%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET018+4 : TPTP v9.2.1. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n005.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 08:46:58 AM UTC 2026 % Result : Theorem 0.51s 0.71s % Output : Proof 0.51s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET018+4 : TPTP v9.2.1. Released v2.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n005.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:40:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.51/0.71 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.51/0.71 % SZS status Theorem % 0.51/0.71 % SZS output start Proof % 0.51/0.71 ( % 0.51/0.71 (declare-sort $$unsorted 0) % 0.51/0.71 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.difference (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.union (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.product (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.empty_set $$unsorted) % 0.51/0.71 (declare-const tptp.intersection (-> $$unsorted $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.power_set (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.equal_set (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.sum (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.51/0.71 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (declare-const tptp.member (-> $$unsorted $$unsorted Bool)) % 0.51/0.71 (define @t1 () (@var "B" $$unsorted)) % 0.51/0.71 (define @t2 () (@var "X" $$unsorted)) % 0.51/0.71 (define @t3 () (tptp.member @t2 @t1)) % 0.51/0.71 (define @t4 () (@var "A" $$unsorted)) % 0.51/0.71 (define @t5 () (tptp.member @t2 @t4)) % 0.51/0.71 (define @t6 () (@list @t2)) % 0.51/0.71 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.51/0.71 (define @t8 () (tptp.subset @t4 @t1)) % 0.51/0.71 (define @t9 () (= @t8 @t7)) % 0.51/0.71 (define @t10 () (@list @t4 @t1)) % 0.51/0.71 (define @t11 () (forall @t10 @t9)) % 0.51/0.71 (define @t12 () (@list @t2 @t4)) % 0.51/0.71 (define @t13 () (@list @t2 @t4 @t1)) % 0.51/0.71 (define @t14 () (@var "E" $$unsorted)) % 0.51/0.71 (define @t15 () (= @t2 @t4)) % 0.51/0.71 (define @t16 () (tptp.singleton @t4)) % 0.51/0.71 (define @t17 () (tptp.member @t2 @t16)) % 0.51/0.71 (define @t18 () (= @t17 @t15)) % 0.51/0.71 (define @t19 () (forall @t12 @t18)) % 0.51/0.71 (define @t20 () (or @t15 (= @t2 @t1))) % 0.51/0.71 (define @t21 () (tptp.unordered_pair @t4 @t1)) % 0.51/0.71 (define @t22 () (tptp.member @t2 @t21)) % 0.51/0.71 (define @t23 () (= @t22 @t20)) % 0.51/0.71 (define @t24 () (forall @t13 @t23)) % 0.51/0.71 (define @t25 () (@var "Y" $$unsorted)) % 0.51/0.71 (define @t26 () (tptp.member @t2 @t25)) % 0.51/0.71 (define @t27 () (tptp.member @t25 @t4)) % 0.51/0.71 (define @t28 () (@list @t25)) % 0.51/0.71 (define @t29 () (@var "V" $$unsorted)) % 0.51/0.71 (define @t30 () (= @t1 @t29)) % 0.51/0.71 (define @t31 () (@var "U" $$unsorted)) % 0.51/0.71 (define @t32 () (tptp.equal_set (tptp.unordered_pair @t16 @t21) (tptp.unordered_pair (tptp.singleton @t31) (tptp.unordered_pair @t31 @t29)))) % 0.51/0.71 (define @t33 () (@list @t4 @t1 @t31 @t29)) % 0.51/0.71 (define @t34 () (forall @t33 (=> @t32 @t30))) % 0.51/0.71 (define @t35 () (not @t34)) % 0.51/0.71 (define @t36 () (forall @t33 (or (not @t32) @t30))) % 0.51/0.71 (define @t37 () (@quantifiers_skolemize @t36 3)) % 0.51/0.71 (define @t38 () (@quantifiers_skolemize @t36 2)) % 0.51/0.71 (define @t39 () (tptp.unordered_pair @t38 @t37)) % 0.51/0.71 (define @t40 () (tptp.member @t38 @t39)) % 0.51/0.71 (define @t41 () (= @t38 @t37)) % 0.51/0.71 (define @t42 () (= @t37 @t38)) % 0.51/0.71 (define @t43 () (or (= @t38 @t38) @t42)) % 0.51/0.71 (define @t44 () (= @t40 @t43)) % 0.51/0.71 (define @t45 () (= @t4 @t2)) % 0.51/0.71 (define @t46 () (forall @t13 (= @t22 (or @t45 (= @t1 @t2))))) % 0.51/0.71 (define @t47 () (@list false)) % 0.51/0.71 (define @t48 () (@list @t46)) % 0.51/0.71 (define @t49 () (@quantifiers_skolemize @t36 1)) % 0.51/0.71 (define @t50 () (@quantifiers_skolemize @t36 0)) % 0.51/0.71 (define @t51 () (tptp.member @t37 @t39)) % 0.51/0.71 (define @t52 () (or @t41 (= @t37 @t37))) % 0.51/0.71 (define @t53 () (= @t51 @t52)) % 0.51/0.71 (define @t54 () (tptp.unordered_pair @t50 @t49)) % 0.51/0.71 (define @t55 () (tptp.singleton @t38)) % 0.51/0.71 (define @t56 () (or (= @t55 @t54) (= @t39 @t54))) % 0.51/0.71 (define @t57 () (tptp.unordered_pair @t55 @t39)) % 0.51/0.71 (define @t58 () (tptp.member @t54 @t57)) % 0.51/0.71 (define @t59 () (= @t58 @t56)) % 0.51/0.71 (define @t60 () (= @t54 @t39)) % 0.51/0.71 (define @t61 () (= @t54 @t55)) % 0.51/0.71 (define @t62 () (or @t61 @t60)) % 0.51/0.71 (define @t63 () (= @t58 @t62)) % 0.51/0.71 (define @t64 () (tptp.singleton @t50)) % 0.51/0.71 (define @t65 () (tptp.unordered_pair @t64 @t54)) % 0.51/0.71 (define @t66 () (@list @t65 @t57)) % 0.51/0.71 (define @t67 () (tptp.equal_set @t65 @t57)) % 0.51/0.71 (define @t68 () (= @t49 @t37)) % 0.51/0.71 (define @t69 () (not @t67)) % 0.51/0.71 (define @t70 () (or @t69 @t68)) % 0.51/0.71 (define @t71 () (@list true)) % 0.51/0.71 (define @t72 () (@list @t70)) % 0.51/0.71 (define @t73 () (tptp.subset @t57 @t65)) % 0.51/0.71 (define @t74 () (tptp.subset @t65 @t57)) % 0.51/0.71 (define @t75 () (and @t74 @t73)) % 0.51/0.71 (define @t76 () (= @t67 @t75)) % 0.51/0.71 (define @t77 () (@list false false)) % 0.51/0.71 (define @t78 () (not @t75)) % 0.51/0.71 (define @t79 () (@list @t75)) % 0.51/0.71 (define @t80 () (tptp.member @t2 @t57)) % 0.51/0.71 (define @t81 () (tptp.member @t2 @t65)) % 0.51/0.71 (define @t82 () (forall @t6 (or (not @t81) @t80))) % 0.51/0.71 (define @t83 () (= @t74 @t82)) % 0.51/0.71 (define @t84 () (tptp.member @t54 @t65)) % 0.51/0.71 (define @t85 () (= @t64 @t54)) % 0.51/0.71 (define @t86 () (or @t85 (= @t54 @t54))) % 0.51/0.71 (define @t87 () (= @t84 @t86)) % 0.51/0.71 (define @t88 () (not @t84)) % 0.51/0.71 (define @t89 () (or @t88 @t58)) % 0.51/0.71 (define @t90 () (forall @t6 (or (not @t80) @t81))) % 0.51/0.71 (define @t91 () (= @t73 @t90)) % 0.51/0.71 (define @t92 () (tptp.member @t39 @t57)) % 0.51/0.71 (define @t93 () (= @t55 @t39)) % 0.51/0.71 (define @t94 () (or @t93 (= @t39 @t39))) % 0.51/0.71 (define @t95 () (= @t92 @t94)) % 0.51/0.71 (define @t96 () (tptp.member @t39 @t65)) % 0.51/0.71 (define @t97 () (not @t92)) % 0.51/0.71 (define @t98 () (or @t97 @t96)) % 0.51/0.71 (define @t99 () (= @t64 @t39)) % 0.51/0.71 (define @t100 () (or @t99 @t60)) % 0.51/0.71 (define @t101 () (= @t96 @t100)) % 0.51/0.71 (define @t102 () (tptp.member @t50 @t54)) % 0.51/0.71 (define @t103 () (= @t50 @t49)) % 0.51/0.71 (define @t104 () (= @t50 @t50)) % 0.51/0.71 (define @t105 () (or @t104 (= @t49 @t50))) % 0.51/0.71 (define @t106 () (= @t102 @t105)) % 0.51/0.71 (define @t107 () (tptp.member @t50 @t55)) % 0.51/0.71 (define @t108 () (and @t102 @t61)) % 0.51/0.71 (define @t109 () (not @t61)) % 0.51/0.71 (define @t110 () (= @t107 (= @t38 @t50))) % 0.51/0.71 (define @t111 () (forall @t12 (= @t17 @t45))) % 0.51/0.71 (define @t112 () (= @t50 @t38)) % 0.51/0.71 (define @t113 () (= @t107 @t112)) % 0.51/0.71 (define @t114 () (@list @t111)) % 0.51/0.71 (define @t115 () (not @t107)) % 0.51/0.71 (define @t116 () (and @t112 @t99 @t61)) % 0.51/0.71 (define @t117 () (not @t99)) % 0.51/0.71 (define @t118 () (tptp.member @t37 @t54)) % 0.51/0.71 (define @t119 () (not @t51)) % 0.51/0.71 (define @t120 () (not @t60)) % 0.51/0.71 (define @t121 () (not @t118)) % 0.51/0.71 (define @t122 () (and @t121 @t60 @t51)) % 0.51/0.71 (define @t123 () (= @t50 @t37)) % 0.51/0.71 (define @t124 () (or @t123 @t68)) % 0.51/0.71 (define @t125 () (= @t118 @t124)) % 0.51/0.71 (define @t126 () (not @t68)) % 0.51/0.71 (define @t127 () (@list true false)) % 0.51/0.71 (define @t128 () (tptp.singleton @t37)) % 0.51/0.71 (define @t129 () (tptp.member @t38 @t128)) % 0.51/0.71 (define @t130 () (= @t129 @t42)) % 0.51/0.71 (define @t131 () (= @t129 @t41)) % 0.51/0.71 (define @t132 () (or (= @t38 @t49) (= @t37 @t49))) % 0.51/0.71 (define @t133 () (tptp.member @t49 @t39)) % 0.51/0.71 (define @t134 () (= @t133 @t132)) % 0.51/0.71 (define @t135 () (= @t49 @t38)) % 0.51/0.71 (define @t136 () (or @t135 @t68)) % 0.51/0.71 (define @t137 () (= @t133 @t136)) % 0.51/0.71 (define @t138 () (tptp.member @t49 @t54)) % 0.51/0.71 (define @t139 () (or @t103 (= @t49 @t49))) % 0.51/0.71 (define @t140 () (= @t138 @t139)) % 0.51/0.71 (define @t141 () (and @t60 @t138)) % 0.51/0.71 (define @t142 () (not @t41)) % 0.51/0.71 (define @t143 () (not @t135)) % 0.51/0.71 (define @t144 () (and @t126 @t135)) % 0.51/0.71 (define @t145 () (not @t129)) % 0.51/0.71 (define @t146 () (or (= @t55 @t64) (= @t39 @t64))) % 0.51/0.71 (define @t147 () (tptp.member @t64 @t57)) % 0.51/0.71 (define @t148 () (= @t147 @t146)) % 0.51/0.71 (define @t149 () (= @t64 @t55)) % 0.51/0.71 (define @t150 () (or @t149 @t99)) % 0.51/0.71 (define @t151 () (= @t147 @t150)) % 0.51/0.71 (define @t152 () (tptp.member @t64 @t65)) % 0.51/0.71 (define @t153 () (or (= @t64 @t64) (= @t54 @t64))) % 0.51/0.71 (define @t154 () (= @t152 @t153)) % 0.51/0.71 (define @t155 () (not @t152)) % 0.51/0.71 (define @t156 () (or @t155 @t147)) % 0.51/0.71 (define @t157 () (tptp.member @t37 @t55)) % 0.51/0.71 (define @t158 () (= @t157 @t41)) % 0.51/0.71 (define @t159 () (= @t41 @t157)) % 0.51/0.71 (define @t160 () (not @t157)) % 0.51/0.71 (define @t161 () (not @t123)) % 0.51/0.71 (define @t162 () (and @t160 @t123)) % 0.51/0.71 (define @t163 () (tptp.member @t50 @t64)) % 0.51/0.71 (define @t164 () (= @t163 @t104)) % 0.51/0.71 (define @t165 () (and @t163 @t149)) % 0.51/0.71 (define @t166 () (not @t149)) % 0.51/0.71 (define @t167 () (not @t40)) % 0.51/0.71 (define @t168 () (and @t40 @t99 @t123 @t145)) % 0.51/0.71 (assume @p1 @t11) % 0.51/0.71 (assume @p2 (forall @t10 (= (tptp.equal_set @t4 @t1) (and @t8 (tptp.subset @t1 @t4))))) % 0.51/0.71 (assume @p3 (forall @t12 (= (tptp.member @t2 (tptp.power_set @t4)) (tptp.subset @t2 @t4)))) % 0.51/0.71 (assume @p4 (forall @t13 (= (tptp.member @t2 (tptp.intersection @t4 @t1)) (and @t5 @t3)))) % 0.51/0.71 (assume @p5 (forall @t13 (= (tptp.member @t2 (tptp.union @t4 @t1)) (or @t5 @t3)))) % 0.51/0.71 (assume @p6 (forall @t6 (not (tptp.member @t2 tptp.empty_set)))) % 0.51/0.71 (assume @p7 (forall (@list @t1 @t4 @t14) (= (tptp.member @t1 (tptp.difference @t14 @t4)) (and (tptp.member @t1 @t14) (not (tptp.member @t1 @t4)))))) % 0.51/0.71 (assume @p8 @t19) % 0.51/0.71 (assume @p9 @t24) % 0.51/0.71 (assume @p10 (forall @t12 (= (tptp.member @t2 (tptp.sum @t4)) (exists @t28 (and @t27 @t26))))) % 0.51/0.71 (assume @p11 (forall @t12 (= (tptp.member @t2 (tptp.product @t4)) (forall @t28 (=> @t27 @t26))))) % 0.51/0.71 (assume @p12 @t35) % 0.51/0.71 (assume @p13 true) % 0.51/0.71 (step @p14 :rule eq-symm :args (@t2 @t1)) % 0.51/0.71 (step @p15 :rule eq-symm :args (@t2 @t4)) % 0.51/0.71 (step @p16 :rule nary_cong :premises (@p15 @p14) :args (@t20)) % 0.51/0.71 (step @p17 :rule refl :args (@t22)) % 0.51/0.71 (step @p18 :rule cong :premises (@p17 @p16) :args (@t23)) % 0.51/0.71 (step @p19 :rule cong :premises (@p18) :args (@t24)) % 0.51/0.71 (step @p20 :rule eq_resolve :premises (@p9 @p19)) % 0.51/0.71 (step @p21 :rule bool-eq-true :args (@t40)) % 0.51/0.71 (step @p22 :rule absorb :args ((= (or true @t41) true))) % 0.51/0.71 (step @p23 :rule eq-symm :args (@t37 @t38)) % 0.51/0.71 (step @p24 :rule eq-refl :args (@t38)) % 0.51/0.71 (step @p25 :rule nary_cong :premises (@p24 @p23) :args (@t43)) % 0.51/0.71 (step @p26 :rule trans :premises (@p25 @p22)) % 0.51/0.71 (step @p27 :rule refl :args (@t40)) % 0.51/0.71 (step @p28 :rule cong :premises (@p27 @p26) :args (@t44)) % 0.51/0.71 (step @p29 :rule trans :premises (@p28 @p21)) % 0.51/0.71 (step @p30 :rule refl :args (@t46)) % 0.51/0.71 (step @p31 :rule cong :premises (@p30 @p29) :args ((=> @t46 @t44))) % 0.51/0.71 (assume-push @p531 @t46) % 0.51/0.71 (step @p33 :rule instantiate :premises (@p20) :args ((@list @t38 @t38 @t37))) % 0.51/0.71 (step-pop @p532 :rule scope :premises (@p33)) % 0.51/0.71 (step @p34 :rule process_scope :premises (@p532) :args (@t44)) % 0.51/0.71 (step @p36 :rule eq_resolve :premises (@p34 @p31)) % 0.51/0.71 (step @p37 :rule implies_elim :premises (@p36)) % 0.51/0.71 (step @p38 :rule chain_m_resolution :premises (@p37 @p20) :args (@t40 @t47 @t48)) % 0.51/0.71 (step @p39 :rule instantiate :premises (@p20) :args ((@list @t37 @t50 @t49))) % 0.51/0.71 (step @p40 :rule bool-eq-true :args (@t51)) % 0.51/0.71 (step @p41 :rule absorb :args ((= (or @t41 true) true))) % 0.51/0.71 (step @p42 :rule eq-refl :args (@t37)) % 0.51/0.71 (step @p43 :rule refl :args (@t41)) % 0.51/0.71 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t52)) % 0.51/0.71 (step @p45 :rule trans :premises (@p44 @p41)) % 0.51/0.71 (step @p46 :rule refl :args (@t51)) % 0.51/0.71 (step @p47 :rule cong :premises (@p46 @p45) :args (@t53)) % 0.51/0.71 (step @p48 :rule trans :premises (@p47 @p40)) % 0.51/0.71 (step @p49 :rule cong :premises (@p30 @p48) :args ((=> @t46 @t53))) % 0.51/0.71 (assume-push @p533 @t46) % 0.51/0.71 (step @p51 :rule instantiate :premises (@p20) :args ((@list @t37 @t38 @t37))) % 0.51/0.71 (step-pop @p534 :rule scope :premises (@p51)) % 0.51/0.71 (step @p52 :rule process_scope :premises (@p534) :args (@t53)) % 0.51/0.71 (step @p54 :rule eq_resolve :premises (@p52 @p49)) % 0.51/0.71 (step @p55 :rule implies_elim :premises (@p54)) % 0.51/0.71 (step @p56 :rule chain_m_resolution :premises (@p55 @p20) :args (@t51 @t47 @t48)) % 0.51/0.71 (step @p57 :rule eq-symm :args (@t39 @t54)) % 0.51/0.71 (step @p58 :rule eq-symm :args (@t55 @t54)) % 0.51/0.71 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t56)) % 0.51/0.71 (step @p60 :rule refl :args (@t58)) % 0.51/0.71 (step @p61 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(step @p352 :rule nary_cong :premises (@p351 @p350 @p349) :args ((or (not @t126) @t143 @t142))) % 0.51/0.71 (assume-push @p591 @t126) % 0.51/0.71 (assume-push @p592 @t135) % 0.51/0.71 (assume-push @p593 @t126) % 0.51/0.71 (assume-push @p594 @t135) % 0.51/0.71 (step @p357 :rule false_intro :premises (@p277)) % 0.51/0.71 (step @p250 :rule refl :args (@t37)) % 0.51/0.71 (step @p358 :rule symm :premises (@p592)) % 0.51/0.71 (step @p359 :rule cong :premises (@p358 @p250) :args (@t41)) % 0.51/0.71 (step @p360 :rule trans :premises (@p359 @p357)) % 0.51/0.71 (step @p361 :rule false_elim :premises (@p360)) % 0.51/0.71 (step-pop @p595 :rule scope :premises (@p361)) % 0.51/0.71 (step-pop @p596 :rule scope :premises (@p595)) % 0.51/0.71 (step @p362 :rule process_scope :premises (@p596) :args (@t142)) % 0.51/0.71 (step @p365 :rule and_intro :premises (@p277 @p592)) % 0.51/0.71 (step @p366 :rule modus_ponens :premises (@p365 @p362)) % 0.51/0.71 (step-pop @p597 :rule scope :premises (@p366)) % 0.51/0.71 (step-pop @p598 :rule scope :premises (@p597)) % 0.51/0.71 (step @p367 :rule process_scope :premises (@p598) :args (@t142)) % 0.51/0.71 (step @p370 :rule implies_elim :premises (@p367)) % 0.51/0.71 (step @p371 :rule cnf_and_neg :args (@t144)) % 0.51/0.71 (step @p372 :rule resolution :premises (@p371 @p370) :args (true @t144)) % 0.51/0.71 (step @p373 :rule eq_resolve :premises (@p372 @p352)) % 0.51/0.71 (step @p374 :rule chain_m_resolution :premises (@p373 @p277 @p348) :args (@t142 @t127 (@list @t68 @t135))) % 0.51/0.71 (step @p375 :rule cnf_equiv_pos1 :args (@t131)) % 0.51/0.71 (step @p376 :rule reordering :premises (@p375) :args ((or @t41 @t145 (not @t131)))) % 0.51/0.71 (step @p377 :rule chain_m_resolution :premises (@p376 @p374 @p290) :args (@t145 @t127 (@list @t41 @t131))) % 0.51/0.71 (step @p378 :rule eq-symm :args (@t39 @t64)) % 0.51/0.71 (step @p379 :rule eq-symm :args (@t55 @t64)) % 0.51/0.71 (step @p380 :rule nary_cong :premises (@p379 @p378) :args (@t146)) % 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% 0.51/0.71 (step @p423 :rule chain_m_resolution :premises (@p422 @p201) :args (@t159 @t47 @t114)) % 0.51/0.71 (step @p424 :rule cnf_equiv_pos2 :args (@t159)) % 0.51/0.71 (step @p425 :rule reordering :premises (@p424) :args ((or @t41 @t160 (not @t159)))) % 0.51/0.71 (step @p426 :rule chain_m_resolution :premises (@p425 @p374 @p423) :args (@t160 @t127 (@list @t41 @t159))) % 0.51/0.71 (step @p427 :rule refl :args (@t115)) % 0.51/0.71 (step @p428 :rule refl :args (@t161)) % 0.51/0.71 (step @p429 :rule bool-double-not-elim :args (@t157)) % 0.51/0.71 (step @p430 :rule nary_cong :premises (@p429 @p428 @p427) :args ((or (not @t160) @t161 @t115))) % 0.51/0.71 (assume-push @p605 @t160) % 0.51/0.71 (assume-push @p606 @t123) % 0.51/0.71 (assume-push @p607 @t160) % 0.51/0.71 (assume-push @p608 @t123) % 0.51/0.71 (step @p435 :rule false_intro :premises (@p605)) % 0.51/0.71 (step @p436 :rule refl :args (@t55)) % 0.51/0.71 (step @p437 :rule cong :premises (@p606 @p436) :args (@t107)) % 0.51/0.71 (step @p438 :rule trans :premises (@p437 @p435)) % 0.51/0.71 (step @p439 :rule false_elim :premises (@p438)) % 0.51/0.71 (step-pop @p609 :rule scope :premises (@p439)) % 0.51/0.71 (step-pop @p610 :rule scope :premises (@p609)) % 0.51/0.71 (step @p440 :rule process_scope :premises (@p610) :args (@t115)) % 0.51/0.71 (step @p443 :rule and_intro :premises (@p605 @p606)) % 0.51/0.71 (step @p444 :rule modus_ponens :premises (@p443 @p440)) % 0.51/0.71 (step-pop @p611 :rule scope :premises (@p444)) % 0.51/0.71 (step-pop @p612 :rule scope :premises (@p611)) % 0.51/0.71 (step @p445 :rule process_scope :premises (@p612) :args (@t115)) % 0.51/0.71 (step @p448 :rule implies_elim :premises (@p445)) % 0.51/0.71 (step @p449 :rule cnf_and_neg :args (@t162)) % 0.51/0.71 (step @p450 :rule resolution :premises (@p449 @p448) :args (true @t162)) % 0.51/0.71 (step @p451 :rule eq_resolve :premises (@p450 @p430)) % 0.51/0.71 (step @p452 :rule reordering :premises (@p451) :args ((or @t115 @t157 @t161))) % 0.51/0.71 (step @p453 :rule chain_m_resolution :premises (@p452 @p426 @p280) :args (@t115 @t127 (@list @t157 @t123))) % 0.51/0.71 (step @p454 :rule bool-eq-true :args (@t163)) % 0.51/0.71 (step @p455 :rule refl :args (@t163)) % 0.51/0.71 (step @p456 :rule cong :premises (@p455 @p162) :args (@t164)) % 0.51/0.71 (step @p457 :rule trans :premises (@p456 @p454)) % 0.51/0.71 (step @p458 :rule cong :premises (@p205 @p457) :args ((=> @t111 @t164))) % 0.51/0.71 (assume-push @p613 @t111) % 0.51/0.71 (step @p460 :rule instantiate :premises (@p201) :args ((@list @t50 @t50))) % 0.51/0.71 (step-pop @p614 :rule scope :premises (@p460)) % 0.51/0.71 (step @p461 :rule process_scope :premises (@p614) :args (@t164)) % 0.51/0.71 (step @p463 :rule eq_resolve :premises (@p461 @p458)) % 0.51/0.71 (step @p464 :rule implies_elim :premises (@p463)) % 0.51/0.71 (step @p465 :rule chain_m_resolution :premises (@p464 @p201) :args (@t163 @t47 @t114)) % 0.51/0.71 (assume-push @p615 @t163) % 0.51/0.71 (assume-push @p616 @t149) % 0.51/0.71 (assume-push @p617 @t163) % 0.51/0.71 (assume-push @p618 @t149) % 0.51/0.71 (step @p470 :rule true_intro :premises (@p465)) % 0.51/0.71 (step @p471 :rule symm :premises (@p616)) % 0.51/0.71 (step @p182 :rule refl :args (@t50)) % 0.51/0.71 (step @p472 :rule cong :premises (@p182 @p471) :args (@t107)) % 0.51/0.71 (step @p473 :rule trans :premises (@p472 @p470)) % 0.51/0.71 (step @p474 :rule true_elim :premises (@p473)) % 0.51/0.71 (step-pop @p619 :rule scope :premises (@p474)) % 0.51/0.71 (step-pop @p620 :rule scope :premises (@p619)) % 0.51/0.71 (step @p475 :rule process_scope :premises (@p620) :args (@t107)) % 0.51/0.71 (step @p478 :rule and_intro :premises (@p465 @p616)) % 0.51/0.71 (step @p479 :rule modus_ponens :premises (@p478 @p475)) % 0.51/0.71 (step-pop @p621 :rule scope :premises (@p479)) % 0.51/0.71 (step-pop @p622 :rule scope :premises (@p621)) % 0.51/0.71 (step @p480 :rule process_scope :premises (@p622) :args (@t107)) % 0.51/0.71 (step @p483 :rule implies_elim :premises (@p480)) % 0.51/0.71 (step @p484 :rule cnf_and_neg :args (@t165)) % 0.51/0.71 (step @p485 :rule resolution :premises (@p484 @p483) :args (true @t165)) % 0.51/0.71 (step @p486 :rule reordering :premises (@p485) :args ((or (not @t163) @t107 @t166))) % 0.51/0.71 (step @p487 :rule chain_m_resolution :premises (@p486 @p465 @p453) :args (@t166 (@list false true) (@list @t163 @t107))) % 0.51/0.71 (step @p488 :rule cnf_or_pos :args (@t150)) % 0.51/0.71 (step @p489 :rule reordering :premises (@p488) :args ((or @t149 @t99 (not @t150)))) % 0.51/0.71 (step @p490 :rule chain_m_resolution :premises (@p489 @p487 @p414) :args (@t99 @t127 (@list @t149 @t150))) % 0.51/0.71 (step @p491 :rule bool-double-not-elim :args (@t129)) % 0.51/0.71 (step @p492 :rule refl :args (@t167)) % 0.51/0.71 (step @p493 :rule refl :args (@t117)) % 0.51/0.71 (step @p494 :rule nary_cong :premises (@p493 @p492 @p491 @p428) :args ((or @t117 @t167 (not @t145) @t161))) % 0.51/0.71 (assume-push @p623 @t40) % 0.51/0.71 (assume-push @p624 @t99) % 0.51/0.71 (assume-push @p625 @t123) % 0.51/0.71 (assume-push @p626 @t145) % 0.51/0.71 (step @p499 :rule evaluate :args ((= false true))) % 0.51/0.71 (step @p500 :rule true_intro :premises (@p38)) % 0.51/0.71 (step @p501 :rule symm :premises (@p625)) % 0.51/0.71 (step @p502 :rule cong :premises (@p501) :args (@t128)) % 0.51/0.71 (step @p503 :rule trans :premises (@p502 @p624)) % 0.51/0.71 (step @p504 :rule refl :args (@t38)) % 0.51/0.71 (step @p505 :rule cong :premises (@p504 @p503) :args (@t129)) % 0.51/0.71 (step @p506 :rule false_intro :premises (@p626)) % 0.51/0.71 (step @p507 :rule symm :premises (@p506)) % 0.51/0.71 (step @p508 :rule trans :premises (@p507 @p505 @p500)) % 0.51/0.71 (step @p509 false :rule eq_resolve :premises (@p508 @p499)) % 0.51/0.71 (step-pop @p627 :rule scope :premises (@p509)) % 0.51/0.71 (step-pop @p628 :rule scope :premises (@p627)) % 0.51/0.71 (step-pop @p629 :rule scope :premises (@p628)) % 0.51/0.71 (step-pop @p630 :rule scope :premises (@p629)) % 0.51/0.71 (step @p510 :rule process_scope :premises (@p630) :args (false)) % 0.51/0.71 (assume-push @p631 @t99) % 0.51/0.71 (assume-push @p632 @t40) % 0.51/0.71 (assume-push @p633 @t145) % 0.51/0.71 (assume-push @p634 @t123) % 0.51/0.71 (step @p519 :rule and_intro :premises (@p38 @p631 @p634 @p633)) % 0.51/0.71 (step-pop @p635 :rule scope :premises (@p519)) % 0.51/0.71 (step-pop @p636 :rule scope :premises (@p635)) % 0.51/0.71 (step-pop @p637 :rule scope :premises (@p636)) % 0.51/0.71 (step-pop @p638 :rule scope :premises (@p637)) % 0.51/0.71 (step @p520 :rule process_scope :premises (@p638) :args (@t168)) % 0.51/0.71 (step @p525 :rule implies_elim :premises (@p520)) % 0.51/0.71 (step @p526 :rule resolution :premises (@p525 @p510) :args (true @t168)) % 0.51/0.71 (step @p527 :rule not_and :premises (@p526)) % 0.51/0.71 (step @p528 :rule eq_resolve :premises (@p527 @p494)) % 0.51/0.71 (step @p529 :rule reordering :premises (@p528) :args ((or @t117 @t129 @t167 @t161))) % 0.51/0.71 (step @p530 false :rule chain_m_resolution :premises (@p529 @p490 @p377 @p280 @p38) :args (false (@list false true false false) (@list @t99 @t129 @t123 @t40))) % 0.51/0.71 ) % 0.51/0.71 % SZS output end Proof % 0.51/0.71 % cvc5 exiting %------------------------------------------------------------------------------