 :rule refl :args (@t69)) % 0.15/0.39 (step @p10 :rule eq-symm :args (@t71 @t72)) % 0.15/0.39 (step @p11 :rule refl :args (@t73)) % 0.15/0.39 (step @p12 :rule refl :args (@t74)) % 0.15/0.39 (step @p13 :rule refl :args (@t75)) % 0.15/0.39 (step @p14 :rule refl :args (@t85)) % 0.15/0.39 (step @p15 :rule refl :args (@t88)) % 0.15/0.39 (step @p16 :rule nary_cong :premises (@p15 @p14 @p13 @p12 @p11 @p10) :args (@t90)) % 0.15/0.39 (step @p17 :rule aci_norm :args ((= @t92 @t90))) % 0.15/0.39 (step @p18 :rule trans :premises (@p17 @p16)) % 0.15/0.39 (step @p19 :rule cong :premises (@p18) :args (@t93)) % 0.15/0.39 (step @p20 :rule quant-merge-prenex :args ((= (forall @t9 @t95) @t93))) % 0.15/0.39 (step @p21 :rule alpha_equiv :args (@t96 (@list @t70 @t72) @t98)) % 0.15/0.39 (step @p22 :rule refl :args (@t85)) % 0.15/0.39 (step @p23 :rule refl :args (@t88)) % 0.15/0.39 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t99)) % 0.15/0.39 (step @p25 :rule quant-miniscope-or :args ((= @t95 @t99))) % 0.15/0.39 (step @p26 :rule trans :premises (@p25 @p24)) % 0.15/0.39 (step @p27 :rule symm :premises (@p26)) % 0.15/0.39 (step @p28 :rule cong :premises (@p27) :args ((forall @t9 (or @t88 @t85 @t104)))) % 0.15/0.39 (step @p29 :rule trans :premises (@p28 @p20)) % 0.15/0.39 (step @p30 :rule trans :premises (@p29 @p19)) % 0.15/0.39 (step @p31 :rule refl :args 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0.15/0.39 (step @p63 :rule refl :args (@t102)) % 0.15/0.39 (step @p64 :rule refl :args (@t83)) % 0.15/0.39 (step @p65 :rule nary_cong :premises (@p64 @p63 @p62 @p61) :args (@t111)) % 0.15/0.39 (step @p66 :rule aci_norm :args ((= @t113 @t111))) % 0.15/0.39 (step @p67 :rule trans :premises (@p66 @p65)) % 0.15/0.39 (step @p68 :rule cong :premises (@p67) :args (@t114)) % 0.15/0.39 (step @p69 :rule quant-merge-prenex :args ((= (forall @t25 @t116) @t114))) % 0.15/0.39 (step @p70 :rule alpha_equiv :args (@t117 (@list @t97) (@list @t12))) % 0.15/0.39 (step @p71 :rule refl :args (@t83)) % 0.15/0.39 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t118)) % 0.15/0.39 (step @p73 :rule quant-miniscope-or :args ((= @t116 @t118))) % 0.15/0.39 (step @p74 :rule trans :premises (@p73 @p72)) % 0.15/0.39 (step @p75 :rule symm :premises (@p74)) % 0.15/0.39 (step @p76 :rule cong :premises (@p75) :args ((forall @t25 (or @t83 @t120)))) % 0.15/0.39 (step @p77 :rule trans :premises (@p76 @p69)) % 0.15/0.39 (step @p78 :rule trans :premises (@p77 @p68)) % 0.15/0.39 (step @p79 :rule refl :args (@t120)) % 0.15/0.39 (step @p80 :rule refl :args (@t82)) % 0.15/0.39 (step @p81 :rule refl :args (@t23)) % 0.15/0.39 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t23 @t82))) % 0.15/0.39 (step @p83 :rule symm :premises (@p82)) % 0.15/0.39 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.15/0.39 (step @p85 :rule cong :premises (@p84) :args (@t121)) % 0.15/0.39 (step @p86 :rule nary_cong :premises (@p85 @p79) :args (@t122)) % 0.15/0.39 (step @p87 :rule cong :premises (@p86) :args ((forall @t25 @t122))) % 0.15/0.39 (step @p88 :rule trans :premises (@p87 @p78)) % 0.15/0.39 (step @p89 :rule bool-impl-elim :args (@t23 @t120)) % 0.15/0.39 (step @p90 :rule cong :premises (@p89) :args ((forall @t25 (=> @t23 @t120)))) % 0.15/0.39 (step @p91 :rule trans :premises (@p90 @p88)) % 0.15/0.39 (step @p92 :rule refl :args (@t100)) % 0.15/0.39 (step @p93 :rule refl :args (@t14)) % 0.15/0.39 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t14 @t100))) % 0.15/0.39 (step @p95 :rule symm :premises (@p94)) % 0.15/0.39 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.15/0.39 (step @p97 :rule refl :args (@t12)) % 0.15/0.39 (step @p98 :rule cong :premises (@p97 @p96) :args (@t123)) % 0.15/0.39 (step @p99 :rule refl :args ((tptp.in @t15 @t1))) % 0.15/0.39 (step @p100 :rule refl :args (@t76)) % 0.15/0.39 (step @p101 :rule cong :premises (@p100 @p34) :args (@t77)) % 0.15/0.39 (step @p102 :rule trans :premises (@p101 @p99)) % 0.15/0.39 (step @p103 :rule refl :args (tptp.in)) % 0.15/0.39 (step @p104 :rule ho_cong :premises (@p103 @p100)) % 0.15/0.39 (step @p105 :rule ho_cong :premises (@p104 @p34)) % 0.15/0.39 (step @p106 :rule cong :premises (@p105 @p102) :args ((= (_ @t124 @t1) @t77))) % 0.15/0.39 (step @p107 :rule symm :premises (@p106)) % 0.15/0.39 (step @p108 :rule refl :args (@t17)) % 0.15/0.39 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.15/0.39 (step 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:rule trans :premises (@p170 @p168)) % 0.15/0.39 (step @p172 :rule ho_cong :premises (@p104 @p169)) % 0.15/0.39 (step @p173 :rule cong :premises (@p172 @p171) :args ((= (_ @t124 @t51) @t129))) % 0.15/0.39 (step @p174 :rule symm :premises (@p173)) % 0.15/0.39 (step @p175 :rule refl :args (@t52)) % 0.15/0.39 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.15/0.39 (step @p177 :rule ho_cong :premises (@p114 @p169)) % 0.15/0.39 (step @p178 :rule trans :premises (@p177 @p176)) % 0.15/0.39 (step @p179 :rule cong :premises (@p178) :args (@t53)) % 0.15/0.39 (step @p180 :rule refl :args (@t2)) % 0.15/0.39 (step @p181 :rule cong :premises (@p180 @p179) :args (@t141)) % 0.15/0.39 (step @p182 :rule refl :args (@t80)) % 0.15/0.39 (step @p183 :rule cong :premises (@p182 @p181) :args (@t142)) % 0.15/0.39 (step @p184 :rule cong :premises (@p183) :args (@t143)) % 0.15/0.39 (step @p185 :rule refl :args (@t79)) % 0.15/0.39 (step @p186 :rule cong :premises (@p185 @p181) :args (@t144)) % 0.15/0.39 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@t233 @t234))) % 0.15/0.40 (step @p423 :rule not_implies_elim1 :premises (@p410)) % 0.15/0.40 (step @p424 :rule instantiate :premises (@p423) :args ((@list @t230 @t229 @t231 @t233))) % 0.15/0.40 (step @p425 :rule cnf_or_pos :args (@t249)) % 0.15/0.40 (step @p426 :rule reordering :premises (@p425) :args ((or @t242 @t248 (not @t249)))) % 0.15/0.40 (step @p427 :rule chain_m_resolution :premises (@p426 @p420 @p424) :args (@t248 (@list false false) (@list @t232 @t249))) % 0.15/0.40 (step @p428 :rule cnf_and_pos :args (@t248 0)) % 0.15/0.40 (step @p429 :rule reordering :premises (@p428) :args ((or @t247 (not @t248)))) % 0.15/0.40 (step @p430 :rule chain_m_resolution :premises (@p429 @p427) :args (@t247 (@list false) (@list @t248))) % 0.15/0.40 (step @p431 :rule cnf_or_neg :args (@t243 4)) % 0.15/0.40 (step @p432 :rule chain_m_resolution :premises (@p431 @p413) :args ((not @t235) @t244 @t245)) % 0.15/0.40 (step @p433 :rule bool-double-not-elim :args (@t236)) % 0.15/0.40 (step @p434 :rule nary_cong :premises (@p415 @p433) :args ((or @t243 (not @t237)))) % 0.15/0.40 (step @p435 :rule cnf_or_neg :args (@t243 3)) % 0.15/0.40 (step @p436 :rule eq_resolve :premises (@p435 @p434)) % 0.15/0.40 (step @p437 :rule reordering :premises (@p436) :args ((or @t236 @t243))) % 0.15/0.40 (step @p438 :rule chain_m_resolution :premises (@p437 @p413) :args (@t236 @t244 @t245)) % 0.15/0.40 (step @p439 :rule bool-double-not-elim :args (@t238)) % 0.15/0.40 (step @p440 :rule nary_cong :premises (@p415 @p439) :args ((or @t243 (not @t239)))) % 0.15/0.40 (step @p441 :rule cnf_or_neg :args (@t243 2)) % 0.15/0.40 (step @p442 :rule eq_resolve :premises (@p441 @p440)) % 0.15/0.40 (step @p443 :rule reordering :premises (@p442) :args ((or @t238 @t243))) % 0.15/0.40 (step @p444 :rule chain_m_resolution :premises (@p443 @p413) :args (@t238 @t244 @t245)) % 0.15/0.40 (step @p445 :rule bool-double-not-elim :args (@t240)) % 0.15/0.40 (step @p446 :rule nary_cong :premises (@p415 @p445) :args ((or @t243 (not @t241)))) % 0.15/0.40 (step @p447 :rule cnf_or_neg :args (@t243 1)) % 0.15/0.40 (step @p448 :rule eq_resolve :premises (@p447 @p446)) % 0.15/0.40 (step @p449 :rule reordering :premises (@p448) :args ((or @t240 @t243))) % 0.15/0.40 (step @p450 :rule chain_m_resolution :premises (@p449 @p413) :args (@t240 @t244 @t245)) % 0.15/0.40 (step @p451 :rule cnf_or_pos :args (@t254)) % 0.15/0.40 (step @p452 :rule reordering :premises (@p451) :args ((or @t241 @t239 @t237 @t235 @t253 @t252 (not @t254)))) % 0.15/0.40 (step @p453 :rule chain_m_resolution :premises (@p452 @p450 @p444 @p438 @p432 @p430 @p422) :args (@t252 (@list false false false true false false) (@list @t240 @t238 @t236 @t235 @t247 @t254))) % 0.15/0.40 (step @p454 :rule skolemize :premises (@p453)) % 0.15/0.40 (step @p455 :rule cnf_and_pos :args (@t258 1)) % 0.15/0.40 (step @p456 :rule reordering :premises (@p455) :args ((or @t257 @t259))) % 0.15/0.40 (step @p457 :rule chain_m_resolution :premises (@p456 @p454) :args (@t259 @t244 (@list @t257))) % 0.15/0.40 (step @p458 :rule instantiate :premises (@p423) :args ((@list @t230 @t229 @t231 @t255))) % 0.15/0.40 (step @p459 :rule cnf_or_pos :args (@t260)) % 0.15/0.40 (step @p460 :rule reordering :premises (@p459) :args ((or @t242 @t258 (not @t260)))) % 0.15/0.40 (step @p461 false :rule chain_m_resolution :premises (@p460 @p458 @p457 @p420) :args (false (@list false true false) (@list @t260 @t258 @t232))) % 0.15/0.40 ) % 0.15/0.40 % SZS output end Proof % 0.15/0.40 % cvc5 exiting %------------------------------------------------------------------------------