%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET707+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n002.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 08:48:29 AM UTC 2026 % Result : Theorem 0.51s 0.76s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET707+4 : TPTP v9.2.1. Released v2.2.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n002.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:09:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.76 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.76 % SZS status Theorem % 0.51/0.76 % SZS output start Proof % 0.51/0.76 ( % 0.51/0.76 (declare-sort $$unsorted 0) % 0.51/0.76 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.empty_set $$unsorted) % 0.51/0.76 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.51/0.76 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.51/0.76 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.51/0.76 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.51/0.76 (define @t1 () (@var "B" $$unsorted)) % 0.51/0.76 (define @t2 () (@var "X" $$unsorted)) % 0.51/0.76 (define @t3 () (tptp.member @t2 @t1)) % 0.51/0.76 (define @t4 () (@var "A" $$unsorted)) % 0.51/0.76 (define @t5 () (tptp.member @t2 @t4)) % 0.51/0.76 (define @t6 () (@list @t2)) % 0.51/0.76 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.51/0.76 (define @t8 () (tptp.subset @t4 @t1)) % 0.51/0.76 (define @t9 () (= @t8 @t7)) % 0.51/0.76 (define @t10 () (@list @t4 @t1)) % 0.51/0.76 (define @t11 () (forall @t10 @t9)) % 0.51/0.76 (define @t12 () (@list @t2 @t4)) % 0.51/0.76 (define @t13 () (@list @t2 @t4 @t1)) % 0.51/0.76 (define @t14 () (@var "E" $$unsorted)) % 0.51/0.76 (define @t15 () (= @t2 @t4)) % 0.51/0.76 (define @t16 () (tptp.singleton @t4)) % 0.51/0.76 (define @t17 () (tptp.member @t2 @t16)) % 0.51/0.76 (define @t18 () (= @t17 @t15)) % 0.51/0.76 (define @t19 () (forall @t12 @t18)) % 0.51/0.76 (define @t20 () (or @t15 (= @t2 @t1))) % 0.51/0.76 (define @t21 () (tptp.unordered_pair @t4 @t1)) % 0.51/0.76 (define @t22 () (tptp.member @t2 @t21)) % 0.51/0.76 (define @t23 () (= @t22 @t20)) % 0.51/0.76 (define @t24 () (forall @t13 @t23)) % 0.51/0.76 (define @t25 () (@var "Y" $$unsorted)) % 0.51/0.76 (define @t26 () (tptp.member @t2 @t25)) % 0.51/0.76 (define @t27 () (tptp.member @t25 @t4)) % 0.51/0.76 (define @t28 () (@list @t25)) % 0.51/0.76 (define @t29 () (@var "V" $$unsorted)) % 0.51/0.76 (define @t30 () (@var "U" $$unsorted)) % 0.51/0.76 (define @t31 () (and (= @t4 @t30) (= @t1 @t29))) % 0.51/0.76 (define @t32 () (tptp.equal_set (tptp.unordered_pair @t16 @t21) (tptp.unordered_pair (tptp.singleton @t30) (tptp.unordered_pair @t30 @t29)))) % 0.51/0.76 (define @t33 () (@list @t4 @t1 @t30 @t29)) % 0.51/0.76 (define @t34 () (forall @t33 (=> @t32 @t31))) % 0.51/0.76 (define @t35 () (not @t34)) % 0.51/0.76 (define @t36 () (forall @t33 (or (not @t32) @t31))) % 0.51/0.76 (define @t37 () (@quantifiers_skolemize @t36 3)) % 0.51/0.76 (define @t38 () (@quantifiers_skolemize @t36 2)) % 0.51/0.76 (define @t39 () (tptp.singleton @t37)) % 0.51/0.76 (define @t40 () (tptp.member @t38 @t39)) % 0.51/0.76 (define @t41 () (= @t37 @t38)) % 0.51/0.76 (define @t42 () (= @t40 @t41)) % 0.51/0.76 (define @t43 () (= @t4 @t2)) % 0.51/0.76 (define @t44 () (forall @t12 (= @t17 @t43))) % 0.51/0.76 (define @t45 () (= @t38 @t37)) % 0.51/0.76 (define @t46 () (= @t40 @t45)) % 0.51/0.76 (define @t47 () (@list false)) % 0.51/0.76 (define @t48 () (@list @t44)) % 0.51/0.76 (define @t49 () (tptp.unordered_pair @t38 @t37)) % 0.51/0.76 (define @t50 () (tptp.member @t38 @t49)) % 0.51/0.76 (define @t51 () (or (= @t38 @t38) @t41)) % 0.51/0.76 (define @t52 () (= @t50 @t51)) % 0.51/0.76 (define @t53 () (forall @t13 (= @t22 (or @t43 (= @t1 @t2))))) % 0.51/0.76 (define @t54 () (@list @t53)) % 0.51/0.76 (define @t55 () (@quantifiers_skolemize @t36 0)) % 0.51/0.76 (define @t56 () (= @t38 @t55)) % 0.51/0.76 (define @t57 () (or @t56 (= @t37 @t55))) % 0.51/0.76 (define @t58 () (tptp.member @t55 @t49)) % 0.51/0.76 (define @t59 () (= @t58 @t57)) % 0.51/0.76 (define @t60 () (= @t55 @t37)) % 0.51/0.76 (define @t61 () (= @t55 @t38)) % 0.51/0.76 (define @t62 () (or @t61 @t60)) % 0.51/0.76 (define @t63 () (= @t58 @t62)) % 0.51/0.76 (define @t64 () (tptp.singleton @t55)) % 0.51/0.76 (define @t65 () (tptp.singleton @t38)) % 0.51/0.76 (define @t66 () (or (= @t65 @t64) (= @t49 @t64))) % 0.51/0.76 (define @t67 () (tptp.unordered_pair @t65 @t49)) % 0.51/0.76 (define @t68 () (tptp.member @t64 @t67)) % 0.51/0.76 (define @t69 () (= @t68 @t66)) % 0.51/0.76 (define @t70 () (= @t64 @t49)) % 0.51/0.76 (define @t71 () (= @t64 @t65)) % 0.51/0.76 (define @t72 () (or @t71 @t70)) % 0.51/0.76 (define @t73 () (= @t68 @t72)) % 0.51/0.76 (define @t74 () (@quantifiers_skolemize @t36 1)) % 0.51/0.76 (define @t75 () (tptp.unordered_pair @t55 @t74)) % 0.51/0.76 (define @t76 () (tptp.unordered_pair @t64 @t75)) % 0.51/0.76 (define @t77 () (@list @t76 @t67)) % 0.51/0.76 (define @t78 () (tptp.equal_set @t76 @t67)) % 0.51/0.76 (define @t79 () (= @t74 @t37)) % 0.51/0.76 (define @t80 () (and @t61 @t79)) % 0.51/0.76 (define @t81 () (not @t78)) % 0.51/0.76 (define @t82 () (or @t81 @t80)) % 0.51/0.76 (define @t83 () (@list true)) % 0.51/0.76 (define @t84 () (@list @t82)) % 0.51/0.76 (define @t85 () (tptp.subset @t67 @t76)) % 0.51/0.76 (define @t86 () (tptp.subset @t76 @t67)) % 0.51/0.76 (define @t87 () (and @t86 @t85)) % 0.51/0.76 (define @t88 () (= @t78 @t87)) % 0.51/0.76 (define @t89 () (@list false false)) % 0.51/0.76 (define @t90 () (not @t87)) % 0.51/0.76 (define @t91 () (@list @t87)) % 0.51/0.76 (define @t92 () (tptp.member @t2 @t67)) % 0.51/0.76 (define @t93 () (tptp.member @t2 @t76)) % 0.51/0.76 (define @t94 () (forall @t6 (or (not @t93) @t92))) % 0.51/0.76 (define @t95 () (= @t86 @t94)) % 0.51/0.76 (define @t96 () (tptp.member @t64 @t76)) % 0.51/0.76 (define @t97 () (= @t64 @t75)) % 0.51/0.76 (define @t98 () (or (= @t64 @t64) (= @t75 @t64))) % 0.51/0.76 (define @t99 () (= @t96 @t98)) % 0.51/0.76 (define @t100 () (not @t96)) % 0.51/0.76 (define @t101 () (or @t100 @t68)) % 0.51/0.76 (define @t102 () (tptp.member @t55 @t65)) % 0.51/0.76 (define @t103 () (= @t102 @t56)) % 0.51/0.76 (define @t104 () (= @t61 @t102)) % 0.51/0.76 (define @t105 () (or (= @t65 @t75) (= @t49 @t75))) % 0.51/0.76 (define @t106 () (tptp.member @t75 @t67)) % 0.51/0.76 (define @t107 () (= @t106 @t105)) % 0.51/0.76 (define @t108 () (= @t75 @t49)) % 0.51/0.76 (define @t109 () (= @t75 @t65)) % 0.51/0.76 (define @t110 () (or @t109 @t108)) % 0.51/0.76 (define @t111 () (= @t106 @t110)) % 0.51/0.76 (define @t112 () (tptp.member @t75 @t76)) % 0.51/0.76 (define @t113 () (or @t97 (= @t75 @t75))) % 0.51/0.76 (define @t114 () (= @t112 @t113)) % 0.51/0.76 (define @t115 () (not @t112)) % 0.51/0.76 (define @t116 () (or @t115 @t106)) % 0.51/0.76 (define @t117 () (forall @t6 (or (not @t92) @t93))) % 0.51/0.76 (define @t118 () (= @t85 @t117)) % 0.51/0.76 (define @t119 () (tptp.member @t49 @t67)) % 0.51/0.76 (define @t120 () (= @t65 @t49)) % 0.51/0.76 (define @t121 () (or @t120 (= @t49 @t49))) % 0.51/0.76 (define @t122 () (= @t119 @t121)) % 0.51/0.76 (define @t123 () (tptp.member @t49 @t76)) % 0.51/0.76 (define @t124 () (not @t119)) % 0.51/0.76 (define @t125 () (or @t124 @t123)) % 0.51/0.76 (define @t126 () (or @t70 @t108)) % 0.51/0.76 (define @t127 () (= @t123 @t126)) % 0.51/0.76 (define @t128 () (not @t70)) % 0.51/0.76 (define @t129 () (not @t109)) % 0.51/0.76 (define @t130 () (not @t61)) % 0.51/0.76 (define @t131 () (not @t108)) % 0.51/0.76 (define @t132 () (and @t61 @t109 @t131)) % 0.51/0.76 (define @t133 () (tptp.member @t74 @t75)) % 0.51/0.76 (define @t134 () (= @t55 @t74)) % 0.51/0.76 (define @t135 () (or @t134 (= @t74 @t74))) % 0.51/0.76 (define @t136 () (= @t133 @t135)) % 0.51/0.76 (define @t137 () (tptp.member @t74 @t49)) % 0.51/0.76 (define @t138 () (and @t108 @t133)) % 0.51/0.76 (define @t139 () (or (= @t38 @t74) (= @t37 @t74))) % 0.51/0.76 (define @t140 () (= @t137 @t139)) % 0.51/0.76 (define @t141 () (= @t74 @t38)) % 0.51/0.76 (define @t142 () (or @t141 @t79)) % 0.51/0.76 (define @t143 () (= @t137 @t142)) % 0.51/0.76 (define @t144 () (tptp.member @t37 @t49)) % 0.51/0.76 (define @t145 () (or @t45 (= @t37 @t37))) % 0.51/0.76 (define @t146 () (= @t144 @t145)) % 0.51/0.76 (define @t147 () (not @t144)) % 0.51/0.76 (define @t148 () (tptp.member @t37 (tptp.unordered_pair @t38 @t38))) % 0.51/0.76 (define @t149 () (not @t141)) % 0.51/0.76 (define @t150 () (not @t148)) % 0.51/0.76 (define @t151 () (and @t150 @t61 @t141 @t108 @t144)) % 0.51/0.76 (define @t152 () (or @t45 @t45)) % 0.51/0.76 (define @t153 () (= @t148 @t152)) % 0.51/0.76 (define @t154 () (= @t45 @t148)) % 0.51/0.76 (define @t155 () (not @t45)) % 0.51/0.76 (define @t156 () (not @t79)) % 0.51/0.76 (define @t157 () (and @t156 @t141)) % 0.51/0.76 (define @t158 () (not @t102)) % 0.51/0.76 (define @t159 () (@list true false)) % 0.51/0.76 (define @t160 () (tptp.member @t55 @t64)) % 0.51/0.76 (define @t161 () (= @t160 (= @t55 @t55))) % 0.51/0.76 (define @t162 () (not @t71)) % 0.51/0.76 (define @t163 () (not @t160)) % 0.51/0.76 (define @t164 () (not @t158)) % 0.51/0.76 (define @t165 () (and @t160 @t71 @t158)) % 0.51/0.76 (define @t166 () (and @t160 @t70)) % 0.51/0.76 (define @t167 () (and @t70 @t60 @t50)) % 0.51/0.76 (define @t168 () (not @t60)) % 0.51/0.76 (define @t169 () (tptp.member @t37 @t65)) % 0.51/0.76 (define @t170 () (= @t169 @t45)) % 0.51/0.76 (define @t171 () (= @t45 @t169)) % 0.51/0.76 (define @t172 () (not @t169)) % 0.51/0.76 (define @t173 () (and @t158 @t60)) % 0.51/0.76 (assume @p1 @t11) % 0.51/0.76 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.51/0.76 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.51/0.76 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.51/0.76 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.51/0.76 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.51/0.76 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.51/0.76 (assume @p8 @t19) % 0.51/0.76 (assume @p9 @t24) % 0.51/0.76 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t28 (and @t27 @t26))))) % 0.51/0.76 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t28 (=> @t27 @t26))))) % 0.51/0.76 (assume @p12 @t35) % 0.51/0.76 (assume @p13 true) % 0.51/0.76 (step @p14 :rule eq-symm :args (@t2 @t4)) % 0.51/0.76 (step @p15 :rule refl :args (@t17)) % 0.51/0.76 (step @p16 :rule cong :premises (@p15 @p14) :args (@t18)) % 0.51/0.76 (step @p17 :rule cong :premises (@p16) :args (@t19)) % 0.51/0.76 (step @p18 :rule eq_resolve :premises (@p8 @p17)) % 0.51/0.76 (step @p19 :rule eq-symm :args (@t37 @t38)) % 0.51/0.76 (step @p20 :rule refl :args (@t40)) % 0.51/0.76 (step @p21 :rule cong :premises (@p20 @p19) :args (@t42)) % 0.51/0.76 (step @p22 :rule refl :args (@t44)) % 0.51/0.76 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t44 @t42))) % 0.51/0.76 (assume-push @p564 @t44) % 0.51/0.76 (step @p25 :rule instantiate :premises (@p18) :args ((@list @t38 @t37))) % 0.51/0.76 (step-pop @p565 :rule scope :premises (@p25)) % 0.51/0.76 (step @p26 :rule process_scope :premises (@p565) :args (@t42)) % 0.51/0.76 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 0.51/0.76 (step @p29 :rule implies_elim :premises (@p28)) % 0.51/0.76 (step @p30 :rule chain_m_resolution :premises (@p29 @p18) :args (@t46 @t47 @t48)) % 0.51/0.76 (step @p31 :rule eq-symm :args (@t2 @t1)) % 0.51/0.76 (step @p32 :rule nary_cong :premises (@p14 @p31) :args (@t20)) % 0.51/0.76 (step @p33 :rule refl :args (@t22)) % 0.51/0.76 (step @p34 :rule cong :premises (@p33 @p32) :args (@t23)) % 0.51/0.76 (step @p35 :rule cong :premises (@p34) :args (@t24)) % 0.51/0.76 (step @p36 :rule eq_resolve :premises (@p9 @p35)) % 0.51/0.76 (step @p37 :rule bool-eq-true :args (@t50)) % 0.51/0.76 (step @p38 :rule absorb :args ((= (or true @t45) true))) % 0.51/0.76 (step @p39 :rule eq-refl :args (@t38)) % 0.51/0.76 (step @p40 :rule nary_cong :premises (@p39 @p19) :args (@t51)) % 0.51/0.76 (step @p41 :rule trans :premises (@p40 @p38)) % 0.51/0.76 (step @p42 :rule refl :args (@t50)) % 0.51/0.76 (step @p43 :rule cong :premises (@p42 @p41) :args (@t52)) % 0.51/0.76 (step @p44 :rule trans :premises (@p43 @p37)) % 0.51/0.76 (step @p45 :rule refl :args (@t53)) % 0.51/0.76 (step @p46 :rule cong :premises (@p45 @p44) :args ((=> @t53 @t52))) % 0.51/0.76 (assume-push @p566 @t53) % 0.51/0.76 (step @p48 :rule instantiate :premises (@p36) :args ((@list @t38 @t38 @t37))) % 0.51/0.76 (step-pop @p567 :rule scope :premises (@p48)) % 0.51/0.76 (step @p49 :rule process_scope :premises (@p567) :args (@t52)) % 0.51/0.76 (step @p51 :rule eq_resolve :premises (@p49 @p46)) % 0.51/0.76 (step @p52 :rule implies_elim :premises (@p51)) % 0.51/0.76 (step @p53 :rule chain_m_resolution :premises (@p52 @p36) :args (@t50 @t47 @t54)) % 0.51/0.76 (step @p54 :rule eq-symm :args (@t37 @t55)) % 0.51/0.76 (step @p55 :rule eq-symm :args (@t38 @t55)) % 0.51/0.76 (step @p56 :rule nary_cong :premises (@p55 @p54) :args 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:args (@t171)) % 0.51/0.76 (step @p559 :rule reordering :premises (@p558) :args ((or @t155 @t169 (not @t171)))) % 0.51/0.76 (step @p560 :rule chain_m_resolution :premises (@p559 @p557 @p531) :args (@t155 @t159 (@list @t169 @t171))) % 0.51/0.76 (step @p561 :rule cnf_equiv_pos1 :args (@t46)) % 0.51/0.76 (step @p562 :rule reordering :premises (@p561) :args ((or @t45 (not @t40) (not @t46)))) % 0.51/0.76 (step @p563 false :rule chain_m_resolution :premises (@p562 @p560 @p522 @p30) :args (false (@list true false false) (@list @t45 @t40 @t46))) % 0.51/0.76 ) % 0.51/0.76 % SZS output end Proof % 0.51/0.76 % cvc5 exiting %------------------------------------------------------------------------------