%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET004^4 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n018.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 08:46:52 AM UTC 2026 % Result : Theorem 0.38s 0.73s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SET004^4 : TPTP v9.2.1. Released v8.1.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n018.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 14:40:05 EDT 2026 % 0.19/0.35 % CPUTime : % 0.32/0.53 %----Proving TH0 % 0.38/0.73 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.73 % SZS status Theorem % 0.38/0.73 % SZS output start Proof % 0.38/0.73 ( % 0.38/0.73 (declare-sort $$unsorted 0) % 0.38/0.73 (declare-sort tptp.mworld 0) % 0.38/0.73 (declare-const tptp.mactual tptp.mworld) % 0.38/0.73 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.38/0.73 (declare-const tptp.empty_set $$unsorted) % 0.38/0.73 (declare-const tptp.subset (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.73 (declare-const tptp.member (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.73 (declare-const tptp.equal_set (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.73 (declare-const tptp.qmltpeq (-> $$unsorted $$unsorted tptp.mworld Bool)) % 0.38/0.73 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.38/0.73 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.73 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.38/0.73 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.73 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.73 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.73 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.73 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.38/0.73 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.73 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.73 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.73 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.73 (define @t1 () (@var "W" tptp.mworld)) % 0.38/0.73 (define @t2 () (_ tptp.mrel @t1)) % 0.38/0.73 (define @t3 () (@list @t1)) % 0.38/0.73 (define @t4 () (@var "U" tptp.mworld)) % 0.38/0.73 (define @t5 () (@var "V" tptp.mworld)) % 0.38/0.73 (define @t6 () (_ @t2 @t5)) % 0.38/0.73 (define @t7 () (@var "__flatten_var_0" tptp.mworld)) % 0.38/0.73 (define @t8 () (@var "X" $$unsorted)) % 0.38/0.73 (define @t9 () (_ tptp.qmltpeq @t8)) % 0.38/0.73 (define @t10 () (@list @t8 @t7)) % 0.38/0.73 (define @t11 () (@var "Y" $$unsorted)) % 0.38/0.73 (define @t12 () (_ tptp.qmltpeq @t11)) % 0.38/0.73 (define @t13 () (_ @t9 @t11)) % 0.38/0.73 (define @t14 () (@list @t11 @t7)) % 0.38/0.73 (define @t15 () (@var "Z" $$unsorted)) % 0.38/0.73 (define @t16 () (@var "C" $$unsorted)) % 0.38/0.73 (define @t17 () (@var "B" $$unsorted)) % 0.38/0.73 (define @t18 () (@var "A" $$unsorted)) % 0.38/0.73 (define @t19 () (_ (_ tptp.qmltpeq @t18) @t17)) % 0.38/0.73 (define @t20 () (_ tptp.mimplies @t19)) % 0.38/0.73 (define @t21 () (@list @t16 @t7)) % 0.38/0.73 (define @t22 () (@list @t17 @t7)) % 0.38/0.73 (define @t23 () (@list @t18 @t7)) % 0.38/0.73 (define @t24 () (_ tptp.difference @t16)) % 0.38/0.73 (define @t25 () (_ tptp.intersection @t17)) % 0.38/0.73 (define @t26 () (_ tptp.intersection @t18)) % 0.38/0.73 (define @t27 () (_ tptp.intersection @t16)) % 0.38/0.73 (define @t28 () (_ tptp.power_set @t18)) % 0.38/0.73 (define @t29 () (_ tptp.product @t18)) % 0.38/0.73 (define @t30 () (_ tptp.singleton @t18)) % 0.38/0.73 (define @t31 () (_ tptp.sum @t18)) % 0.38/0.73 (define @t32 () (_ tptp.union @t18)) % 0.38/0.73 (define @t33 () (_ tptp.union @t16)) % 0.38/0.73 (define @t34 () (_ tptp.unordered_pair @t18)) % 0.38/0.73 (define @t35 () (_ tptp.unordered_pair @t16)) % 0.38/0.73 (define @t36 () (_ tptp.equal_set @t18)) % 0.38/0.73 (define @t37 () (_ tptp.mand @t19)) % 0.38/0.73 (define @t38 () (_ tptp.equal_set @t16)) % 0.38/0.73 (define @t39 () (_ tptp.member @t17)) % 0.38/0.73 (define @t40 () (_ tptp.member @t16)) % 0.38/0.73 (define @t41 () (_ tptp.subset @t17)) % 0.38/0.73 (define @t42 () (_ tptp.subset @t18)) % 0.38/0.73 (define @t43 () (_ tptp.subset @t16)) % 0.38/0.73 (define @t44 () (_ tptp.member @t8)) % 0.38/0.73 (define @t45 () (_ @t44 @t17)) % 0.38/0.73 (define @t46 () (_ @t44 @t18)) % 0.38/0.73 (define @t47 () (lambda @t10 (_ (_ (_ tptp.mimplies @t46) @t45) @t7))) % 0.38/0.73 (define @t48 () (_ @t42 @t17)) % 0.38/0.73 (define @t49 () (lambda @t22 (_ (_ (_ tptp.mequiv @t48) (_ tptp.mforall_di @t47)) @t7))) % 0.38/0.73 (define @t50 () (lambda @t23 (_ (_ tptp.mforall_di @t49) @t7))) % 0.38/0.73 (define @t51 () (_ @t41 @t18)) % 0.38/0.73 (define @t52 () (_ @t36 @t17)) % 0.38/0.73 (define @t53 () (lambda @t22 (_ (_ (_ tptp.mequiv @t52) (_ (_ tptp.mand @t48) @t51)) @t7))) % 0.38/0.73 (define @t54 () (lambda @t23 (_ (_ tptp.mforall_di @t53) @t7))) % 0.38/0.73 (define @t55 () (_ (_ tptp.subset @t8) @t18)) % 0.38/0.73 (define @t56 () (_ @t26 @t17)) % 0.38/0.73 (define @t57 () (_ @t44 @t56)) % 0.38/0.73 (define @t58 () (lambda @t22 (_ (_ (_ tptp.mequiv @t57) (_ (_ tptp.mand @t46) @t45)) @t7))) % 0.38/0.73 (define @t59 () (lambda @t23 (_ (_ tptp.mforall_di @t58) @t7))) % 0.38/0.73 (define @t60 () (lambda @t10 (_ (_ tptp.mforall_di @t59) @t7))) % 0.38/0.73 (define @t61 () (@var "E" $$unsorted)) % 0.38/0.73 (define @t62 () (_ @t9 @t18)) % 0.38/0.73 (define @t63 () (_ @t44 @t11)) % 0.38/0.74 (define @t64 () (_ (_ tptp.member @t11) @t18)) % 0.38/0.74 (define @t65 () (lambda @t22 (_ (_ (_ tptp.equal_set @t56) (_ @t25 @t18)) @t7))) % 0.38/0.74 (define @t66 () (lambda @t23 (_ (_ tptp.mforall_di @t65) @t7))) % 0.38/0.74 (define @t67 () (not (_ tptp.mlocal (_ tptp.mforall_di @t66)))) % 0.38/0.74 (define @t68 () (@var "Phi" (-> tptp.mworld Bool))) % 0.38/0.74 (define @t69 () (lambda (@list @t68) (_ @t68 tptp.mactual))) % 0.38/0.74 (define @t70 () (@var "A" (-> tptp.mworld Bool))) % 0.38/0.74 (define @t71 () (_ @t70 @t1)) % 0.38/0.74 (define @t72 () (lambda (@list @t70 @t1) (not @t71))) % 0.38/0.74 (define @t73 () (@var "B" (-> tptp.mworld Bool))) % 0.38/0.74 (define @t74 () (_ @t73 @t1)) % 0.38/0.74 (define @t75 () (@list @t70 @t73 @t1)) % 0.38/0.74 (define @t76 () (lambda @t75 (and @t71 @t74))) % 0.38/0.74 (define @t77 () (lambda @t75 (or @t71 @t74))) % 0.38/0.74 (define @t78 () (lambda @t75 (=> @t71 @t74))) % 0.38/0.74 (define @t79 () (lambda @t75 (= @t71 @t74))) % 0.38/0.74 (define @t80 () (_ @t68 @t5)) % 0.38/0.74 (define @t81 () (@list @t5)) % 0.38/0.74 (define @t82 () (@list @t68 @t1)) % 0.38/0.74 (define @t83 () (lambda @t82 (forall @t81 (=> @t6 @t80)))) % 0.38/0.74 (define @t84 () (lambda @t82 (exists @t81 (and @t6 @t80)))) % 0.38/0.74 (define @t85 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.38/0.74 (define @t86 () (_ (_ @t85 @t8) @t1)) % 0.38/0.74 (define @t87 () (@list @t8)) % 0.38/0.74 (define @t88 () (forall @t87 @t86)) % 0.38/0.74 (define @t89 () (@list @t85 @t1)) % 0.38/0.74 (define @t90 () (lambda @t89 @t88)) % 0.38/0.74 (define @t91 () (lambda @t89 (exists @t87 @t86))) % 0.38/0.74 (define @t92 () (@var "BOUND_VARIABLE_10819" $$unsorted)) % 0.38/0.74 (define @t93 () (@var "BOUND_VARIABLE_10856" $$unsorted)) % 0.38/0.74 (define @t94 () (tptp.intersection @t93 @t92)) % 0.38/0.74 (define @t95 () (@list @t8 @t93 @t92)) % 0.38/0.74 (define @t96 () (tptp.member @t8 @t92 @t1)) % 0.38/0.74 (define @t97 () (= (tptp.member @t8 @t94 @t1) (and (tptp.member @t8 @t93 @t1) @t96))) % 0.38/0.74 (define @t98 () (forall @t95 @t97)) % 0.38/0.74 (define @t99 () (lambda @t3 @t98)) % 0.38/0.74 (define @t100 () (_ @t99 tptp.mactual)) % 0.38/0.74 (define @t101 () (@list @t93 @t92)) % 0.38/0.74 (define @t102 () (forall @t101 @t97)) % 0.38/0.74 (define @t103 () (tptp.member @t8 @t92 @t7)) % 0.38/0.74 (define @t104 () (forall @t101 (= (tptp.member @t8 @t94 @t7) (and (tptp.member @t8 @t93 @t7) @t103)))) % 0.38/0.74 (define @t105 () (lambda @t10 @t104)) % 0.38/0.74 (define @t106 () (_ @t105 @t8 @t1)) % 0.38/0.74 (define @t107 () (forall @t87 @t106)) % 0.38/0.74 (define @t108 () (lambda @t3 @t107)) % 0.38/0.74 (define @t109 () (_ @t85 @t8 @t1)) % 0.38/0.74 (define @t110 () (forall @t87 @t109)) % 0.38/0.74 (define @t111 () (lambda @t89 @t110)) % 0.38/0.74 (define @t112 () (@list @t92)) % 0.38/0.74 (define @t113 () (forall @t112 @t97)) % 0.38/0.74 (define @t114 () (@list @t93)) % 0.38/0.74 (define @t115 () (tptp.member @t8 @t18 @t7)) % 0.38/0.74 (define @t116 () (tptp.intersection @t18 @t92)) % 0.38/0.74 (define @t117 () (forall @t112 (= (tptp.member @t8 @t116 @t7) (and @t115 @t103)))) % 0.38/0.74 (define @t118 () (lambda @t23 @t117)) % 0.38/0.74 (define @t119 () (_ @t118 @t93 @t1)) % 0.38/0.74 (define @t120 () (forall @t114 @t119)) % 0.38/0.74 (define @t121 () (lambda @t3 @t120)) % 0.38/0.74 (define @t122 () (@list @t8)) % 0.38/0.74 (define @t123 () (tptp.member @t8 @t18 @t1)) % 0.38/0.74 (define @t124 () (tptp.member @t8 @t116 @t1)) % 0.38/0.74 (define @t125 () (_ (_ @t44 @t92) @t1)) % 0.38/0.74 (define @t126 () (_ @t46 @t1)) % 0.38/0.74 (define @t127 () (and @t126 @t125)) % 0.38/0.74 (define @t128 () (_ @t26 @t92)) % 0.38/0.74 (define @t129 () (_ (_ @t44 @t128) @t1)) % 0.38/0.74 (define @t130 () (= @t129 @t127)) % 0.38/0.74 (define @t131 () (_ @t45 @t7)) % 0.38/0.74 (define @t132 () (_ @t46 @t7)) % 0.38/0.74 (define @t133 () (= (_ @t57 @t7) (and @t132 @t131))) % 0.38/0.74 (define @t134 () (lambda @t22 @t133)) % 0.38/0.74 (define @t135 () (_ @t134 @t92 @t1)) % 0.38/0.74 (define @t136 () (forall @t112 @t135)) % 0.38/0.74 (define @t137 () (lambda @t3 @t136)) % 0.38/0.74 (define @t138 () (_ @t45 @t1)) % 0.38/0.74 (define @t139 () (and @t126 @t138)) % 0.38/0.74 (define @t140 () (_ @t57 @t1)) % 0.38/0.74 (define @t141 () (lambda @t3 @t139)) % 0.38/0.74 (define @t142 () (_ @t141 @t1)) % 0.38/0.74 (define @t143 () (lambda @t3 (= @t142 @t140))) % 0.38/0.74 (define @t144 () (@list @t73 @t1)) % 0.38/0.74 (define @t145 () (lambda @t144 (and @t126 @t74))) % 0.38/0.74 (define @t146 () (_ @t76 @t46)) % 0.38/0.74 (define @t147 () (lambda @t144 (= @t140 @t74))) % 0.38/0.74 (define @t148 () (_ @t79 @t57)) % 0.38/0.74 (define @t149 () (lambda @t22 (_ (_ @t148 (_ @t146 @t45)) @t7))) % 0.38/0.74 (define @t150 () (lambda @t23 (_ (_ @t111 @t149) @t7))) % 0.38/0.74 (define @t151 () (@var "BOUND_VARIABLE_11720" $$unsorted)) % 0.38/0.74 (define @t152 () (tptp.intersection @t151 @t8)) % 0.38/0.74 (define @t153 () (tptp.intersection @t8 @t151)) % 0.38/0.74 (define @t154 () (@list @t8 @t151)) % 0.38/0.74 (define @t155 () (forall @t154 (tptp.equal_set @t153 @t152 tptp.mactual))) % 0.38/0.74 (define @t156 () (@quantifiers_skolemize @t155 1)) % 0.38/0.74 (define @t157 () (@quantifiers_skolemize @t155 0)) % 0.38/0.74 (define @t158 () (tptp.intersection @t157 @t156)) % 0.38/0.74 (define @t159 () (@var "BOUND_VARIABLE_10550" $$unsorted)) % 0.38/0.74 (define @t160 () (tptp.member @t159 @t158 tptp.mactual)) % 0.38/0.74 (define @t161 () (tptp.intersection @t156 @t157)) % 0.38/0.74 (define @t162 () (tptp.member @t159 @t161 tptp.mactual)) % 0.38/0.74 (define @t163 () (@list @t159)) % 0.38/0.74 (define @t164 () (forall @t163 (or (not @t162) @t160))) % 0.38/0.74 (define @t165 () (@quantifiers_skolemize @t164 0)) % 0.38/0.74 (define @t166 () (@var "BOUND_VARIABLE_10584" $$unsorted)) % 0.38/0.74 (define @t167 () (@list @t8 @t166)) % 0.38/0.74 (define @t168 () (tptp.member @t159 @t8 @t1)) % 0.38/0.74 (define @t169 () (= (tptp.subset @t8 @t166 @t1) (forall @t163 (or (not @t168) (tptp.member @t159 @t166 @t1))))) % 0.38/0.74 (define @t170 () (forall @t167 @t169)) % 0.38/0.74 (define @t171 () (lambda @t3 @t170)) % 0.38/0.74 (define @t172 () (_ @t171 tptp.mactual)) % 0.38/0.74 (define @t173 () (@list @t166)) % 0.38/0.74 (define @t174 () (forall @t173 @t169)) % 0.38/0.74 (define @t175 () (not (tptp.member @t159 @t18 @t7))) % 0.38/0.74 (define @t176 () (tptp.subset @t18 @t8 @t7)) % 0.38/0.74 (define @t177 () (forall @t87 (= @t176 (forall @t163 (or @t175 (tptp.member @t159 @t8 @t7)))))) % 0.38/0.74 (define @t178 () (lambda @t23 @t177)) % 0.38/0.74 (define @t179 () (forall @t87 (_ @t178 @t8 @t1))) % 0.38/0.74 (define @t180 () (lambda @t3 @t179)) % 0.38/0.74 (define @t181 () (forall @t163 (or (not (tptp.member @t159 @t18 @t1)) @t168))) % 0.38/0.74 (define @t182 () (tptp.subset @t18 @t8 @t1)) % 0.38/0.74 (define @t183 () (_ (_ @t42 @t8) @t1)) % 0.38/0.74 (define @t184 () (= @t183 @t181)) % 0.38/0.74 (define @t185 () (_ @t48 @t7)) % 0.38/0.74 (define @t186 () (forall @t87 (or (not @t115) (tptp.member @t8 @t17 @t7)))) % 0.38/0.74 (define @t187 () (= @t186 @t185)) % 0.38/0.74 (define @t188 () (lambda @t22 @t187)) % 0.38/0.74 (define @t189 () (forall @t87 (_ @t188 @t8 @t1))) % 0.38/0.74 (define @t190 () (lambda @t3 @t189)) % 0.38/0.74 (define @t191 () (_ @t48 @t1)) % 0.38/0.74 (define @t192 () (tptp.member @t8 @t17 @t1)) % 0.38/0.74 (define @t193 () (forall @t87 (or (not @t123) @t192))) % 0.38/0.74 (define @t194 () (lambda @t3 @t193)) % 0.38/0.74 (define @t195 () (_ @t194 @t1)) % 0.38/0.74 (define @t196 () (lambda @t3 (= @t195 @t191))) % 0.38/0.74 (define @t197 () (not @t126)) % 0.38/0.74 (define @t198 () (or @t197 @t138)) % 0.38/0.74 (define @t199 () (=> @t126 @t138)) % 0.38/0.74 (define @t200 () (=> @t132 @t131)) % 0.38/0.74 (define @t201 () (lambda @t10 @t200)) % 0.38/0.74 (define @t202 () (_ @t201 @t8 @t1)) % 0.38/0.74 (define @t203 () (forall @t87 @t202)) % 0.38/0.74 (define @t204 () (lambda @t3 @t203)) % 0.38/0.74 (define @t205 () (lambda @t3 @t199)) % 0.38/0.74 (define @t206 () (lambda @t144 (=> @t126 @t74))) % 0.38/0.74 (define @t207 () (_ @t78 @t46)) % 0.38/0.74 (define @t208 () (lambda @t10 (_ (_ @t207 @t45) @t7))) % 0.38/0.74 (define @t209 () (lambda @t144 (= @t191 @t74))) % 0.38/0.74 (define @t210 () (_ @t79 @t48)) % 0.38/0.74 (define @t211 () (lambda @t22 (_ (_ @t210 (_ @t111 @t208)) @t7))) % 0.38/0.74 (define @t212 () (@list @t158 @t161)) % 0.38/0.74 (define @t213 () (forall @t163 (or (not @t160) @t162))) % 0.38/0.74 (define @t214 () (@quantifiers_skolemize @t213 0)) % 0.38/0.74 (define @t215 () (tptp.member @t214 @t158 tptp.mactual)) % 0.38/0.74 (define @t216 () (tptp.member @t214 @t161 tptp.mactual)) % 0.38/0.74 (define @t217 () (not @t215)) % 0.38/0.74 (define @t218 () (or @t217 @t216)) % 0.38/0.74 (define @t219 () (tptp.member @t214 @t156 tptp.mactual)) % 0.38/0.74 (define @t220 () (tptp.member @t214 @t157 tptp.mactual)) % 0.38/0.74 (define @t221 () (and @t220 @t219)) % 0.38/0.74 (define @t222 () (= @t215 @t221)) % 0.38/0.74 (define @t223 () (and @t219 @t220)) % 0.38/0.74 (define @t224 () (= @t216 @t223)) % 0.38/0.74 (define @t225 () (not @t221)) % 0.38/0.74 (define @t226 () (not @t218)) % 0.38/0.74 (define @t227 () (not @t213)) % 0.38/0.74 (define @t228 () (@list false)) % 0.38/0.74 (define @t229 () (tptp.subset @t158 @t161 tptp.mactual)) % 0.38/0.74 (define @t230 () (= @t229 @t213)) % 0.38/0.74 (define @t231 () (@list false false)) % 0.38/0.74 (define @t232 () (@var "BOUND_VARIABLE_10676" $$unsorted)) % 0.38/0.74 (define @t233 () (@list @t8 @t232)) % 0.38/0.74 (define @t234 () (= (tptp.equal_set @t8 @t232 @t1) (and (tptp.subset @t8 @t232 @t1) (tptp.subset @t232 @t8 @t1)))) % 0.38/0.74 (define @t235 () (forall @t233 @t234)) % 0.38/0.74 (define @t236 () (lambda @t3 @t235)) % 0.38/0.74 (define @t237 () (_ @t236 tptp.mactual)) % 0.38/0.74 (define @t238 () (@list @t232)) % 0.38/0.74 (define @t239 () (forall @t238 @t234)) % 0.38/0.74 (define @t240 () (forall @t87 (= (tptp.equal_set @t18 @t8 @t7) (and @t176 (tptp.subset @t8 @t18 @t7))))) % 0.38/0.74 (define @t241 () (lambda @t23 @t240)) % 0.38/0.74 (define @t242 () (forall @t87 (_ @t241 @t8 @t1))) % 0.38/0.74 (define @t243 () (lambda @t3 @t242)) % 0.38/0.74 (define @t244 () (tptp.subset @t8 @t18 @t1)) % 0.38/0.74 (define @t245 () (tptp.equal_set @t18 @t8 @t1)) % 0.38/0.74 (define @t246 () (_ @t55 @t1)) % 0.38/0.74 (define @t247 () (and @t183 @t246)) % 0.38/0.74 (define @t248 () (_ (_ @t36 @t8) @t1)) % 0.38/0.74 (define @t249 () (= @t248 @t247)) % 0.38/0.74 (define @t250 () (= (_ @t52 @t7) (and @t185 (_ @t51 @t7)))) % 0.38/0.74 (define @t251 () (lambda @t22 @t250)) % 0.38/0.74 (define @t252 () (_ @t251 @t8 @t1)) % 0.38/0.74 (define @t253 () (forall @t87 @t252)) % 0.38/0.74 (define @t254 () (lambda @t3 @t253)) % 0.38/0.74 (define @t255 () (and @t191 (_ @t51 @t1))) % 0.38/0.74 (define @t256 () (_ @t52 @t1)) % 0.38/0.74 (define @t257 () (lambda @t3 @t255)) % 0.38/0.74 (define @t258 () (_ @t257 @t1)) % 0.38/0.74 (define @t259 () (lambda @t3 (= @t258 @t256))) % 0.38/0.74 (define @t260 () (lambda @t144 (and @t191 @t74))) % 0.38/0.74 (define @t261 () (_ @t76 @t48)) % 0.38/0.74 (define @t262 () (lambda @t144 (= @t256 @t74))) % 0.38/0.74 (define @t263 () (_ @t79 @t52)) % 0.38/0.74 (define @t264 () (lambda @t22 (_ (_ @t263 (_ @t261 @t51)) @t7))) % 0.38/0.74 (define @t265 () (tptp.equal_set @t153 @t152 @t1)) % 0.38/0.74 (define @t266 () (forall @t154 @t265)) % 0.38/0.74 (define @t267 () (lambda @t3 @t266)) % 0.38/0.74 (define @t268 () (_ @t267 tptp.mactual)) % 0.38/0.74 (define @t269 () (@list @t151)) % 0.38/0.74 (define @t270 () (forall @t269 @t265)) % 0.38/0.74 (define @t271 () (tptp.intersection @t8 @t18)) % 0.38/0.74 (define @t272 () (tptp.intersection @t18 @t8)) % 0.38/0.74 (define @t273 () (forall @t87 (tptp.equal_set @t272 @t271 @t7))) % 0.38/0.74 (define @t274 () (lambda @t23 @t273)) % 0.38/0.74 (define @t275 () (forall @t87 (_ @t274 @t8 @t1))) % 0.38/0.74 (define @t276 () (lambda @t3 @t275)) % 0.38/0.74 (define @t277 () (tptp.equal_set @t272 @t271 @t1)) % 0.38/0.74 (define @t278 () (_ (_ tptp.intersection @t8) @t18)) % 0.38/0.74 (define @t279 () (_ @t26 @t8)) % 0.38/0.74 (define @t280 () (_ (_ (_ tptp.equal_set @t279) @t278) @t1)) % 0.38/0.74 (define @t281 () (_ @t65 @t8 @t1)) % 0.38/0.74 (define @t282 () (forall @t87 @t281)) % 0.38/0.74 (define @t283 () (lambda @t3 @t282)) % 0.38/0.74 (define @t284 () (_ @t111 @t65)) % 0.38/0.74 (define @t285 () (lambda @t23 (_ @t284 @t7))) % 0.38/0.74 (define @t286 () (tptp.subset @t161 @t158 tptp.mactual)) % 0.38/0.74 (define @t287 () (and @t229 @t286)) % 0.38/0.74 (define @t288 () (tptp.equal_set @t158 @t161 tptp.mactual)) % 0.38/0.74 (define @t289 () (= @t288 @t287)) % 0.38/0.74 (define @t290 () (not @t287)) % 0.38/0.74 (define @t291 () (@list true false)) % 0.38/0.74 (define @t292 () (= @t286 @t164)) % 0.38/0.74 (define @t293 () (not @t164)) % 0.38/0.74 (define @t294 () (tptp.member @t165 @t158 tptp.mactual)) % 0.38/0.74 (define @t295 () (tptp.member @t165 @t161 tptp.mactual)) % 0.38/0.74 (define @t296 () (not @t295)) % 0.38/0.74 (define @t297 () (or @t296 @t294)) % 0.38/0.74 (define @t298 () (not @t297)) % 0.38/0.74 (define @t299 () (@list true)) % 0.38/0.74 (define @t300 () (@list @t297)) % 0.38/0.74 (define @t301 () (tptp.member @t165 @t156 tptp.mactual)) % 0.38/0.74 (define @t302 () (tptp.member @t165 @t157 tptp.mactual)) % 0.38/0.74 (define @t303 () (and @t302 @t301)) % 0.38/0.74 (define @t304 () (= @t294 @t303)) % 0.38/0.74 (define @t305 () (not @t303)) % 0.38/0.74 (define @t306 () (and @t301 @t302)) % 0.38/0.74 (define @t307 () (= @t295 @t306)) % 0.38/0.74 (define @t308 () (not @t306)) % 0.38/0.74 (define @t309 () (@list @t306)) % 0.38/0.74 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.38/0.74 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.mrel @t5) @t4)) (_ @t2 @t4)))) % 0.38/0.74 (assume @p3 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ @t9 @t8) @t7))))) % 0.38/0.74 (assume @p4 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t14 (_ (_ (_ tptp.mimplies @t13) (_ @t12 @t8)) @t7))) @t7))))) % 0.38/0.74 (assume @p5 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t14 (_ (_ tptp.mforall_di (lambda (@list @t15 @t7) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t13) (_ @t12 @t15))) (_ @t9 @t15)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p6 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ (_ tptp.difference @t18) @t16)) (_ (_ tptp.difference @t17) @t16))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p7 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t24 @t18)) (_ @t24 @t17))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p8 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t26 @t16)) (_ @t25 @t16))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p9 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t27 @t18)) (_ @t27 @t17))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p10 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t20 (_ (_ tptp.qmltpeq @t28) (_ tptp.power_set @t17))) @t7))) @t7))))) % 0.38/0.74 (assume @p11 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t20 (_ (_ tptp.qmltpeq @t29) (_ tptp.product @t17))) @t7))) @t7))))) % 0.38/0.74 (assume @p12 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t20 (_ (_ tptp.qmltpeq @t30) (_ tptp.singleton @t17))) @t7))) @t7))))) % 0.38/0.74 (assume @p13 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ @t20 (_ (_ tptp.qmltpeq @t31) (_ tptp.sum @t17))) @t7))) @t7))))) % 0.38/0.74 (assume @p14 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t32 @t16)) (_ (_ tptp.union @t17) @t16))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p15 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t33 @t18)) (_ @t33 @t17))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p16 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t34 @t16)) (_ (_ tptp.unordered_pair @t17) @t16))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p17 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ @t20 (_ (_ tptp.qmltpeq (_ @t35 @t18)) (_ @t35 @t17))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p18 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ @t36 @t16))) (_ (_ tptp.equal_set @t17) @t16)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p19 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ @t38 @t18))) (_ @t38 @t17)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p20 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ (_ tptp.member @t18) @t16))) (_ @t39 @t16)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p21 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ @t40 @t18))) (_ @t40 @t17)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p22 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ @t42 @t16))) (_ @t41 @t16)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p23 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t21 (_ (_ (_ tptp.mimplies (_ @t37 (_ @t43 @t18))) (_ @t43 @t17)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p24 (_ tptp.mlocal (_ tptp.mforall_di @t50))) % 0.38/0.74 (assume @p25 (_ tptp.mlocal (_ tptp.mforall_di @t54))) % 0.38/0.74 (assume @p26 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mequiv (_ @t44 @t28)) @t55) @t7))) @t7))))) % 0.38/0.74 (assume @p27 (_ tptp.mlocal (_ tptp.mforall_di @t60))) % 0.38/0.74 (assume @p28 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mequiv (_ @t44 (_ @t32 @t17))) (_ (_ tptp.mor @t46) @t45)) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p29 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mnot (_ @t44 tptp.empty_set)) @t7))))) % 0.38/0.74 (assume @p30 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t22 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda (@list @t61 @t7) (_ (_ (_ tptp.mequiv (_ @t39 (_ (_ tptp.difference @t61) @t18))) (_ (_ tptp.mand (_ @t39 @t61)) (_ tptp.mnot (_ @t39 @t18)))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p31 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mequiv (_ @t44 @t30)) @t62) @t7))) @t7))))) % 0.38/0.74 (assume @p32 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ tptp.mforall_di (lambda @t22 (_ (_ (_ tptp.mequiv (_ @t44 (_ @t34 @t17))) (_ (_ tptp.mor @t62) (_ @t9 @t17))) @t7))) @t7))) @t7))))) % 0.38/0.74 (assume @p33 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mequiv (_ @t44 @t31)) (_ tptp.mexists_di (lambda @t14 (_ (_ (_ tptp.mand @t64) @t63) @t7)))) @t7))) @t7))))) % 0.38/0.74 (assume @p34 (_ tptp.mlocal (_ tptp.mforall_di (lambda @t10 (_ (_ tptp.mforall_di (lambda @t23 (_ (_ (_ tptp.mequiv (_ @t44 @t29)) (_ tptp.mforall_di (lambda @t14 (_ (_ (_ tptp.mimplies @t64) @t63) @t7)))) @t7))) @t7))))) % 0.38/0.74 (assume @p35 @t67) % 0.38/0.74 (assume @p36 true) % 0.38/0.74 (step @p37 (= tptp.mlocal @t69) :rule refl :args (@t69)) % 0.38/0.74 (step @p38 (= tptp.mnot @t72) :rule refl :args (@t72)) % 0.38/0.74 (step @p39 (= tptp.mand @t76) :rule refl :args (@t76)) % 0.38/0.74 (step @p40 (= tptp.mor @t77) :rule refl :args (@t77)) % 0.38/0.74 (step @p41 (= tptp.mimplies @t78) :rule refl :args (@t78)) % 0.38/0.74 (step @p42 (= tptp.mequiv @t79) :rule refl :args (@t79)) % 0.38/0.74 (step @p43 (= tptp.mbox @t83) :rule refl :args (@t83)) % 0.38/0.74 (step @p44 (= tptp.mdia @t84) :rule refl :args (@t84)) % 0.38/0.74 (step @p45 (= tptp.mforall_di @t90) :rule refl :args (@t90)) % 0.38/0.74 (step @p46 (= tptp.mexists_di @t91) :rule refl :args (@t91)) % 0.38/0.74 (step @p47 :rule beta-reduce :args ((= @t100 (forall @t95 (= (tptp.member @t8 @t94 tptp.mactual) (and (tptp.member @t8 @t93 tptp.mactual) (tptp.member @t8 @t92 tptp.mactual))))))) % 0.38/0.74 (step @p48 :rule beta-reduce :args ((= (_ @t69 @t99) @t100))) % 0.38/0.74 (step @p49 :rule trans :premises (@p48 @p47)) % 0.38/0.74 (step @p50 :rule quant-merge-prenex :args ((= (forall @t87 @t102) @t98))) % 0.38/0.74 (step @p51 :rule beta-reduce :args ((= @t106 @t102))) % 0.38/0.74 (step @p52 :rule cong :premises (@p51) :args (@t107)) % 0.38/0.74 (step @p53 :rule trans :premises (@p52 @p50)) % 0.38/0.74 (step @p54 :rule cong :premises (@p53) :args (@t108)) % 0.38/0.74 (step @p55 :rule beta-reduce :args ((= (_ @t111 @t105) @t108))) % 0.38/0.74 (step @p56 :rule trans :premises (@p55 @p54)) % 0.38/0.74 (step @p57 :rule beta-reduce :args ((= (_ (lambda @t3 @t102) @t7) @t104))) % 0.38/0.74 (step @p58 :rule refl :args (@t7)) % 0.38/0.74 (step @p59 :rule quant-merge-prenex :args ((= (forall @t114 @t113) @t102))) % 0.38/0.74 (step @p60 :rule beta-reduce :args ((= @t119 @t113))) % 0.38/0.74 (step @p61 :rule cong :premises (@p60) :args (@t120)) % 0.38/0.74 (step @p62 :rule trans :premises (@p61 @p59)) % 0.38/0.74 (step @p63 :rule cong :premises (@p62) :args (@t121)) % 0.38/0.74 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t89 (forall @t114 (_ @t85 @t93 @t1))) @t118) @t121))) % 0.38/0.74 (step @p65 :rule trans :premises (@p64 @p63)) % 0.38/0.74 (step @p66 :rule refl :args (@t118)) % 0.38/0.74 (step @p67 :rule alpha_equiv :args (@t110 @t122 (@list @t93))) % 0.38/0.74 (step @p68 :rule cong :premises (@p67) :args (@t111)) % 0.38/0.74 (step @p69 :rule ho_cong :premises (@p68 @p66)) % 0.38/0.74 (step @p70 :rule trans :premises (@p69 @p65)) % 0.38/0.74 (step @p71 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t112 (= @t124 (and @t123 @t96)))) @t7) @t117))) % 0.38/0.74 (step @p72 :rule refl :args (@t96)) % 0.38/0.74 (step @p73 :rule refl :args (@t125)) % 0.38/0.74 (step @p74 :rule 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:premises (@p514 @p512 @p509 @p495) :args (false (@list false false true) (@list @t302 @t301 @t303))) % 0.38/0.74 ) % 0.38/0.74 % SZS output end Proof % 0.38/0.74 % cvc5 exiting %------------------------------------------------------------------------------