%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU673^2 : 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 : n014.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 08:52:40 AM UTC 2026 % Result : Theorem 0.34s 0.66s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU673^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n014.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 17:45:43 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.52 %----Proving TH0 % 0.34/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.66 % SZS status Theorem % 0.34/0.66 % SZS output start Proof % 0.34/0.66 ( % 0.34/0.66 (declare-sort $$unsorted 0) % 0.34/0.66 (declare-const tptp.emptyset $$unsorted) % 0.34/0.66 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.66 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.34/0.66 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.34/0.66 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.66 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.34/0.66 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.66 (declare-const tptp.funcImageSingleton Bool) % 0.34/0.66 (declare-const tptp.theprop Bool) % 0.34/0.66 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.34/0.66 (declare-const tptp.dsetconstrEL Bool) % 0.34/0.66 (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)))))))) % 0.34/0.66 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.34/0.66 (define tptp.breln () (let ((_let_1 (@var "B" $$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))))))) % 0.34/0.66 (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" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.34/0.66 (define @t1 () (@var "A" $$unsorted)) % 0.34/0.66 (define @t2 () (@var "Xx" $$unsorted)) % 0.34/0.66 (define @t3 () (_ tptp.in @t2)) % 0.34/0.66 (define @t4 () (_ @t3 @t1)) % 0.34/0.66 (define @t5 () (@var "Xy" $$unsorted)) % 0.34/0.66 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.34/0.66 (define @t7 () (_ @t6 @t5)) % 0.34/0.66 (define @t8 () (@list @t5)) % 0.34/0.66 (define @t9 () (lambda @t8 @t7)) % 0.34/0.66 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.34/0.66 (define @t11 () (_ @t10 @t9)) % 0.34/0.66 (define @t12 () (_ @t3 @t11)) % 0.34/0.66 (define @t13 () (@list @t1 @t6 @t2)) % 0.34/0.66 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.34/0.66 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.34/0.66 (define @t16 () (@var "X" $$unsorted)) % 0.34/0.66 (define @t17 () (_ tptp.setunion @t16)) % 0.34/0.66 (define @t18 () (_ (_ tptp.in @t17) @t16)) % 0.34/0.66 (define @t19 () (=> (_ tptp.singleton @t16) @t18)) % 0.34/0.66 (define @t20 () (@list @t16)) % 0.34/0.66 (define @t21 () (forall @t20 @t19)) % 0.34/0.66 (define @t22 () (= tptp.theprop @t21)) % 0.34/0.66 (define @t23 () (@var "Xf" $$unsorted)) % 0.34/0.66 (define @t24 () (_ (_ tptp.kpair @t2) @t5)) % 0.34/0.66 (define @t25 () (_ tptp.in @t24)) % 0.34/0.66 (define @t26 () (_ @t25 @t23)) % 0.34/0.66 (define @t27 () (lambda @t8 @t26)) % 0.34/0.66 (define @t28 () (@var "B" $$unsorted)) % 0.34/0.66 (define @t29 () (_ tptp.dsetconstr @t28)) % 0.34/0.66 (define @t30 () (_ @t29 @t27)) % 0.34/0.66 (define @t31 () (=> @t4 (_ tptp.singleton @t30))) % 0.34/0.66 (define @t32 () (@list @t2)) % 0.34/0.66 (define @t33 () (forall @t32 @t31)) % 0.34/0.66 (define @t34 () (_ (_ (_ tptp.func @t1) @t28) @t23)) % 0.34/0.66 (define @t35 () (=> @t34 @t33)) % 0.34/0.66 (define @t36 () (@list @t1 @t28 @t23)) % 0.34/0.66 (define @t37 () (forall @t36 @t35)) % 0.34/0.66 (define @t38 () (= tptp.funcImageSingleton @t37)) % 0.34/0.66 (define @t39 () (_ tptp.setunion @t30)) % 0.34/0.66 (define @t40 () (_ (_ tptp.in @t39) @t28)) % 0.34/0.66 (define @t41 () (forall @t32 (=> @t4 @t40))) % 0.34/0.66 (define @t42 () (=> @t34 @t41)) % 0.34/0.66 (define @t43 () (forall @t36 @t42)) % 0.34/0.66 (define @t44 () (=> tptp.funcImageSingleton @t43)) % 0.34/0.66 (define @t45 () (=> tptp.theprop @t44)) % 0.34/0.66 (define @t46 () (=> tptp.dsetconstrEL @t45)) % 0.34/0.66 (define @t47 () (not @t46)) % 0.34/0.66 (define @t48 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.34/0.66 (define @t49 () (= @t1 @t48)) % 0.34/0.66 (define @t50 () (and @t4 @t49)) % 0.34/0.66 (define @t51 () (exists @t32 @t50)) % 0.34/0.66 (define @t52 () (@list @t1)) % 0.34/0.66 (define @t53 () (lambda @t52 @t51)) % 0.34/0.66 (define @t54 () (lambda @t32 (_ @t6 @t2))) % 0.34/0.66 (define @t55 () (_ @t10 @t54)) % 0.34/0.66 (define @t56 () (@list @t1 @t6)) % 0.34/0.66 (define @t57 () (lambda @t56 (_ tptp.singleton @t55))) % 0.34/0.66 (define @t58 () (_ (_ tptp.cartprod @t1) @t28)) % 0.34/0.66 (define @t59 () (@var "C" $$unsorted)) % 0.34/0.66 (define @t60 () (_ (_ tptp.subset @t59) @t58)) % 0.34/0.66 (define @t61 () (lambda (@list @t1 @t28 @t59) @t60)) % 0.34/0.66 (define @t62 () (@var "R" $$unsorted)) % 0.34/0.66 (define @t63 () (_ @t25 @t62)) % 0.34/0.66 (define @t64 () (lambda @t8 @t63)) % 0.34/0.66 (define @t65 () (=> @t4 (_ (_ tptp.ex1 @t28) @t64))) % 0.34/0.66 (define @t66 () (forall @t32 @t65)) % 0.34/0.66 (define @t67 () (and (_ (_ (_ tptp.breln @t1) @t28) @t62) @t66)) % 0.34/0.66 (define @t68 () (@list @t1 @t28 @t62)) % 0.34/0.66 (define @t69 () (lambda @t68 @t67)) % 0.34/0.66 (define @t70 () (@var "BOUND_VARIABLE_7898" $$unsorted)) % 0.34/0.66 (define @t71 () (tptp.in (tptp.setunion (tptp.dsetconstr @t28 (lambda @t8 (tptp.in (tptp.kpair @t70 @t5) @t23)))) @t28)) % 0.34/0.66 (define @t72 () (not (tptp.in @t70 @t1))) % 0.34/0.66 (define @t73 () (tptp.kpair @t2 @t5)) % 0.34/0.66 (define @t74 () (tptp.in @t73 @t23)) % 0.34/0.66 (define @t75 () (lambda @t8 @t74)) % 0.34/0.66 (define @t76 () (tptp.dsetconstr @t28 @t75)) % 0.34/0.66 (define @t77 () (@var "BOUND_VARIABLE_7597" $$unsorted)) % 0.34/0.66 (define @t78 () (tptp.setadjoin @t77 tptp.emptyset)) % 0.34/0.66 (define @t79 () (@list @t77)) % 0.34/0.66 (define @t80 () (tptp.in @t2 @t1)) % 0.34/0.66 (define @t81 () (not @t80)) % 0.34/0.66 (define @t82 () (forall @t32 (or @t81 (not (forall @t79 (or (not (tptp.in @t77 @t76)) (not (= @t78 @t76)))))))) % 0.34/0.66 (define @t83 () (not @t82)) % 0.34/0.66 (define @t84 () (tptp.cartprod @t1 @t28)) % 0.34/0.66 (define @t85 () (tptp.subset @t23 @t84)) % 0.34/0.66 (define @t86 () (not @t85)) % 0.34/0.66 (define @t87 () (or @t86 @t83 @t72 @t71)) % 0.34/0.66 (define @t88 () (@list @t1 @t28 @t23 @t70)) % 0.34/0.66 (define @t89 () (forall @t88 @t87)) % 0.34/0.66 (define @t90 () (@var "BOUND_VARIABLE_7848" $$unsorted)) % 0.34/0.66 (define @t91 () (tptp.dsetconstr @t28 (lambda @t8 (tptp.in (tptp.kpair @t90 @t5) @t23)))) % 0.34/0.66 (define @t92 () (@var "BOUND_VARIABLE_7799" $$unsorted)) % 0.34/0.66 (define @t93 () (tptp.setadjoin @t92 tptp.emptyset)) % 0.34/0.66 (define @t94 () (not (= @t91 @t93))) % 0.34/0.66 (define @t95 () (not (tptp.in @t92 @t91))) % 0.34/0.66 (define @t96 () (or @t95 @t94)) % 0.34/0.66 (define @t97 () (@list @t92)) % 0.34/0.66 (define @t98 () (forall @t97 @t96)) % 0.34/0.66 (define @t99 () (not @t98)) % 0.34/0.66 (define @t100 () (not (tptp.in @t90 @t1))) % 0.34/0.66 (define @t101 () (or @t86 @t83 @t100 @t99)) % 0.34/0.66 (define @t102 () (or @t100 @t99)) % 0.34/0.66 (define @t103 () (or @t86 @t83 @t102)) % 0.34/0.66 (define @t104 () (forall (@list @t1 @t28 @t23 @t90) @t103)) % 0.34/0.66 (define @t105 () (@list @t90)) % 0.34/0.66 (define @t106 () (forall @t105 @t103)) % 0.34/0.66 (define @t107 () (forall @t105 @t102)) % 0.34/0.66 (define @t108 () (@list @t2)) % 0.34/0.66 (define @t109 () (or @t86 @t83 @t107)) % 0.34/0.66 (define @t110 () (not (forall @t97 (or (not (tptp.in @t92 @t76)) (not (= @t76 @t93)))))) % 0.34/0.66 (define @t111 () (forall @t32 (or @t81 @t110))) % 0.34/0.66 (define @t112 () (_ tptp.subset @t23)) % 0.34/0.66 (define @t113 () (_ @t112 @t58)) % 0.34/0.66 (define @t114 () (not @t113)) % 0.34/0.66 (define @t115 () (or @t114 @t83 @t111)) % 0.34/0.66 (define @t116 () (or @t114 @t83)) % 0.34/0.66 (define @t117 () (and @t113 @t82)) % 0.34/0.66 (define @t118 () (not @t117)) % 0.34/0.66 (define @t119 () (not @t4)) % 0.34/0.66 (define @t120 () (or @t119 @t110)) % 0.34/0.66 (define @t121 () (_ tptp.in @t73)) % 0.34/0.66 (define @t122 () (= @t30 @t93)) % 0.34/0.66 (define @t123 () (not @t122)) % 0.34/0.66 (define @t124 () (tptp.in @t92 @t30)) % 0.34/0.66 (define @t125 () (not @t124)) % 0.34/0.66 (define @t126 () (or @t125 @t123)) % 0.34/0.66 (define @t127 () (forall @t97 @t126)) % 0.34/0.66 (define @t128 () (not @t127)) % 0.34/0.66 (define @t129 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.34/0.66 (define @t130 () (forall @t32 (or @t81 (not (= @t1 @t129))))) % 0.34/0.66 (define @t131 () (not @t130)) % 0.34/0.66 (define @t132 () (lambda @t52 @t131)) % 0.34/0.66 (define @t133 () (=> @t4 (_ @t132 @t30))) % 0.34/0.66 (define @t134 () (forall @t32 @t133)) % 0.34/0.66 (define @t135 () (tptp.in @t73 @t62)) % 0.34/0.66 (define @t136 () (tptp.dsetconstr @t28 (lambda @t8 @t135))) % 0.34/0.66 (define @t137 () (not (forall @t79 (or (not (tptp.in @t77 @t136)) (not (= @t78 @t136)))))) % 0.34/0.66 (define @t138 () (_ (_ tptp.subset @t62) @t58)) % 0.34/0.66 (define @t139 () (and @t138 (forall @t32 (or @t81 @t137)))) % 0.34/0.66 (define @t140 () (lambda (@list @t62) @t139)) % 0.34/0.66 (define @t141 () (lambda (@list @t28 @t62) @t139)) % 0.34/0.66 (define @t142 () (_ (lambda @t68 @t139) @t1)) % 0.34/0.66 (define @t143 () (_ (_ @t142 @t28) @t23)) % 0.34/0.66 (define @t144 () (=> @t143 @t134)) % 0.34/0.66 (define @t145 () (forall @t36 @t144)) % 0.34/0.66 (define @t146 () (not @t49)) % 0.34/0.66 (define @t147 () (or @t119 @t146)) % 0.34/0.66 (define @t148 () (forall @t32 (not @t50))) % 0.34/0.66 (define @t149 () (not @t148)) % 0.34/0.66 (define @t150 () (or @t119 @t137)) % 0.34/0.66 (define @t151 () (tptp.dsetconstr @t28 @t64)) % 0.34/0.66 (define @t152 () (= @t78 @t151)) % 0.34/0.66 (define @t153 () (not @t152)) % 0.34/0.66 (define @t154 () (tptp.in @t77 @t151)) % 0.34/0.66 (define @t155 () (not @t154)) % 0.34/0.66 (define @t156 () (or @t155 @t153)) % 0.34/0.66 (define @t157 () (not (= @t151 @t78))) % 0.34/0.66 (define @t158 () (or @t155 @t157)) % 0.34/0.66 (define @t159 () (forall @t79 @t158)) % 0.34/0.66 (define @t160 () (not @t159)) % 0.34/0.66 (define @t161 () (tptp.dsetconstr @t28 @t6)) % 0.34/0.66 (define @t162 () (not (tptp.in @t77 @t161))) % 0.34/0.66 (define @t163 () (@list @t6)) % 0.34/0.66 (define @t164 () (not (= @t78 @t161))) % 0.34/0.66 (define @t165 () (or @t162 @t164)) % 0.34/0.66 (define @t166 () (forall @t79 @t165)) % 0.34/0.66 (define @t167 () (not @t166)) % 0.34/0.66 (define @t168 () (forall @t32 (or (not (tptp.in @t2 @t161)) (not (= @t129 @t161))))) % 0.34/0.66 (define @t169 () (not @t168)) % 0.34/0.66 (define @t170 () (lambda @t163 @t169)) % 0.34/0.66 (define @t171 () (tptp.dsetconstr @t1 @t6)) % 0.34/0.66 (define @t172 () (not (tptp.in @t2 @t171))) % 0.34/0.66 (define @t173 () (_ (lambda @t56 (not (forall @t32 (or @t172 (not (= @t129 @t171)))))) @t28)) % 0.34/0.66 (define @t174 () (=> @t4 (_ @t173 @t64))) % 0.34/0.66 (define @t175 () (forall @t32 @t174)) % 0.34/0.66 (define @t176 () (lambda (@list @t59) @t60)) % 0.34/0.66 (define @t177 () (lambda (@list @t28 @t59) @t60)) % 0.34/0.66 (define @t178 () (_ @t61 @t1)) % 0.34/0.66 (define @t179 () (@var "BOUND_VARIABLE_7490" $$unsorted)) % 0.34/0.66 (define @t180 () (_ @t6 @t179)) % 0.34/0.66 (define @t181 () (@list @t179)) % 0.34/0.66 (define @t182 () (lambda @t181 @t180)) % 0.34/0.66 (define @t183 () (tptp.dsetconstr @t1 @t182)) % 0.34/0.66 (define @t184 () (= @t129 @t183)) % 0.34/0.66 (define @t185 () (not @t184)) % 0.34/0.66 (define @t186 () (tptp.in @t2 @t183)) % 0.34/0.66 (define @t187 () (not @t186)) % 0.34/0.66 (define @t188 () (or @t187 @t185)) % 0.34/0.66 (define @t189 () (_ @t6 @t179)) % 0.34/0.66 (define @t190 () (lambda @t181 @t189)) % 0.34/0.66 (define @t191 () (_ @t10 @t190)) % 0.34/0.66 (define @t192 () (= @t129 @t191)) % 0.34/0.66 (define @t193 () (not @t192)) % 0.34/0.66 (define @t194 () (tptp.in @t2 @t191)) % 0.34/0.66 (define @t195 () (not @t194)) % 0.34/0.66 (define @t196 () (or @t195 @t193)) % 0.34/0.66 (define @t197 () (= @t129 @t55)) % 0.34/0.66 (define @t198 () (not @t197)) % 0.34/0.66 (define @t199 () (tptp.in @t2 @t55)) % 0.34/0.66 (define @t200 () (not @t199)) % 0.34/0.66 (define @t201 () (or @t200 @t198)) % 0.34/0.66 (define @t202 () (not (= @t55 @t129))) % 0.34/0.66 (define @t203 () (or @t200 @t202)) % 0.34/0.66 (define @t204 () (forall @t32 @t203)) % 0.34/0.66 (define @t205 () (not @t204)) % 0.34/0.66 (define @t206 () (=> tptp.funcImageSingleton @t89)) % 0.34/0.66 (define @t207 () (@var "BOUND_VARIABLE_7733" $$unsorted)) % 0.34/0.66 (define @t208 () (tptp.setadjoin @t207 tptp.emptyset)) % 0.34/0.66 (define @t209 () (not (tptp.in @t207 @t208))) % 0.34/0.66 (define @t210 () (tptp.in (tptp.setunion @t208) @t208)) % 0.34/0.66 (define @t211 () (not (= @t208 @t208))) % 0.34/0.66 (define @t212 () (or @t210 @t209 @t211)) % 0.34/0.66 (define @t213 () (@list @t207)) % 0.34/0.66 (define @t214 () (not (= @t16 @t208))) % 0.34/0.66 (define @t215 () (not (tptp.in @t207 @t16))) % 0.34/0.66 (define @t216 () (tptp.setunion @t16)) % 0.34/0.66 (define @t217 () (tptp.in @t216 @t16)) % 0.34/0.66 (define @t218 () (or @t214 @t217 @t215 @t214)) % 0.34/0.66 (define @t219 () (or @t217 @t215 @t214)) % 0.34/0.66 (define @t220 () (forall @t20 @t219)) % 0.34/0.66 (define @t221 () (forall @t213 @t220)) % 0.34/0.66 (define @t222 () (forall (@list @t207 @t16) @t219)) % 0.34/0.66 (define @t223 () (@list @t16 @t207)) % 0.34/0.66 (define @t224 () (not (= @t208 @t16))) % 0.34/0.66 (define @t225 () (or @t217 @t215 @t224)) % 0.34/0.66 (define @t226 () (or @t215 @t224)) % 0.34/0.66 (define @t227 () (or @t226 @t217)) % 0.34/0.66 (define @t228 () (forall @t223 @t227)) % 0.34/0.66 (define @t229 () (forall @t213 @t227)) % 0.34/0.66 (define @t230 () (forall @t213 @t226)) % 0.34/0.66 (define @t231 () (or @t230 @t217)) % 0.34/0.66 (define @t232 () (not (tptp.in @t2 @t16))) % 0.34/0.66 (define @t233 () (forall @t32 (or @t232 (not (= @t129 @t16))))) % 0.34/0.66 (define @t234 () (or @t233 @t18)) % 0.34/0.66 (define @t235 () (not @t233)) % 0.34/0.66 (define @t236 () (not (= @t16 @t129))) % 0.34/0.66 (define @t237 () (or @t232 @t236)) % 0.34/0.66 (define @t238 () (forall @t32 @t237)) % 0.34/0.66 (define @t239 () (not @t238)) % 0.34/0.66 (define @t240 () (_ @t132 @t16)) % 0.34/0.66 (define @t241 () (=> @t240 @t18)) % 0.34/0.66 (define @t242 () (forall @t20 @t241)) % 0.34/0.66 (define @t243 () (=> tptp.theprop @t206)) % 0.34/0.66 (define @t244 () (_ @t6 @t5)) % 0.34/0.66 (define @t245 () (lambda @t8 @t244)) % 0.34/0.66 (define @t246 () (tptp.dsetconstr @t1 @t245)) % 0.34/0.66 (define @t247 () (tptp.in @t2 @t246)) % 0.34/0.66 (define @t248 () (not @t247)) % 0.34/0.66 (define @t249 () (or @t248 @t80)) % 0.34/0.66 (define @t250 () (not @t12)) % 0.34/0.66 (define @t251 () (or @t250 @t4)) % 0.34/0.66 (define @t252 () (=> tptp.dsetconstrEL @t243)) % 0.34/0.66 (define @t253 () (or @t72 @t71)) % 0.34/0.66 (define @t254 () (or @t86 @t83 @t253)) % 0.34/0.66 (define @t255 () (forall @t88 @t254)) % 0.34/0.66 (define @t256 () (@list @t70)) % 0.34/0.66 (define @t257 () (forall @t256 @t254)) % 0.34/0.66 (define @t258 () (forall @t256 @t253)) % 0.34/0.66 (define @t259 () (or @t86 @t83 @t258)) % 0.34/0.66 (define @t260 () (tptp.setunion @t76)) % 0.34/0.66 (define @t261 () (tptp.in @t260 @t28)) % 0.34/0.66 (define @t262 () (forall @t32 (or @t81 @t261))) % 0.34/0.66 (define @t263 () (or @t114 @t83 @t262)) % 0.34/0.66 (define @t264 () (or @t119 @t40)) % 0.34/0.66 (define @t265 () (=> @t143 @t41)) % 0.34/0.66 (define @t266 () (forall @t36 @t265)) % 0.34/0.66 (define @t267 () (=> tptp.funcImageSingleton @t266)) % 0.34/0.66 (define @t268 () (=> tptp.theprop @t267)) % 0.34/0.66 (define @t269 () (=> tptp.dsetconstrEL @t268)) % 0.34/0.66 (define @t270 () (@quantifiers_skolemize @t89 2)) % 0.34/0.66 (define @t271 () (@quantifiers_skolemize @t89 3)) % 0.34/0.66 (define @t272 () (lambda @t8 (tptp.in (tptp.kpair @t271 @t5) @t270))) % 0.34/0.66 (define @t273 () (@quantifiers_skolemize @t89 1)) % 0.34/0.66 (define @t274 () (tptp.dsetconstr @t273 @t272)) % 0.34/0.66 (define @t275 () (forall @t97 (or (not (tptp.in @t92 @t274)) (not (= @t93 @t274))))) % 0.34/0.66 (define @t276 () (@quantifiers_skolemize @t275 0)) % 0.34/0.66 (define @t277 () (@quantifiers_skolemize @t89 0)) % 0.34/0.66 (define @t278 () (@purify @t272)) % 0.34/0.66 (define @t279 () (tptp.dsetconstr @t273 @t278)) % 0.34/0.66 (define @t280 () (tptp.setunion @t279)) % 0.34/0.66 (define @t281 () (tptp.in @t280 @t273)) % 0.34/0.66 (define @t282 () (tptp.in @t271 @t277)) % 0.34/0.66 (define @t283 () (not @t282)) % 0.34/0.66 (define @t284 () (tptp.dsetconstr @t273 (lambda @t8 (tptp.in @t73 @t270)))) % 0.34/0.66 (define @t285 () (forall @t32 (or (not (tptp.in @t2 @t277)) (not (forall @t79 (or (not (tptp.in @t77 @t284)) (not (= @t78 @t284)))))))) % 0.34/0.66 (define @t286 () (not @t285)) % 0.34/0.66 (define @t287 () (tptp.subset @t270 (tptp.cartprod @t277 @t273))) % 0.34/0.66 (define @t288 () (not @t287)) % 0.34/0.66 (define @t289 () (or @t288 @t286 @t283 @t281)) % 0.34/0.66 (define @t290 () (not @t289)) % 0.34/0.66 (define @t291 () (not @t89)) % 0.34/0.66 (define @t292 () (tptp.setunion @t274)) % 0.34/0.66 (define @t293 () (tptp.in @t292 @t273)) % 0.34/0.66 (define @t294 () (or @t288 @t286 @t283 @t293)) % 0.34/0.66 (define @t295 () (not @t294)) % 0.34/0.66 (define @t296 () (@list true)) % 0.34/0.66 (define @t297 () (@list @t289)) % 0.34/0.66 (define @t298 () (not @t275)) % 0.34/0.66 (define @t299 () (or @t288 @t286 @t283 @t298)) % 0.34/0.66 (define @t300 () (tptp.setadjoin @t276 tptp.emptyset)) % 0.34/0.66 (define @t301 () (= @t279 @t300)) % 0.34/0.66 (define @t302 () (not @t301)) % 0.34/0.66 (define @t303 () (tptp.in @t276 @t279)) % 0.34/0.66 (define @t304 () (not @t303)) % 0.34/0.66 (define @t305 () (or @t304 @t302)) % 0.34/0.66 (define @t306 () (not @t305)) % 0.34/0.66 (define @t307 () (= @t274 @t300)) % 0.34/0.66 (define @t308 () (not @t307)) % 0.34/0.66 (define @t309 () (tptp.in @t276 @t274)) % 0.34/0.66 (define @t310 () (not @t309)) % 0.34/0.66 (define @t311 () (or @t310 @t308)) % 0.34/0.66 (define @t312 () (not @t311)) % 0.34/0.66 (define @t313 () (not (= @t300 @t274))) % 0.34/0.66 (define @t314 () (or @t310 @t313)) % 0.34/0.66 (define @t315 () (not @t314)) % 0.34/0.66 (define @t316 () (@list @t305)) % 0.34/0.66 (define @t317 () (tptp.in @t276 @t300)) % 0.34/0.66 (define @t318 () (not @t317)) % 0.34/0.66 (define @t319 () (tptp.in (tptp.setunion @t300) @t300)) % 0.34/0.66 (define @t320 () (or @t319 @t318)) % 0.34/0.66 (define @t321 () (tptp.in @t280 @t279)) % 0.34/0.66 (define @t322 () (not @t321)) % 0.34/0.66 (define @t323 () (or @t322 @t281)) % 0.34/0.66 (define @t324 () (not @t323)) % 0.34/0.66 (define @t325 () (@list true false)) % 0.34/0.66 (define @t326 () (forall @t13 (or @t172 @t80))) % 0.34/0.66 (assume @p1 @t15) % 0.34/0.66 (assume @p2 @t22) % 0.34/0.66 (assume @p3 @t38) % 0.34/0.66 (assume @p4 @t47) % 0.34/0.66 (assume @p5 true) % 0.34/0.66 (step @p6 (= tptp.singleton @t53) :rule refl :args (@t53)) % 0.34/0.66 (step @p7 (= tptp.ex1 @t57) :rule refl :args (@t57)) % 0.34/0.66 (step @p8 (= tptp.breln @t61) :rule refl :args (@t61)) % 0.34/0.66 (step @p9 (= tptp.func @t69) :rule refl :args (@t69)) % 0.34/0.66 (step @p10 :rule refl :args (@t89)) % 0.34/0.66 (step @p11 :rule eq-symm :args (@t91 @t93)) % 0.34/0.66 (step @p12 :rule cong :premises (@p11) :args (@t94)) % 0.34/0.66 (step @p13 :rule refl :args (@t95)) % 0.34/0.66 (step @p14 :rule nary_cong :premises (@p13 @p12) :args (@t96)) % 0.34/0.66 (step @p15 :rule cong :premises (@p14) :args (@t98)) % 0.34/0.66 (step @p16 :rule cong :premises (@p15) :args (@t99)) % 0.34/0.66 (step @p17 :rule refl :args (@t100)) % 0.34/0.66 (step @p18 :rule refl :args (@t83)) % 0.34/0.66 (step @p19 :rule refl :args (@t86)) % 0.34/0.66 (step @p20 :rule nary_cong :premises (@p19 @p18 @p17 @p16) :args (@t101)) % 0.34/0.66 (step @p21 :rule aci_norm :args ((= @t103 @t101))) % 0.34/0.66 (step @p22 :rule trans :premises (@p21 @p20)) % 0.34/0.66 (step @p23 :rule cong :premises (@p22) :args (@t104)) % 0.34/0.66 (step @p24 :rule quant-merge-prenex :args ((= (forall @t36 @t106) @t104))) % 0.34/0.66 (step @p25 :rule alpha_equiv :args (@t107 (@list @t90) @t108)) % 0.34/0.66 (step @p26 :rule refl :args (@t83)) % 0.34/0.66 (step @p27 :rule refl :args (@t86)) % 0.34/0.66 (step @p28 :rule nary_cong :premises (@p27 @p26 @p25) :args (@t109)) % 0.34/0.66 (step @p29 :rule quant-miniscope-or :args ((= @t106 @t109))) % 0.34/0.66 (step @p30 :rule trans :premises (@p29 @p28)) % 0.34/0.66 (step @p31 :rule symm :premises (@p30)) % 0.34/0.66 (step @p32 :rule cong :premises (@p31) :args ((forall @t36 (or @t86 @t83 @t111)))) % 0.34/0.66 (step @p33 :rule trans :premises (@p32 @p24)) % 0.34/0.66 (step @p34 :rule trans :premises (@p33 @p23)) % 0.34/0.66 (step @p35 :rule refl :args (@t111)) % 0.34/0.66 (step @p36 :rule refl :args ((tptp.subset @t23 @t58))) % 0.34/0.66 (step @p37 :rule refl :args (@t84)) % 0.34/0.66 (step @p38 :rule refl :args (@t23)) % 0.34/0.66 (step @p39 :rule cong :premises (@p38 @p37) :args (@t85)) % 0.34/0.66 (step @p40 :rule trans :premises (@p39 @p36)) % 0.34/0.66 (step @p41 :rule refl :args (@t112)) % 0.34/0.66 (step @p42 :rule ho_cong :premises (@p41 @p37)) % 0.34/0.66 (step @p43 :rule cong :premises (@p42 @p40) :args ((= (_ @t112 @t84) @t85))) % 0.34/0.66 (step @p44 :rule symm :premises (@p43)) % 0.34/0.66 (step @p45 :rule refl :args (@t113)) % 0.34/0.66 (step @p46 :rule eq_resolve :premises (@p45 @p44)) % 0.34/0.66 (step @p47 :rule refl :args (@t58)) % 0.34/0.66 (step @p48 :rule cong :premises (@p47 @p37) :args ((= @t58 @t84))) % 0.34/0.66 (step @p49 :rule symm :premises (@p48)) % 0.34/0.66 (step @p50 :rule eq_resolve :premises 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@p65 :rule refl :args (@t110)) % 0.34/0.66 (step @p66 :rule refl :args (@t80)) % 0.34/0.66 (step @p67 :rule refl :args (@t4)) % 0.34/0.66 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t4 @t80))) % 0.34/0.66 (step @p69 :rule symm :premises (@p68)) % 0.34/0.66 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 0.34/0.66 (step @p71 :rule cong :premises (@p70) :args (@t119)) % 0.34/0.66 (step @p72 :rule nary_cong :premises (@p71 @p65) :args (@t120)) % 0.34/0.66 (step @p73 :rule cong :premises (@p72) :args ((forall @t32 @t120))) % 0.34/0.66 (step @p74 :rule bool-impl-elim :args (@t4 @t110)) % 0.34/0.66 (step @p75 :rule cong :premises (@p74) :args ((forall @t32 (=> @t4 @t110)))) % 0.34/0.66 (step @p76 :rule trans :premises (@p75 @p73)) % 0.34/0.66 (step @p77 :rule refl :args (@t93)) % 0.34/0.66 (step @p78 :rule refl :args ((tptp.dsetconstr @t28 @t27))) % 0.34/0.66 (step @p79 :rule refl :args ((tptp.in @t24 @t23))) % 0.34/0.66 (step @p80 :rule refl :args (@t73)) % 0.34/0.66 (step @p81 :rule cong :premises (@p80 @p38) :args (@t74)) % 0.34/0.66 (step @p82 :rule trans :premises (@p81 @p79)) % 0.34/0.66 (step @p83 :rule cong :premises (@p82) :args (@t75)) % 0.34/0.66 (step @p84 :rule refl :args (@t28)) % 0.34/0.66 (step @p85 :rule cong :premises (@p84 @p83) :args (@t76)) % 0.34/0.66 (step @p86 :rule trans :premises (@p85 @p78)) % 0.34/0.66 (step @p87 :rule refl :args (@t29)) % 0.34/0.66 (step @p88 :rule ho_cong :premises (@p87 @p83)) % 0.34/0.66 (step @p89 :rule cong :premises (@p88 @p86) :args ((= (_ @t29 @t75) @t76))) % 0.34/0.66 (step @p90 :rule symm :premises (@p89)) % 0.34/0.66 (step @p91 :rule refl :args (@t30)) % 0.34/0.66 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.34/0.66 (step @p93 :rule refl :args (tptp.in)) % 0.34/0.66 (step @p94 :rule ho_cong :premises (@p93 @p80)) % 0.34/0.66 (step @p95 :rule ho_cong :premises (@p94 @p38)) % 0.34/0.66 (step @p96 :rule cong :premises (@p95 @p82) :args ((= (_ @t121 @t23) @t74))) % 0.34/0.66 (step @p97 :rule 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@p109) :args (@t124)) % 0.34/0.66 (step @p114 :rule cong :premises (@p113) :args (@t125)) % 0.34/0.66 (step @p115 :rule nary_cong :premises (@p114 @p111) :args (@t126)) % 0.34/0.66 (step @p116 :rule cong :premises (@p115) :args (@t127)) % 0.34/0.66 (step @p117 :rule cong :premises (@p116) :args (@t128)) % 0.34/0.66 (step @p118 :rule beta-reduce :args ((= (_ (lambda @t52 (not (forall @t97 (or (not (tptp.in @t92 @t1)) (not (= @t1 @t93)))))) @t30) @t128))) % 0.34/0.66 (step @p119 :rule trans :premises (@p118 @p117)) % 0.34/0.66 (step @p120 :rule alpha_equiv :args (@t130 @t108 (@list @t92))) % 0.34/0.66 (step @p121 :rule cong :premises (@p120) :args (@t131)) % 0.34/0.66 (step @p122 :rule cong :premises (@p121) :args (@t132)) % 0.34/0.66 (step @p123 :rule ho_cong :premises (@p122 @p91)) % 0.34/0.66 (step @p124 :rule trans :premises (@p123 @p119)) % 0.34/0.66 (step @p125 :rule refl :args (@t4)) % 0.34/0.66 (step @p126 :rule cong :premises (@p125 @p124) :args (@t133)) % 0.34/0.66 (step @p127 :rule cong :premises (@p126) :args (@t134)) % 0.34/0.66 (step @p128 :rule trans :premises (@p127 @p76)) % 0.34/0.66 (step @p129 :rule beta-reduce :args ((= (_ @t140 @t23) @t117))) % 0.34/0.66 (step @p130 :rule refl :args (@t23)) % 0.34/0.66 (step @p131 :rule beta-reduce :args ((= (_ @t141 @t28) @t140))) % 0.34/0.66 (step @p132 :rule refl :args (@t28)) % 0.34/0.66 (step @p133 :rule beta-reduce :args ((= @t142 @t141))) % 0.34/0.66 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.34/0.66 (step @p135 :rule trans :premises (@p134 @p131)) % 0.34/0.66 (step @p136 :rule ho_cong :premises (@p135 @p130)) % 0.34/0.66 (step @p137 :rule trans :premises (@p136 @p129)) % 0.34/0.66 (step @p138 :rule cong :premises (@p137 @p128) :args (@t144)) % 0.34/0.66 (step @p139 :rule cong :premises (@p138) :args (@t145)) % 0.34/0.66 (step @p140 :rule trans :premises (@p139 @p64)) % 0.34/0.66 (step @p141 :rule refl :args (tptp.funcImageSingleton)) % 0.34/0.66 (step @p142 :rule cong :premises (@p141 @p140) 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0.34/0.66 (step @p629 :rule chain_m_resolution :premises (@p628 @p551) :args ((not @t281) @t296 @t297)) % 0.34/0.66 (step @p630 :rule cnf_or_pos :args (@t323)) % 0.34/0.66 (step @p631 :rule reordering :premises (@p630) :args ((or @t281 @t322 @t324))) % 0.34/0.66 (step @p632 :rule chain_m_resolution :premises (@p631 @p629 @p627) :args (@t324 @t325 (@list @t281 @t321))) % 0.34/0.66 (assume-push @p643 @t326) % 0.34/0.66 (step @p634 :rule instantiate :premises (@p516) :args ((@list @t273 @t278 @t280))) % 0.34/0.66 (step-pop @p644 :rule scope :premises (@p634)) % 0.34/0.66 (step @p635 :rule process_scope :premises (@p644) :args (@t323)) % 0.34/0.66 (step @p637 :rule implies_elim :premises (@p635)) % 0.34/0.66 (step @p638 false :rule chain_m_resolution :premises (@p637 @p632 @p516) :args (false @t325 (@list @t323 @t326))) % 0.34/0.66 ) % 0.34/0.66 % SZS output end Proof % 0.34/0.66 % cvc5 exiting %------------------------------------------------------------------------------