%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU779^2 : 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 : n011.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 08:53:10 AM UTC 2026 % Result : Theorem 0.46s 0.63s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU779^2 : TPTP v9.2.1. Released v3.7.0. % 0.14/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n011.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:51:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.46/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.63 % SZS status Theorem % 0.46/0.63 % SZS output start Proof % 0.46/0.63 ( % 0.46/0.63 (declare-sort $$unsorted 0) % 0.46/0.63 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.63 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.46/0.63 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.46/0.63 (declare-const tptp.dpsetconstrI Bool) % 0.46/0.63 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.46/0.63 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.46/0.63 (define tptp.breln1compset () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xz" $$unsorted))) (let ((_let_4 (@var "R" $$unsorted))) (let ((_let_5 (@var "Xx" $$unsorted))) (let ((_let_6 (@var "A" $$unsorted))) (lambda (@list _let_6 _let_4 _let_1) (_ (_ (_ tptp.dpsetconstr _let_6) _let_6) (lambda (@list _let_5 _let_2) (exists (@list _let_3) (and (_ (_ tptp.in _let_3) _let_6) (_ (_ tptp.in (_ (_ tptp.kpair _let_5) _let_3)) _let_4) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.46/0.63 (define @t1 () (@var "Xu" $$unsorted)) % 0.46/0.63 (define @t2 () (@var "Xz" $$unsorted)) % 0.46/0.63 (define @t3 () (@var "Xphi" (-> $$unsorted $$unsorted Bool))) % 0.46/0.63 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.46/0.63 (define @t5 () (@list @t2 @t1)) % 0.46/0.63 (define @t6 () (lambda @t5 @t4)) % 0.46/0.63 (define @t7 () (@var "B" $$unsorted)) % 0.46/0.63 (define @t8 () (@var "A" $$unsorted)) % 0.46/0.63 (define @t9 () (_ tptp.dpsetconstr @t8)) % 0.46/0.63 (define @t10 () (_ @t9 @t7)) % 0.46/0.63 (define @t11 () (_ @t10 @t6)) % 0.46/0.63 (define @t12 () (@var "Xy" $$unsorted)) % 0.46/0.63 (define @t13 () (@var "Xx" $$unsorted)) % 0.46/0.63 (define @t14 () (_ tptp.kpair @t13)) % 0.46/0.63 (define @t15 () (_ @t14 @t12)) % 0.46/0.63 (define @t16 () (_ tptp.in @t15)) % 0.46/0.63 (define @t17 () (_ @t16 @t11)) % 0.46/0.63 (define @t18 () (_ (_ @t3 @t13) @t12)) % 0.46/0.63 (define @t19 () (=> @t18 @t17)) % 0.46/0.63 (define @t20 () (_ tptp.in @t12)) % 0.46/0.63 (define @t21 () (_ @t20 @t7)) % 0.46/0.63 (define @t22 () (@list @t12)) % 0.46/0.63 (define @t23 () (forall @t22 (=> @t21 @t19))) % 0.46/0.63 (define @t24 () (_ (_ tptp.in @t13) @t8)) % 0.46/0.63 (define @t25 () (=> @t24 @t23)) % 0.46/0.63 (define @t26 () (@list @t8 @t7 @t3 @t13)) % 0.46/0.63 (define @t27 () (forall @t26 @t25)) % 0.46/0.63 (define @t28 () (= tptp.dpsetconstrI @t27)) % 0.46/0.63 (define @t29 () (@var "S" $$unsorted)) % 0.46/0.63 (define @t30 () (@var "R" $$unsorted)) % 0.46/0.63 (define @t31 () (_ (_ tptp.kpair @t2) @t12)) % 0.46/0.63 (define @t32 () (_ (_ tptp.in @t31) @t29)) % 0.46/0.63 (define @t33 () (=> @t32 (_ @t16 (_ (_ (_ tptp.breln1compset @t8) @t30) @t29)))) % 0.46/0.63 (define @t34 () (_ @t14 @t2)) % 0.46/0.63 (define @t35 () (_ (_ tptp.in @t34) @t30)) % 0.46/0.63 (define @t36 () (=> @t35 @t33)) % 0.46/0.63 (define @t37 () (_ (_ tptp.in @t2) @t8)) % 0.46/0.63 (define @t38 () (=> @t37 @t36)) % 0.46/0.63 (define @t39 () (@list @t2)) % 0.46/0.63 (define @t40 () (forall @t39 @t38)) % 0.46/0.63 (define @t41 () (_ @t20 @t8)) % 0.46/0.63 (define @t42 () (=> @t41 @t40)) % 0.46/0.63 (define @t43 () (forall @t22 @t42)) % 0.46/0.63 (define @t44 () (=> @t24 @t43)) % 0.46/0.63 (define @t45 () (@list @t13)) % 0.46/0.63 (define @t46 () (forall @t45 @t44)) % 0.46/0.63 (define @t47 () (_ tptp.breln1 @t8)) % 0.46/0.63 (define @t48 () (=> (_ @t47 @t29) @t46)) % 0.46/0.63 (define @t49 () (@list @t29)) % 0.46/0.63 (define @t50 () (forall @t49 @t48)) % 0.46/0.63 (define @t51 () (=> (_ @t47 @t30) @t50)) % 0.46/0.63 (define @t52 () (@list @t8 @t30)) % 0.46/0.63 (define @t53 () (forall @t52 @t51)) % 0.46/0.63 (define @t54 () (=> tptp.dpsetconstrI @t53)) % 0.46/0.63 (define @t55 () (not @t54)) % 0.46/0.63 (define @t56 () (_ tptp.cartprod @t8)) % 0.46/0.63 (define @t57 () (@var "C" $$unsorted)) % 0.46/0.63 (define @t58 () (_ tptp.subset @t57)) % 0.46/0.63 (define @t59 () (_ @t58 (_ @t56 @t7))) % 0.46/0.63 (define @t60 () (lambda (@list @t8 @t7 @t57) @t59)) % 0.46/0.63 (define @t61 () (lambda @t52 (_ (_ (_ tptp.breln @t8) @t8) @t30))) % 0.46/0.63 (define @t62 () (and @t37 @t35 @t32)) % 0.46/0.63 (define @t63 () (exists @t39 @t62)) % 0.46/0.63 (define @t64 () (@list @t13 @t12)) % 0.46/0.63 (define @t65 () (lambda @t64 @t63)) % 0.46/0.63 (define @t66 () (_ @t9 @t8)) % 0.46/0.63 (define @t67 () (@list @t8 @t30 @t29)) % 0.46/0.63 (define @t68 () (lambda @t67 (_ @t66 @t65))) % 0.46/0.63 (define @t69 () (@var "BOUND_VARIABLE_7696" $$unsorted)) % 0.46/0.63 (define @t70 () (@var "BOUND_VARIABLE_7740" $$unsorted)) % 0.46/0.63 (define @t71 () (@var "BOUND_VARIABLE_7829" $$unsorted)) % 0.46/0.63 (define @t72 () (@var "BOUND_VARIABLE_7833" $$unsorted)) % 0.46/0.63 (define @t73 () (@var "BOUND_VARIABLE_7835" $$unsorted)) % 0.46/0.63 (define @t74 () (not (tptp.in (tptp.kpair @t73 @t72) @t71))) % 0.46/0.63 (define @t75 () (@var "BOUND_VARIABLE_7831" $$unsorted)) % 0.46/0.63 (define @t76 () (not (tptp.in (tptp.kpair @t75 @t73) @t30))) % 0.46/0.63 (define @t77 () (not (tptp.in @t73 @t8))) % 0.46/0.63 (define @t78 () (@var "BOUND_VARIABLE_7667" $$unsorted)) % 0.46/0.63 (define @t79 () (tptp.kpair @t78 @t69)) % 0.46/0.63 (define @t80 () (tptp.kpair @t70 @t78)) % 0.46/0.63 (define @t81 () (not (tptp.in @t80 @t30))) % 0.46/0.63 (define @t82 () (tptp.in @t78 @t8)) % 0.46/0.63 (define @t83 () (not @t82)) % 0.46/0.63 (define @t84 () (@list @t78)) % 0.46/0.63 (define @t85 () (@list @t70 @t69)) % 0.46/0.63 (define @t86 () (tptp.in (tptp.kpair @t75 @t72) (tptp.dpsetconstr @t8 @t8 (lambda @t85 (not (forall @t84 (or @t83 @t81 (not (tptp.in @t79 @t71))))))))) % 0.46/0.63 (define @t87 () (not (tptp.in @t72 @t8))) % 0.46/0.63 (define @t88 () (not (tptp.in @t75 @t8))) % 0.46/0.63 (define @t89 () (tptp.cartprod @t8 @t8)) % 0.46/0.63 (define @t90 () (not (tptp.subset @t71 @t89))) % 0.46/0.63 (define @t91 () (tptp.subset @t30 @t89)) % 0.46/0.63 (define @t92 () (not @t91)) % 0.46/0.63 (define @t93 () (or @t92 @t90 @t88 @t87 @t86 @t77 @t76 @t74)) % 0.46/0.63 (define @t94 () (@list @t8 @t30 @t71 @t75 @t72 @t73)) % 0.46/0.63 (define @t95 () (forall @t94 @t93)) % 0.46/0.63 (define @t96 () (@quantifiers_skolemize @t95 2)) % 0.46/0.63 (define @t97 () (@quantifiers_skolemize @t95 1)) % 0.46/0.63 (define @t98 () (@quantifiers_skolemize @t95 0)) % 0.46/0.63 (define @t99 () (not (tptp.in @t78 @t98))) % 0.46/0.63 (define @t100 () (not (forall @t84 (or @t99 (not (tptp.in @t80 @t97)) (not (tptp.in @t79 @t96)))))) % 0.46/0.63 (define @t101 () (lambda @t85 @t100)) % 0.46/0.63 (define @t102 () (@purify @t101)) % 0.46/0.63 (define @t103 () (_ @t102 @t70 @t69)) % 0.46/0.63 (define @t104 () (_ @t101 @t70 @t69)) % 0.46/0.63 (define @t105 () (= @t103 @t104)) % 0.46/0.63 (define @t106 () (forall @t85 @t105)) % 0.46/0.63 (define @t107 () (@quantifiers_skolemize @t95 4)) % 0.46/0.63 (define @t108 () (@quantifiers_skolemize @t95 3)) % 0.46/0.63 (define @t109 () (forall @t84 (or @t99 (not (tptp.in (tptp.kpair @t108 @t78) @t97)) (not (tptp.in (tptp.kpair @t78 @t107) @t96))))) % 0.46/0.63 (define @t110 () (not @t109)) % 0.46/0.63 (define @t111 () (_ @t102 @t108 @t107)) % 0.46/0.63 (define @t112 () (forall @t85 (= @t100 @t103))) % 0.46/0.63 (define @t113 () (= @t110 @t111)) % 0.46/0.63 (define @t114 () (= @t111 @t110)) % 0.46/0.63 (define @t115 () (tptp.dpsetconstr @t8 @t7 @t3)) % 0.46/0.63 (define @t116 () (@var "BOUND_VARIABLE_7608" $$unsorted)) % 0.46/0.63 (define @t117 () (tptp.in (tptp.kpair @t13 @t116) @t115)) % 0.46/0.63 (define @t118 () (not (_ @t3 @t13 @t116))) % 0.46/0.63 (define @t119 () (not (tptp.in @t116 @t7))) % 0.46/0.63 (define @t120 () (tptp.in @t13 @t8)) % 0.46/0.63 (define @t121 () (not @t120)) % 0.46/0.63 (define @t122 () (or @t119 @t118 @t117)) % 0.46/0.63 (define @t123 () (or @t121 @t122)) % 0.46/0.63 (define @t124 () (forall (@list @t8 @t7 @t3 @t13 @t116) @t123)) % 0.46/0.63 (define @t125 () (@list @t116)) % 0.46/0.63 (define @t126 () (forall @t125 @t123)) % 0.46/0.63 (define @t127 () (forall @t125 @t122)) % 0.46/0.63 (define @t128 () (@list @t12)) % 0.46/0.63 (define @t129 () (or @t121 @t127)) % 0.46/0.63 (define @t130 () (tptp.kpair @t13 @t12)) % 0.46/0.63 (define @t131 () (_ @t3 @t13 @t12)) % 0.46/0.63 (define @t132 () (not @t131)) % 0.46/0.63 (define @t133 () (tptp.in @t12 @t7)) % 0.46/0.63 (define @t134 () (not @t133)) % 0.46/0.63 (define @t135 () (forall @t22 (or @t134 @t132 (tptp.in @t130 @t115)))) % 0.46/0.63 (define @t136 () (not @t24)) % 0.46/0.63 (define @t137 () (or @t136 @t135)) % 0.46/0.63 (define @t138 () (_ @t3 @t2 @t1)) % 0.46/0.63 (define @t139 () (lambda @t5 @t138)) % 0.46/0.63 (define @t140 () (tptp.dpsetconstr @t8 @t7 @t139)) % 0.46/0.63 (define @t141 () (tptp.in @t130 @t140)) % 0.46/0.63 (define @t142 () (or @t134 @t132 @t141)) % 0.46/0.63 (define @t143 () (_ tptp.in @t130)) % 0.46/0.63 (define @t144 () (not @t18)) % 0.46/0.63 (define @t145 () (not @t21)) % 0.46/0.63 (define @t146 () (or @t145 @t144 @t17)) % 0.46/0.63 (define @t147 () (=> tptp.dpsetconstrI @t95)) % 0.46/0.63 (define @t148 () (or @t90 @t88 @t87 @t86 @t77 @t76 @t74)) % 0.46/0.63 (define @t149 () (or @t92 @t148)) % 0.46/0.63 (define @t150 () (forall @t94 @t149)) % 0.46/0.63 (define @t151 () (@list @t71 @t75 @t72 @t73)) % 0.46/0.63 (define @t152 () (forall @t151 @t149)) % 0.46/0.63 (define @t153 () (forall @t151 @t148)) % 0.46/0.63 (define @t154 () (@var "BOUND_VARIABLE_7797" $$unsorted)) % 0.46/0.63 (define @t155 () (@var "BOUND_VARIABLE_7795" $$unsorted)) % 0.46/0.63 (define @t156 () (@var "BOUND_VARIABLE_7793" $$unsorted)) % 0.46/0.63 (define @t157 () (or @t92 @t153)) % 0.46/0.63 (define @t158 () (not (tptp.in (tptp.kpair @t154 @t155) @t29))) % 0.46/0.63 (define @t159 () (not (tptp.in (tptp.kpair @t156 @t154) @t30))) % 0.46/0.63 (define @t160 () (not (tptp.in @t154 @t8))) % 0.46/0.63 (define @t161 () (tptp.in @t79 @t29)) % 0.46/0.63 (define @t162 () (not @t161)) % 0.46/0.63 (define @t163 () (tptp.dpsetconstr @t8 @t8 (lambda @t85 (not (forall @t84 (or @t83 @t81 @t162)))))) % 0.46/0.63 (define @t164 () (tptp.in (tptp.kpair @t156 @t155) @t163)) % 0.46/0.63 (define @t165 () (not (tptp.in @t155 @t8))) % 0.46/0.63 (define @t166 () (not (tptp.in @t156 @t8))) % 0.46/0.63 (define @t167 () (tptp.subset @t29 @t89)) % 0.46/0.63 (define @t168 () (not @t167)) % 0.46/0.63 (define @t169 () (or @t168 @t166 @t165 @t164 @t160 @t159 @t158)) % 0.46/0.63 (define @t170 () (@list @t29 @t156 @t155 @t154)) % 0.46/0.63 (define @t171 () (forall @t170 @t169)) % 0.46/0.63 (define @t172 () (_ @t56 @t8)) % 0.46/0.63 (define @t173 () (_ tptp.subset @t30)) % 0.46/0.63 (define @t174 () (_ @t173 @t172)) % 0.46/0.63 (define @t175 () (not @t174)) % 0.46/0.63 (define @t176 () (or @t175 @t171)) % 0.46/0.63 (define @t177 () (or @t166 @t165 @t164 @t160 @t159 @t158)) % 0.46/0.63 (define @t178 () (or @t168 @t177)) % 0.46/0.63 (define @t179 () (forall @t170 @t178)) % 0.46/0.63 (define @t180 () (@list @t156 @t155 @t154)) % 0.46/0.63 (define @t181 () (forall @t180 @t178)) % 0.46/0.63 (define @t182 () (forall @t180 @t177)) % 0.46/0.63 (define @t183 () (@var "BOUND_VARIABLE_7762" $$unsorted)) % 0.46/0.63 (define @t184 () (@var "BOUND_VARIABLE_7760" $$unsorted)) % 0.46/0.63 (define @t185 () (or @t168 @t182)) % 0.46/0.63 (define @t186 () (not (tptp.in (tptp.kpair @t183 @t184) @t29))) % 0.46/0.63 (define @t187 () (not (tptp.in (tptp.kpair @t13 @t183) @t30))) % 0.46/0.63 (define @t188 () (not (tptp.in @t183 @t8))) % 0.46/0.63 (define @t189 () (tptp.in (tptp.kpair @t13 @t184) @t163)) % 0.46/0.63 (define @t190 () (not (tptp.in @t184 @t8))) % 0.46/0.63 (define @t191 () (or @t121 @t190 @t189 @t188 @t187 @t186)) % 0.46/0.63 (define @t192 () (@list @t13 @t184 @t183)) % 0.46/0.63 (define @t193 () (forall @t192 @t191)) % 0.46/0.63 (define @t194 () (_ tptp.subset @t29)) % 0.46/0.63 (define @t195 () (_ @t194 @t172)) % 0.46/0.63 (define @t196 () (not @t195)) % 0.46/0.63 (define @t197 () (or @t196 @t193)) % 0.46/0.63 (define @t198 () (or @t190 @t189 @t188 @t187 @t186)) % 0.46/0.63 (define @t199 () (or @t121 @t198)) % 0.46/0.63 (define @t200 () (forall @t192 @t199)) % 0.46/0.63 (define @t201 () (@list @t184 @t183)) % 0.46/0.63 (define @t202 () (forall @t201 @t199)) % 0.46/0.63 (define @t203 () (forall @t201 @t198)) % 0.46/0.63 (define @t204 () (@var "BOUND_VARIABLE_7722" $$unsorted)) % 0.46/0.63 (define @t205 () (or @t121 @t203)) % 0.46/0.63 (define @t206 () (not (tptp.in (tptp.kpair @t204 @t12) @t29))) % 0.46/0.63 (define @t207 () (not (tptp.in (tptp.kpair @t13 @t204) @t30))) % 0.46/0.63 (define @t208 () (not (tptp.in @t204 @t8))) % 0.46/0.63 (define @t209 () (tptp.in @t12 @t8)) % 0.46/0.63 (define @t210 () (not @t209)) % 0.46/0.63 (define @t211 () (@list @t12 @t204)) % 0.46/0.63 (define @t212 () (forall @t211 (or @t210 (tptp.in @t130 @t163) @t208 @t207 @t206))) % 0.46/0.63 (define @t213 () (or @t136 @t212)) % 0.46/0.63 (define @t214 () (tptp.kpair @t13 @t78)) % 0.46/0.63 (define @t215 () (tptp.in @t214 @t30)) % 0.46/0.63 (define @t216 () (not @t215)) % 0.46/0.63 (define @t217 () (or @t83 @t216 @t162)) % 0.46/0.63 (define @t218 () (forall @t84 @t217)) % 0.46/0.63 (define @t219 () (not @t218)) % 0.46/0.63 (define @t220 () (@list @t13 @t69)) % 0.46/0.63 (define @t221 () (lambda @t220 @t219)) % 0.46/0.63 (define @t222 () (tptp.dpsetconstr @t8 @t8 @t221)) % 0.46/0.63 (define @t223 () (tptp.in @t130 @t222)) % 0.46/0.63 (define @t224 () (or @t210 @t223 @t208 @t207 @t206)) % 0.46/0.63 (define @t225 () (forall @t211 @t224)) % 0.46/0.63 (define @t226 () (=> @t24 @t225)) % 0.46/0.63 (define @t227 () (or @t208 @t207 @t206)) % 0.46/0.63 (define @t228 () (or @t210 @t223 @t227)) % 0.46/0.63 (define @t229 () (forall @t211 @t228)) % 0.46/0.63 (define @t230 () (@list @t204)) % 0.46/0.63 (define @t231 () (forall @t230 @t228)) % 0.46/0.63 (define @t232 () (forall @t230 @t227)) % 0.46/0.63 (define @t233 () (@list @t2)) % 0.46/0.63 (define @t234 () (or @t210 @t223 @t232)) % 0.46/0.63 (define @t235 () (tptp.kpair @t2 @t12)) % 0.46/0.63 (define @t236 () (tptp.in @t235 @t29)) % 0.46/0.63 (define @t237 () (tptp.kpair @t13 @t2)) % 0.46/0.63 (define @t238 () (tptp.in @t237 @t30)) % 0.46/0.63 (define @t239 () (tptp.in @t2 @t8)) % 0.46/0.63 (define @t240 () (forall @t39 (or (not @t239) (not @t238) (not @t236)))) % 0.46/0.63 (define @t241 () (_ (_ tptp.kpair @t78) @t69)) % 0.46/0.63 (define @t242 () (_ @t14 @t78)) % 0.46/0.63 (define @t243 () (lambda @t220 (not (forall @t84 (or (not (_ (_ tptp.in @t78) @t8)) (not (_ (_ tptp.in @t242) @t30)) (not (_ (_ tptp.in @t241) @t29))))))) % 0.46/0.63 (define @t244 () (_ @t66 @t243)) % 0.46/0.63 (define @t245 () (_ @t66 @t221)) % 0.46/0.63 (define @t246 () (not @t41)) % 0.46/0.63 (define @t247 () (_ @t16 @t245)) % 0.46/0.63 (define @t248 () (or @t246 @t247 @t240)) % 0.46/0.63 (define @t249 () (or @t247 @t240)) % 0.46/0.63 (define @t250 () (lambda @t64 (not (forall @t84 (or @t83 @t216 (not (tptp.in (tptp.kpair @t78 @t12) @t29))))))) % 0.46/0.63 (define @t251 () (_ @t16 (_ @t66 @t250))) % 0.46/0.63 (define @t252 () (or @t251 @t240)) % 0.46/0.63 (define @t253 () (=> @t41 @t252)) % 0.46/0.63 (define @t254 () (not @t32)) % 0.46/0.63 (define @t255 () (not @t35)) % 0.46/0.63 (define @t256 () (not @t37)) % 0.46/0.63 (define @t257 () (or @t256 @t255 @t254)) % 0.46/0.63 (define @t258 () (forall @t39 @t257)) % 0.46/0.63 (define @t259 () (or @t251 @t258)) % 0.46/0.63 (define @t260 () (or @t251 @t257)) % 0.46/0.63 (define @t261 () (or @t256 @t255 @t254 @t251)) % 0.46/0.63 (define @t262 () (or @t255 @t254 @t251)) % 0.46/0.63 (define @t263 () (=> @t32 @t251)) % 0.46/0.63 (define @t264 () (=> @t35 @t263)) % 0.46/0.63 (define @t265 () (not @t240)) % 0.46/0.63 (define @t266 () (lambda @t64 @t265)) % 0.46/0.63 (define @t267 () (_ @t66 @t266)) % 0.46/0.63 (define @t268 () (=> @t32 (_ @t16 @t267))) % 0.46/0.63 (define @t269 () (=> @t35 @t268)) % 0.46/0.63 (define @t270 () (=> @t37 @t269)) % 0.46/0.63 (define @t271 () (lambda @t49 @t267)) % 0.46/0.63 (define @t272 () (lambda (@list @t30 @t29) @t267)) % 0.46/0.63 (define @t273 () (_ (lambda @t67 @t267) @t8)) % 0.46/0.63 (define @t274 () (=> @t32 (_ @t16 (_ (_ @t273 @t30) @t29)))) % 0.46/0.63 (define @t275 () (=> @t35 @t274)) % 0.46/0.63 (define @t276 () (=> @t37 @t275)) % 0.46/0.63 (define @t277 () (forall @t39 @t276)) % 0.46/0.63 (define @t278 () (=> @t41 @t277)) % 0.46/0.63 (define @t279 () (forall @t22 @t278)) % 0.46/0.63 (define @t280 () (=> @t24 @t279)) % 0.46/0.63 (define @t281 () (forall @t45 @t280)) % 0.46/0.63 (define @t282 () (lambda (@list @t30) @t174)) % 0.46/0.63 (define @t283 () (_ (lambda @t52 @t174) @t8)) % 0.46/0.63 (define @t284 () (=> (_ @t283 @t29) @t281)) % 0.46/0.63 (define @t285 () (forall @t49 @t284)) % 0.46/0.63 (define @t286 () (=> (_ @t283 @t30) @t285)) % 0.46/0.63 (define @t287 () (forall @t52 @t286)) % 0.46/0.63 (define @t288 () (=> tptp.dpsetconstrI @t287)) % 0.46/0.63 (define @t289 () (forall @t39 (not @t62))) % 0.46/0.63 (define @t290 () (not @t289)) % 0.46/0.63 (define @t291 () (lambda (@list @t57) (_ @t58 @t172))) % 0.46/0.63 (define @t292 () (lambda (@list @t7 @t57) @t59)) % 0.46/0.63 (define @t293 () (@quantifiers_skolemize @t95 5)) % 0.46/0.63 (define @t294 () (tptp.in (tptp.kpair @t293 @t107) @t96)) % 0.46/0.63 (define @t295 () (not @t294)) % 0.46/0.63 (define @t296 () (tptp.in (tptp.kpair @t108 @t293) @t97)) % 0.46/0.63 (define @t297 () (not @t296)) % 0.46/0.63 (define @t298 () (tptp.in @t293 @t98)) % 0.46/0.63 (define @t299 () (not @t298)) % 0.46/0.63 (define @t300 () (tptp.kpair @t108 @t107)) % 0.46/0.63 (define @t301 () (tptp.in @t300 (tptp.dpsetconstr @t98 @t98 @t102))) % 0.46/0.63 (define @t302 () (tptp.in @t107 @t98)) % 0.46/0.63 (define @t303 () (not @t302)) % 0.46/0.63 (define @t304 () (tptp.in @t108 @t98)) % 0.46/0.63 (define @t305 () (not @t304)) % 0.46/0.63 (define @t306 () (tptp.cartprod @t98 @t98)) % 0.46/0.63 (define @t307 () (not (tptp.subset @t96 @t306))) % 0.46/0.63 (define @t308 () (not (tptp.subset @t97 @t306))) % 0.46/0.63 (define @t309 () (or @t308 @t307 @t305 @t303 @t301 @t299 @t297 @t295)) % 0.46/0.63 (define @t310 () (not @t309)) % 0.46/0.63 (define @t311 () (not @t95)) % 0.46/0.63 (define @t312 () (tptp.dpsetconstr @t98 @t98 @t101)) % 0.46/0.63 (define @t313 () (tptp.in @t300 @t312)) % 0.46/0.63 (define @t314 () (or @t308 @t307 @t305 @t303 @t313 @t299 @t297 @t295)) % 0.46/0.63 (define @t315 () (not @t314)) % 0.46/0.63 (define @t316 () (@list true)) % 0.46/0.63 (define @t317 () (@list @t309)) % 0.46/0.63 (define @t318 () (not @t111)) % 0.46/0.63 (define @t319 () (or @t305 @t303 @t318 @t301)) % 0.46/0.63 (define @t320 () (not @t114)) % 0.46/0.63 (define @t321 () (@list true false)) % 0.46/0.63 (define @t322 () (or @t299 @t297 @t295)) % 0.46/0.63 (define @t323 () (not @t322)) % 0.46/0.63 (assume @p1 @t28) % 0.46/0.63 (assume @p2 @t55) % 0.46/0.63 (assume @p3 true) % 0.46/0.63 (step @p4 (= tptp.breln @t60) :rule refl :args (@t60)) % 0.46/0.63 (step @p5 (= tptp.breln1 @t61) :rule refl :args (@t61)) % 0.46/0.63 (step @p6 (= tptp.breln1compset @t68) :rule refl :args (@t68)) % 0.46/0.63 (step @p7 :rule eq-symm :args (@t103 @t100)) % 0.46/0.63 (step @p8 :rule beta-reduce :args ((= @t104 @t100))) % 0.46/0.63 (step @p9 :rule refl :args (@t103)) % 0.46/0.63 (step @p10 :rule cong :premises (@p9 @p8) :args (@t105)) % 0.46/0.63 (step @p11 :rule trans :premises (@p10 @p7)) % 0.46/0.63 (step @p12 :rule cong :premises (@p11) :args (@t106)) % 0.46/0.63 (step @p13 :rule quant-unused-vars :args ((= (forall @t85 true) true))) % 0.46/0.63 (step @p14 :rule eq-refl :args (@t104)) % 0.46/0.63 (step @p15 :rule cong :premises (@p14) :args ((forall @t85 (= @t104 @t104)))) % 0.46/0.63 (step @p16 :rule trans :premises (@p15 @p13)) % 0.46/0.63 (step @p17 :rule refl :args (@t104)) % 0.46/0.63 (step @p18 :rule refl :args (@t69)) % 0.46/0.63 (step @p19 :rule refl :args (@t70)) % 0.46/0.63 (step @p20 :rule skolem_intro :args (@t102)) % 0.46/0.63 (step @p21 :rule ho_cong :premises (@p20 @p19 @p18)) % 0.46/0.63 (step @p22 :rule cong :premises (@p21 @p17) :args (@t105)) % 0.46/0.63 (step @p23 :rule cong :premises (@p22) :args (@t106)) % 0.46/0.63 (step @p24 :rule trans :premises (@p23 @p16)) % 0.46/0.63 (step @p25 :rule true_elim :premises (@p24)) % 0.46/0.63 (step @p26 :rule eq_resolve :premises (@p25 @p12)) % 0.46/0.63 (step @p27 :rule eq-symm :args (@t110 @t111)) % 0.46/0.63 (step @p28 :rule refl :args (@t112)) % 0.46/0.63 (step @p29 :rule cong :premises (@p28 @p27) :args ((=> @t112 @t113))) % 0.46/0.63 (assume-push @p571 @t112) % 0.46/0.63 (step @p31 :rule instantiate :premises (@p26) :args ((@list @t108 @t107))) % 0.46/0.63 (step-pop @p572 :rule scope :premises (@p31)) % 0.46/0.63 (step @p32 :rule process_scope :premises (@p572) :args (@t113)) % 0.46/0.63 (step @p34 :rule 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trans :premises (@p47 @p40)) % 0.46/0.63 (step @p49 :rule trans :premises (@p48 @p39)) % 0.46/0.63 (step @p50 :rule refl :args (@t135)) % 0.46/0.63 (step @p51 :rule refl :args (@t120)) % 0.46/0.63 (step @p52 :rule refl :args (@t24)) % 0.46/0.63 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t24 @t120))) % 0.46/0.63 (step @p54 :rule symm :premises (@p53)) % 0.46/0.63 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.46/0.63 (step @p56 :rule cong :premises (@p55) :args (@t136)) % 0.46/0.63 (step @p57 :rule nary_cong :premises (@p56 @p50) :args (@t137)) % 0.46/0.63 (step @p58 :rule cong :premises (@p57) :args ((forall @t26 @t137))) % 0.46/0.63 (step @p59 :rule trans :premises (@p58 @p49)) % 0.46/0.63 (step @p60 :rule bool-impl-elim :args (@t24 @t135)) % 0.46/0.63 (step @p61 :rule cong :premises (@p60) :args ((forall @t26 (=> @t24 @t135)))) % 0.46/0.63 (step @p62 :rule trans :premises (@p61 @p59)) % 0.46/0.63 (step @p63 :rule lambda-elim :args ((= @t139 @t3))) % 0.46/0.63 (step @p64 :rule refl :args (@t7)) % 0.46/0.63 (step @p65 :rule refl :args (@t8)) % 0.46/0.63 (step @p66 :rule cong :premises (@p65 @p64 @p63) :args (@t140)) % 0.46/0.63 (step @p67 :rule refl :args (@t130)) % 0.46/0.63 (step @p68 :rule cong :premises (@p67 @p66) :args (@t141)) % 0.46/0.63 (step @p69 :rule refl :args (@t132)) % 0.46/0.63 (step @p70 :rule refl :args (@t134)) % 0.46/0.63 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68) :args (@t142)) % 0.46/0.63 (step @p72 :rule cong :premises (@p71) :args ((forall @t22 @t142))) % 0.46/0.63 (step @p73 :rule refl :args ((tptp.in @t15 @t11))) % 0.46/0.63 (step @p74 :rule refl :args ((tptp.dpsetconstr @t8 @t7 @t6))) % 0.46/0.63 (step @p75 :rule refl :args (@t138)) % 0.46/0.63 (step @p76 :rule cong :premises (@p75) :args (@t139)) % 0.46/0.63 (step @p77 :rule refl :args (@t7)) % 0.46/0.63 (step @p78 :rule refl :args (@t8)) % 0.46/0.63 (step @p79 :rule cong :premises (@p78 @p77 @p76) :args (@t140)) % 0.46/0.63 (step @p80 :rule trans 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(step @p97 :rule refl :args (@t4)) % 0.46/0.63 (step @p98 :rule cong :premises (@p97 @p75) :args ((= @t4 @t138))) % 0.46/0.63 (step @p99 :rule symm :premises (@p98)) % 0.46/0.63 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.46/0.63 (step @p101 :rule cong :premises (@p100) :args (@t6)) % 0.46/0.63 (step @p102 :rule ho_cong :premises (@p91 @p101)) % 0.46/0.63 (step @p103 :rule trans :premises (@p102 @p96)) % 0.46/0.63 (step @p104 :rule refl :args (@t15)) % 0.46/0.63 (step @p105 :rule cong :premises (@p104 @p81) :args ((= @t15 @t130))) % 0.46/0.63 (step @p106 :rule symm :premises (@p105)) % 0.46/0.63 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.46/0.63 (step @p108 :rule ho_cong :premises (@p84 @p107)) % 0.46/0.63 (step @p109 :rule ho_cong :premises (@p108 @p103)) % 0.46/0.63 (step @p110 :rule trans :premises (@p109 @p90)) % 0.46/0.63 (step @p111 :rule refl :args (@t131)) % 0.46/0.63 (step @p112 :rule refl :args (@t18)) % 0.46/0.63 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t18 @t131))) % 0.46/0.63 (step @p114 :rule symm :premises (@p113)) % 0.46/0.63 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.46/0.63 (step @p116 :rule cong :premises (@p115) :args (@t144)) % 0.46/0.63 (step @p117 :rule refl :args (@t133)) % 0.46/0.63 (step @p118 :rule refl :args (@t21)) % 0.46/0.63 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t21 @t133))) % 0.46/0.63 (step @p120 :rule symm :premises (@p119)) % 0.46/0.63 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.46/0.63 (step @p122 :rule cong :premises (@p121) :args (@t145)) % 0.46/0.63 (step @p123 :rule nary_cong :premises (@p122 @p116 @p110) :args (@t146)) % 0.46/0.63 (step @p124 :rule cong :premises (@p123) :args ((forall @t22 @t146))) % 0.46/0.63 (step @p125 :rule trans :premises (@p124 @p72)) % 0.46/0.63 (step @p126 :rule aci_norm :args ((= (or @t145 (or @t144 @t17)) @t146))) % 0.46/0.63 (step @p127 :rule bool-impl-elim :args (@t18 @t17)) % 0.46/0.63 (step @p128 :rule refl :args (@t145)) % 0.46/0.63 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or @t145 @t19))) % 0.46/0.63 (step @p130 :rule trans :premises (@p129 @p126)) % 0.46/0.63 (step @p131 :rule bool-impl-elim :args (@t21 @t19)) % 0.46/0.63 (step @p132 :rule trans :premises (@p131 @p130)) % 0.46/0.63 (step @p133 :rule cong :premises (@p132) :args (@t23)) % 0.46/0.63 (step @p134 :rule trans :premises (@p133 @p125)) % 0.46/0.63 (step @p135 :rule refl :args (@t24)) % 0.46/0.63 (step @p136 :rule cong :premises (@p135 @p134) :args (@t25)) % 0.46/0.63 (step @p137 :rule cong :premises (@p136) :args (@t27)) % 0.46/0.63 (step @p138 :rule trans :premises (@p137 @p62)) % 0.46/0.63 (step @p139 :rule refl :args (tptp.dpsetconstrI)) % 0.46/0.63 (step @p140 :rule cong :premises (@p139 @p138) :args (@t28)) % 0.46/0.63 (step @p141 :rule eq_resolve :premises (@p1 @p140)) % 0.46/0.63 (step @p142 :rule cong :premises (@p141 @p37) :args (@t147)) % 0.46/0.63 (step @p143 :rule cong :premises 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(step @p486 :rule not_implies_elim2 :premises (@p483)) % 0.46/0.63 (step @p487 :rule refl :args (@t310)) % 0.46/0.63 (step @p488 :rule bool-double-not-elim :args (@t95)) % 0.46/0.63 (step @p489 :rule nary_cong :premises (@p488 @p487) :args ((or (not @t311) @t310))) % 0.46/0.63 (step @p490 :rule refl :args (@t295)) % 0.46/0.63 (step @p491 :rule refl :args (@t297)) % 0.46/0.63 (step @p492 :rule refl :args (@t299)) % 0.46/0.63 (step @p493 :rule eq-refl :args (@t101)) % 0.46/0.63 (step @p494 :rule refl :args (@t101)) % 0.46/0.63 (step @p495 :rule cong :premises (@p494 @p20) :args ((= @t101 @t102))) % 0.46/0.63 (step @p496 :rule trans :premises (@p495 @p493)) % 0.46/0.63 (step @p497 :rule true_elim :premises (@p496)) % 0.46/0.63 (step @p498 :rule refl :args (@t98)) % 0.46/0.63 (step @p499 :rule cong :premises (@p498 @p498 @p497) :args (@t312)) % 0.46/0.63 (step @p500 :rule refl :args (@t300)) % 0.46/0.63 (step @p501 :rule cong :premises (@p500 @p499) :args (@t313)) % 0.46/0.63 (step @p502 :rule refl :args (@t303)) % 0.46/0.63 (step @p503 :rule refl :args (@t305)) % 0.46/0.63 (step @p504 :rule refl :args (@t307)) % 0.46/0.63 (step @p505 :rule refl :args (@t308)) % 0.46/0.63 (step @p506 :rule nary_cong :premises (@p505 @p504 @p503 @p502 @p501 @p492 @p491 @p490) :args (@t314)) % 0.46/0.63 (step @p507 :rule cong :premises (@p506) :args (@t315)) % 0.46/0.63 (step @p508 :rule refl :args (@t311)) % 0.46/0.63 (step @p509 :rule cong :premises (@p508 @p507) :args ((=> @t311 @t315))) % 0.46/0.63 (assume-push @p573 @t311) % 0.46/0.63 (step @p511 :rule skolemize :premises (@p486)) % 0.46/0.63 (step-pop @p574 :rule scope :premises (@p511)) % 0.46/0.63 (step @p512 :rule process_scope :premises (@p574) :args (@t315)) % 0.46/0.63 (step @p514 :rule eq_resolve :premises (@p512 @p509)) % 0.46/0.63 (step @p515 :rule implies_elim :premises (@p514)) % 0.46/0.63 (step @p516 :rule eq_resolve :premises (@p515 @p489)) % 0.46/0.63 (step @p517 :rule chain_m_resolution :premises (@p516 @p486) :args 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0.46/0.63 (step @p531 :rule reordering :premises (@p530) :args ((or @t304 @t309))) % 0.46/0.63 (step @p532 :rule chain_m_resolution :premises (@p531 @p517) :args (@t304 @t316 @t317)) % 0.46/0.63 (step @p533 :rule cnf_or_pos :args (@t319)) % 0.46/0.63 (step @p534 :rule reordering :premises (@p533) :args ((or @t305 @t303 @t301 @t318 (not @t319)))) % 0.46/0.63 (step @p535 :rule chain_m_resolution :premises (@p534 @p532 @p526 @p519 @p485) :args (@t318 (@list false false true false) (@list @t304 @t302 @t301 @t319))) % 0.46/0.63 (step @p536 :rule bool-double-not-elim :args (@t109)) % 0.46/0.63 (step @p537 :rule refl :args (@t111)) % 0.46/0.63 (step @p538 :rule refl :args (@t320)) % 0.46/0.63 (step @p539 :rule nary_cong :premises (@p538 @p537 @p536) :args ((or @t320 @t111 (not @t110)))) % 0.46/0.63 (step @p540 :rule cnf_equiv_pos2 :args (@t114)) % 0.46/0.63 (step @p541 :rule eq_resolve :premises (@p540 @p539)) % 0.46/0.63 (step @p542 :rule reordering :premises (@p541) :args ((or @t111 @t109 @t320))) % 0.46/0.63 (step @p543 :rule chain_m_resolution :premises (@p542 @p535 @p36) :args (@t109 @t321 (@list @t111 @t114))) % 0.46/0.63 (step @p544 :rule bool-double-not-elim :args (@t294)) % 0.46/0.63 (step @p545 :rule nary_cong :premises (@p521 @p544) :args ((or @t309 (not @t295)))) % 0.46/0.63 (step @p546 :rule cnf_or_neg :args (@t309 7)) % 0.46/0.64 (step @p547 :rule eq_resolve :premises (@p546 @p545)) % 0.46/0.64 (step @p548 :rule reordering :premises (@p547) :args ((or @t294 @t309))) % 0.46/0.64 (step @p549 :rule chain_m_resolution :premises (@p548 @p517) :args (@t294 @t316 @t317)) % 0.46/0.64 (step @p550 :rule bool-double-not-elim :args (@t296)) % 0.46/0.64 (step @p551 :rule nary_cong :premises (@p521 @p550) :args ((or @t309 (not @t297)))) % 0.46/0.64 (step @p552 :rule cnf_or_neg :args (@t309 6)) % 0.46/0.64 (step @p553 :rule eq_resolve :premises (@p552 @p551)) % 0.46/0.64 (step @p554 :rule reordering :premises (@p553) :args ((or @t296 @t309))) % 0.46/0.64 (step @p555 :rule chain_m_resolution :premises (@p554 @p517) :args (@t296 @t316 @t317)) % 0.46/0.64 (step @p556 :rule bool-double-not-elim :args (@t298)) % 0.46/0.64 (step @p557 :rule nary_cong :premises (@p521 @p556) :args ((or @t309 (not @t299)))) % 0.46/0.64 (step @p558 :rule cnf_or_neg :args (@t309 5)) % 0.46/0.64 (step @p559 :rule eq_resolve :premises (@p558 @p557)) % 0.46/0.64 (step @p560 :rule reordering :premises (@p559) :args ((or @t298 @t309))) % 0.46/0.64 (step @p561 :rule chain_m_resolution :premises (@p560 @p517) :args (@t298 @t316 @t317)) % 0.46/0.64 (step @p562 :rule cnf_or_pos :args (@t322)) % 0.46/0.64 (step @p563 :rule reordering :premises (@p562) :args ((or @t299 @t297 @t295 @t323))) % 0.46/0.64 (step @p564 :rule chain_m_resolution :premises (@p563 @p561 @p555 @p549) :args (@t323 (@list false false false) (@list @t298 @t296 @t294))) % 0.46/0.64 (assume-push @p575 @t109) % 0.46/0.64 (step @p566 :rule instantiate :premises (@p543) :args ((@list @t293))) % 0.46/0.64 (step-pop @p576 :rule scope :premises (@p566)) % 0.46/0.64 (step @p567 :rule process_scope :premises (@p576) :args (@t322)) % 0.46/0.64 (step @p569 :rule implies_elim :premises (@p567)) % 0.46/0.64 (step @p570 false :rule chain_m_resolution :premises (@p569 @p564 @p543) :args (false @t321 (@list @t322 @t109))) % 0.46/0.64 ) % 0.46/0.64 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------