%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET937+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:49:01 AM UTC 2026 % Result : Theorem 34.54s 34.77s % Output : Proof 34.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET937+1 : TPTP v9.2.1. Released v3.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n022.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:18:08 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TF0_NAR, FOF, or CNF % 34.54/34.77 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 34.54/34.77 --- Run --no-e-matching --full-saturate-quant at 6... % 34.54/34.77 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 34.54/34.77 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 34.54/34.77 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 34.54/34.77 % SZS status Theorem % 34.54/34.77 % SZS output start Proof % 34.54/34.77 ( % 34.54/34.77 (declare-sort $$unsorted 0) % 34.54/34.77 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 34.54/34.77 (declare-const tptp.empty_set $$unsorted) % 34.54/34.77 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 34.54/34.77 (declare-const tptp.set_difference (-> $$unsorted $$unsorted $$unsorted)) % 34.54/34.77 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 34.54/34.77 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 34.54/34.77 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 34.54/34.77 (declare-const tptp.empty (-> $$unsorted Bool)) % 34.54/34.77 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 34.54/34.77 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 34.54/34.77 (define @t1 () (@var "A" $$unsorted)) % 34.54/34.77 (define @t2 () (@var "B" $$unsorted)) % 34.54/34.77 (define @t3 () (@list @t1 @t2)) % 34.54/34.77 (define @t4 () (tptp.set_union2 @t2 @t1)) % 34.54/34.77 (define @t5 () (tptp.set_union2 @t1 @t2)) % 34.54/34.77 (define @t6 () (tptp.set_intersection2 @t1 @t2)) % 34.54/34.77 (define @t7 () (@var "C" $$unsorted)) % 34.54/34.77 (define @t8 () (tptp.in @t7 @t2)) % 34.54/34.77 (define @t9 () (= @t8 (= @t7 @t1))) % 34.54/34.77 (define @t10 () (@list @t7)) % 34.54/34.77 (define @t11 () (forall @t10 @t9)) % 34.54/34.77 (define @t12 () (= @t2 (tptp.singleton @t1))) % 34.54/34.77 (define @t13 () (= @t12 @t11)) % 34.54/34.77 (define @t14 () (forall @t3 @t13)) % 34.54/34.77 (define @t15 () (tptp.powerset @t1)) % 34.54/34.77 (define @t16 () (forall @t3 (= (= @t2 @t15) (forall @t10 (= @t8 (tptp.subset @t7 @t1)))))) % 34.54/34.77 (define @t17 () (@var "D" $$unsorted)) % 34.54/34.77 (define @t18 () (tptp.in @t17 @t2)) % 34.54/34.77 (define @t19 () (tptp.in @t17 @t1)) % 34.54/34.77 (define @t20 () (tptp.in @t17 @t7)) % 34.54/34.77 (define @t21 () (@list @t17)) % 34.54/34.77 (define @t22 () (forall @t21 (= @t20 (or @t19 @t18)))) % 34.54/34.77 (define @t23 () (= (= @t7 @t5) @t22)) % 34.54/34.77 (define @t24 () (@list @t1 @t2 @t7)) % 34.54/34.77 (define @t25 () (forall @t24 @t23)) % 34.54/34.77 (define @t26 () (tptp.in @t7 @t1)) % 34.54/34.77 (define @t27 () (forall @t10 (=> @t26 @t8))) % 34.54/34.77 (define @t28 () (tptp.subset @t1 @t2)) % 34.54/34.77 (define @t29 () (= @t28 @t27)) % 34.54/34.77 (define @t30 () (forall @t3 @t29)) % 34.54/34.77 (define @t31 () (tptp.set_difference @t1 @t2)) % 34.54/34.77 (define @t32 () (forall @t24 (= (= @t7 @t31) (forall @t21 (= @t20 (and @t19 (not @t18))))))) % 34.54/34.77 (define @t33 () (tptp.disjoint @t1 @t2)) % 34.54/34.77 (define @t34 () (forall @t3 (= @t33 (= @t6 tptp.empty_set)))) % 34.54/34.77 (define @t35 () (tptp.empty @t1)) % 34.54/34.77 (define @t36 () (not @t35)) % 34.54/34.77 (define @t37 () (@list @t1)) % 34.54/34.77 (define @t38 () (tptp.disjoint @t2 @t1)) % 34.54/34.77 (define @t39 () (forall @t3 (=> @t33 @t38))) % 34.54/34.77 (define @t40 () (tptp.subset @t1 @t7)) % 34.54/34.77 (define @t41 () (tptp.subset @t2 @t7)) % 34.54/34.77 (define @t42 () (and @t28 @t41)) % 34.54/34.77 (define @t43 () (forall @t24 (=> @t42 @t40))) % 34.54/34.77 (define @t44 () (=> @t28 (= @t6 @t1))) % 34.54/34.77 (define @t45 () (forall @t3 @t44)) % 34.54/34.77 (define @t46 () (tptp.disjoint @t1 @t7)) % 34.54/34.77 (define @t47 () (tptp.disjoint @t2 @t7)) % 34.54/34.77 (define @t48 () (and @t28 @t47)) % 34.54/34.77 (define @t49 () (forall @t24 (=> @t48 @t46))) % 34.54/34.77 (define @t50 () (tptp.singleton tptp.empty_set)) % 34.54/34.77 (define @t51 () (forall @t3 (tptp.subset (tptp.powerset @t31) (tptp.set_union2 @t50 (tptp.set_difference @t15 (tptp.powerset @t2)))))) % 34.54/34.77 (define @t52 () (@quantifiers_skolemize @t51 1)) % 34.54/34.77 (define @t53 () (tptp.powerset @t52)) % 34.54/34.77 (define @t54 () (forall @t10 (= (tptp.in @t7 @t53) (tptp.subset @t7 @t52)))) % 34.54/34.77 (define @t55 () (= (= @t53 @t53) @t54)) % 34.54/34.77 (define @t56 () (@list false)) % 34.54/34.77 (define @t57 () (@list @t16)) % 34.54/34.77 (define @t58 () (not @t47)) % 34.54/34.77 (define @t59 () (not @t28)) % 34.54/34.77 (define @t60 () (@quantifiers_skolemize @t51 0)) % 34.54/34.77 (define @t61 () (tptp.set_difference @t60 @t52)) % 34.54/34.77 (define @t62 () (tptp.powerset @t60)) % 34.54/34.77 (define @t63 () (tptp.set_difference @t62 @t53)) % 34.54/34.77 (define @t64 () (tptp.set_union2 @t50 @t63)) % 34.54/34.77 (define @t65 () (tptp.powerset @t61)) % 34.54/34.77 (define @t66 () (tptp.in @t7 @t65)) % 34.54/34.77 (define @t67 () (forall @t10 (or (not @t66) (tptp.in @t7 @t64)))) % 34.54/34.77 (define @t68 () (@quantifiers_skolemize @t67 0)) % 34.54/34.77 (define @t69 () (tptp.set_intersection2 @t68 @t61)) % 34.54/34.77 (define @t70 () (tptp.disjoint @t68 @t61)) % 34.54/34.77 (define @t71 () (= @t70 (= @t69 tptp.empty_set))) % 34.54/34.77 (define @t72 () (@list @t68 @t61)) % 34.54/34.77 (define @t73 () (= tptp.empty_set @t69)) % 34.54/34.77 (define @t74 () (= @t70 @t73)) % 34.54/34.77 (define @t75 () (tptp.in @t7 @t50)) % 34.54/34.77 (define @t76 () (forall @t10 (= @t75 (= @t7 tptp.empty_set)))) % 34.54/34.77 (define @t77 () (= @t75 (= tptp.empty_set @t7))) % 34.54/34.77 (define @t78 () (forall @t10 @t77)) % 34.54/34.77 (define @t79 () (= (= @t50 @t50) @t78)) % 34.54/34.77 (define @t80 () (forall @t3 (= @t12 (forall @t10 (= @t8 (= @t1 @t7)))))) % 34.54/34.77 (define @t81 () (tptp.in @t68 @t50)) % 34.54/34.77 (define @t82 () (= @t81 (= @t68 tptp.empty_set))) % 34.54/34.77 (define @t83 () (@list @t68)) % 34.54/34.77 (define @t84 () (= tptp.empty_set @t68)) % 34.54/34.77 (define @t85 () (= @t81 @t84)) % 34.54/34.77 (define @t86 () (= @t5 @t7)) % 34.54/34.77 (define @t87 () (tptp.in @t17 @t63)) % 34.54/34.77 (define @t88 () (forall @t21 (= (tptp.in @t17 @t64) (or (tptp.in @t17 @t50) @t87)))) % 34.54/34.77 (define @t89 () (= @t88 (= @t64 @t64))) % 34.54/34.77 (define @t90 () (forall @t24 (= @t22 @t86))) % 34.54/34.77 (define @t91 () (tptp.subset @t65 @t64)) % 34.54/34.77 (define @t92 () (= @t91 @t67)) % 34.54/34.77 (define @t93 () (not @t67)) % 34.54/34.77 (define @t94 () (@list true false)) % 34.54/34.77 (define @t95 () (tptp.in @t68 @t64)) % 34.54/34.77 (define @t96 () (tptp.in @t68 @t65)) % 34.54/34.77 (define @t97 () (not @t96)) % 34.54/34.77 (define @t98 () (or @t97 @t95)) % 34.54/34.77 (define @t99 () (@list true)) % 34.54/34.77 (define @t100 () (@list @t98)) % 34.54/34.77 (define @t101 () (tptp.in @t68 @t63)) % 34.54/34.77 (define @t102 () (or @t81 @t101)) % 34.54/34.77 (define @t103 () (= @t95 @t102)) % 34.54/34.77 (define @t104 () (not @t102)) % 34.54/34.77 (define @t105 () (@list @t102)) % 34.54/34.77 (define @t106 () (not @t84)) % 34.54/34.77 (define @t107 () (= @t1 @t6)) % 34.54/34.77 (define @t108 () (forall @t10 (= @t66 (tptp.subset @t7 @t61)))) % 34.54/34.77 (define @t109 () (= (= @t65 @t65) @t108)) % 34.54/34.77 (define @t110 () (tptp.subset @t68 @t61)) % 34.54/34.77 (define @t111 () (= @t96 @t110)) % 34.54/34.77 (define @t112 () (@list false false)) % 34.54/34.77 (define @t113 () (= @t68 @t69)) % 34.54/34.77 (define @t114 () (not @t110)) % 34.54/34.77 (define @t115 () (or @t114 @t113)) % 34.54/34.77 (define @t116 () (not @t70)) % 34.54/34.77 (define @t117 () (@list @t60 @t52)) % 34.54/34.77 (define @t118 () (tptp.disjoint @t52 @t61)) % 34.54/34.77 (define @t119 () (tptp.disjoint @t61 @t52)) % 34.54/34.77 (define @t120 () (not @t119)) % 34.54/34.77 (define @t121 () (or @t120 @t118)) % 34.54/34.77 (define @t122 () (not @t118)) % 34.54/34.77 (define @t123 () (tptp.subset @t68 @t52)) % 34.54/34.77 (define @t124 () (not @t123)) % 34.54/34.77 (define @t125 () (or @t124 @t122 @t70)) % 34.54/34.77 (define @t126 () (forall @t10 (= (tptp.in @t7 @t62) (tptp.subset @t7 @t60)))) % 34.54/34.77 (define @t127 () (= (= @t62 @t62) @t126)) % 34.54/34.77 (define @t128 () (not @t41)) % 34.54/34.77 (define @t129 () (tptp.subset @t68 @t60)) % 34.54/34.77 (define @t130 () (tptp.subset @t61 @t60)) % 34.54/34.77 (define @t131 () (not @t130)) % 34.54/34.77 (define @t132 () (or @t114 @t131 @t129)) % 34.54/34.77 (define @t133 () (tptp.in @t68 @t62)) % 34.54/34.77 (define @t134 () (= @t133 @t129)) % 34.54/34.77 (define @t135 () (forall @t21 (= @t87 (and (tptp.in @t17 @t62) (not (tptp.in @t17 @t53)))))) % 34.54/34.77 (define @t136 () (= (= @t63 @t63) @t135)) % 34.54/34.77 (define @t137 () (tptp.in @t68 @t53)) % 34.54/34.77 (define @t138 () (not @t137)) % 34.54/34.77 (define @t139 () (and @t133 @t138)) % 34.54/34.77 (define @t140 () (= @t101 @t139)) % 34.54/34.77 (define @t141 () (not @t139)) % 34.54/34.77 (define @t142 () (not @t133)) % 34.54/34.77 (define @t143 () (= @t137 @t123)) % 34.54/34.77 (define @t144 () (not @t143)) % 34.54/34.77 (assume @p1 (forall @t3 (=> (tptp.in @t1 @t2) (not (tptp.in @t2 @t1))))) % 34.54/34.77 (assume @p2 (forall @t3 (= @t5 @t4))) % 34.54/34.77 (assume @p3 (forall @t3 (= @t6 (tptp.set_intersection2 @t2 @t1)))) % 34.54/34.77 (assume @p4 @t14) % 34.54/34.77 (assume @p5 @t16) % 34.54/34.77 (assume @p6 @t25) % 34.54/34.77 (assume @p7 @t30) % 34.54/34.77 (assume @p8 @t32) % 34.54/34.77 (assume @p9 @t34) % 34.54/34.77 (assume @p10 (tptp.empty tptp.empty_set)) % 34.54/34.77 (assume @p11 (forall @t3 (=> @t36 (not (tptp.empty @t5))))) % 34.54/34.77 (assume @p12 (forall @t3 (=> @t36 (not (tptp.empty @t4))))) % 34.54/34.77 (assume @p13 (forall @t3 (= (tptp.set_union2 @t1 @t1) @t1))) % 34.54/34.77 (assume @p14 (forall @t3 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 34.54/34.77 (assume @p15 (exists @t37 @t35)) % 34.54/34.77 (assume @p16 (exists @t37 @t36)) % 34.54/34.77 (assume @p17 (forall @t3 (tptp.subset @t1 @t1))) % 34.54/34.77 (assume @p18 @t39) % 34.54/34.77 (assume @p19 @t43) % 34.54/34.77 (assume @p20 @t45) % 34.54/34.77 (assume @p21 (forall @t3 (tptp.subset @t31 @t1))) % 34.54/34.77 (assume @p22 @t49) % 34.54/34.77 (assume @p23 (forall @t3 (tptp.disjoint @t31 @t2))) % 34.54/34.77 (assume @p24 (not @t51)) % 34.54/34.77 (assume @p25 true) % 34.54/34.77 (step @p26 :rule bool-eq-true :args (@t54)) % 34.54/34.77 (step @p27 :rule eq-symm :args (true @t54)) % 34.54/34.77 (step @p28 :rule trans :premises (@p27 @p26)) % 34.54/34.77 (step @p29 :rule refl :args (@t54)) % 34.54/34.77 (step @p30 :rule eq-refl :args (@t53)) % 34.54/34.77 (step @p31 :rule cong :premises (@p30 @p29) :args (@t55)) % 34.54/34.77 (step @p32 :rule trans :premises (@p31 @p28)) % 34.54/34.77 (step @p33 :rule refl :args (@t16)) % 34.54/34.77 (step @p34 :rule cong :premises (@p33 @p32) :args ((=> @t16 @t55))) % 34.54/34.77 (assume-push @p276 @t16) % 34.54/34.77 (step @p36 :rule instantiate :premises (@p5) :args ((@list @t52 @t53))) % 34.54/34.77 (step-pop @p277 :rule scope :premises (@p36)) % 34.54/34.77 (step @p37 :rule process_scope :premises (@p277) :args (@t55)) % 34.54/34.77 (step @p39 :rule eq_resolve :premises (@p37 @p34)) % 34.54/34.77 (step @p40 :rule implies_elim :premises (@p39)) % 34.54/34.77 (step @p41 :rule chain_m_resolution :premises (@p40 @p5) :args (@t54 @t56 @t57)) % 34.54/34.77 (step @p42 :rule aci_norm :args ((= (or (or @t59 @t58) @t46) (or @t59 @t58 @t46)))) % 34.54/34.77 (step @p43 :rule refl :args (@t46)) % 34.54/34.77 (step @p44 :rule bool-and-de-morgan :args (@t28 @t47 true)) % 34.54/34.77 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or (not @t48) @t46))) % 34.54/34.77 (step @p46 :rule trans :premises (@p45 @p42)) % 34.54/34.77 (step @p47 :rule bool-impl-elim :args (@t48 @t46)) % 34.54/34.77 (step @p48 :rule trans :premises (@p47 @p46)) % 34.54/34.77 (step @p49 :rule cong :premises (@p48) :args (@t49)) % 34.54/34.77 (step @p50 :rule eq_resolve :premises (@p22 @p49)) % 34.54/34.77 (step @p51 :rule instantiate :premises (@p50) :args ((@list @t68 @t52 @t61))) % 34.54/34.77 (step @p52 :rule eq-symm :args (@t69 tptp.empty_set)) % 34.54/34.77 (step @p53 :rule refl :args (@t70)) % 34.54/34.77 (step @p54 :rule cong :premises (@p53 @p52) :args (@t71)) % 34.54/34.77 (step @p55 :rule refl :args (@t34)) % 34.54/34.77 (step @p56 :rule cong :premises (@p55 @p54) :args ((=> @t34 @t71))) % 34.54/34.77 (assume-push @p278 @t34) % 34.54/34.77 (step @p58 :rule instantiate :premises (@p9) :args (@t72)) % 34.54/34.77 (step-pop @p279 :rule scope :premises (@p58)) % 34.54/34.77 (step @p59 :rule process_scope :premises (@p279) :args (@t71)) % 34.54/34.77 (step @p61 :rule eq_resolve :premises (@p59 @p56)) % 34.54/34.77 (step @p62 :rule implies_elim :premises (@p61)) % 34.54/34.77 (step @p63 :rule chain_m_resolution :premises (@p62 @p9) :args (@t74 @t56 (@list @t34))) % 34.54/34.77 (step @p64 :rule eq-symm :args (@t7 @t1)) % 34.54/34.77 (step @p65 :rule refl :args (@t8)) % 34.54/34.77 (step @p66 :rule cong :premises (@p65 @p64) :args (@t9)) % 34.54/34.77 (step @p67 :rule cong :premises (@p66) :args (@t11)) % 34.54/34.77 (step @p68 :rule refl :args (@t12)) % 34.54/34.77 (step @p69 :rule cong :premises (@p68 @p67) :args (@t13)) % 34.54/34.77 (step @p70 :rule cong :premises (@p69) :args (@t14)) % 34.54/34.77 (step @p71 :rule eq_resolve :premises (@p4 @p70)) % 34.54/34.77 (step @p72 :rule bool-eq-true :args (@t76)) % 34.54/34.77 (step @p73 :rule eq-symm :args (true @t76)) % 34.54/34.77 (step @p74 :rule trans :premises (@p73 @p72)) % 34.54/34.77 (step @p75 :rule eq-symm :args (tptp.empty_set @t7)) % 34.54/34.77 (step @p76 :rule refl :args (@t75)) % 34.54/34.77 (step @p77 :rule cong :premises (@p76 @p75) :args (@t77)) % 34.54/34.77 (step @p78 :rule cong :premises (@p77) :args (@t78)) % 34.54/34.77 (step @p79 :rule eq-refl :args (@t50)) % 34.54/34.77 (step @p80 :rule cong :premises (@p79 @p78) :args (@t79)) % 34.54/34.77 (step @p81 :rule trans :premises (@p80 @p74)) % 34.54/34.77 (step @p82 :rule refl :args (@t80)) % 34.54/34.77 (step @p83 :rule cong :premises (@p82 @p81) :args ((=> @t80 @t79))) % 34.54/34.77 (assume-push @p280 @t80) % 34.54/34.77 (step @p85 :rule instantiate :premises (@p71) :args ((@list tptp.empty_set @t50))) % 34.54/34.77 (step-pop @p281 :rule scope :premises (@p85)) % 34.54/34.77 (step @p86 :rule process_scope :premises (@p281) :args (@t79)) % 34.54/34.77 (step @p88 :rule eq_resolve :premises (@p86 @p83)) % 34.54/34.77 (step @p89 :rule implies_elim :premises (@p88)) % 34.54/34.77 (step @p90 :rule chain_m_resolution :premises (@p89 @p71) :args (@t76 @t56 (@list @t80))) % 34.54/34.77 (step @p91 :rule eq-symm :args (@t68 tptp.empty_set)) % 34.54/34.77 (step @p92 :rule refl :args (@t81)) % 34.54/34.77 (step @p93 :rule cong :premises (@p92 @p91) :args (@t82)) % 34.54/34.77 (step @p94 :rule refl :args (@t76)) % 34.54/34.77 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t76 @t82))) % 34.54/34.77 (assume-push @p282 @t76) % 34.54/34.77 (step @p97 :rule instantiate :premises (@p90) :args (@t83)) % 34.54/34.77 (step-pop @p283 :rule scope :premises (@p97)) % 34.54/34.77 (step @p98 :rule process_scope :premises (@p283) :args (@t82)) % 34.54/34.77 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 34.54/34.77 (step @p101 :rule implies_elim :premises (@p100)) % 34.54/34.77 (step @p102 :rule chain_m_resolution :premises (@p101 @p90) :args (@t85 @t56 (@list @t76))) % 34.54/34.77 (step @p103 :rule eq-symm :args (@t86 @t22)) % 34.54/34.77 (step @p104 :rule refl :args (@t22)) % 34.54/34.77 (step @p105 :rule eq-symm :args (@t7 @t5)) % 34.54/34.77 (step @p106 :rule cong :premises (@p105 @p104) :args (@t23)) % 34.54/34.77 (step @p107 :rule trans :premises (@p106 @p103)) % 34.54/34.77 (step @p108 :rule cong :premises (@p107) :args (@t25)) % 34.54/34.77 (step @p109 :rule eq_resolve :premises (@p6 @p108)) % 34.54/34.77 (step @p110 :rule bool-eq-true :args (@t88)) % 34.54/34.77 (step @p111 :rule eq-refl :args (@t64)) % 34.54/34.77 (step @p112 :rule refl :args (@t88)) % 34.54/34.77 (step @p113 :rule cong :premises (@p112 @p111) :args (@t89)) % 34.54/34.77 (step @p114 :rule trans :premises (@p113 @p110)) % 34.54/34.77 (step @p115 :rule refl :args (@t90)) % 34.54/34.77 (step @p116 :rule cong :premises (@p115 @p114) :args ((=> @t90 @t89))) % 34.54/34.77 (assume-push @p284 @t90) % 34.54/34.77 (step @p118 :rule instantiate :premises (@p109) :args ((@list @t50 @t63 @t64))) % 34.54/34.77 (step-pop @p285 :rule scope :premises (@p118)) % 34.54/34.77 (step @p119 :rule process_scope :premises (@p285) :args (@t89)) % 34.54/34.77 (step @p121 :rule eq_resolve :premises (@p119 @p116)) % 34.54/34.77 (step @p122 :rule implies_elim :premises (@p121)) % 34.54/34.77 (step @p123 :rule chain_m_resolution :premises (@p122 @p109) :args (@t88 @t56 (@list @t90))) % 34.54/34.77 (step @p124 :rule instantiate :premises (@p123) :args (@t83)) % 34.54/34.77 (step @p125 :rule bool-impl-elim :args (@t26 @t8)) % 34.54/34.77 (step @p126 :rule cong :premises (@p125) :args (@t27)) % 34.54/34.77 (step @p127 :rule refl :args (@t28)) % 34.54/34.77 (step @p128 :rule cong :premises (@p127 @p126) :args (@t29)) % 34.54/34.77 (step @p129 :rule cong :premises (@p128) :args (@t30)) % 34.54/34.77 (step @p130 :rule eq_resolve :premises (@p7 @p129)) % 34.54/34.77 (step @p131 :rule instantiate :premises (@p130) :args ((@list @t65 @t64))) % 34.54/34.77 (step @p132 :rule skolemize :premises (@p24)) % 34.54/34.77 (step @p133 :rule cnf_equiv_pos2 :args (@t92)) % 34.54/34.77 (step @p134 :rule reordering :premises (@p133) :args ((or @t91 @t93 (not @t92)))) % 34.54/34.77 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p131) :args (@t93 @t94 (@list @t91 @t92))) % 34.54/34.77 (step @p136 :rule skolemize :premises (@p135)) % 34.54/34.77 (step @p137 :rule cnf_or_neg :args (@t98 1)) % 34.54/34.77 (step @p138 :rule chain_m_resolution :premises (@p137 @p136) :args ((not @t95) @t99 @t100)) % 34.54/34.77 (step @p139 :rule cnf_equiv_pos2 :args (@t103)) % 34.54/34.77 (step @p140 :rule reordering :premises (@p139) :args ((or @t95 @t104 (not @t103)))) % 34.54/34.77 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p124) :args (@t104 @t94 (@list @t95 @t103))) % 34.54/34.77 (step @p142 :rule cnf_or_neg :args (@t102 0)) % 34.54/34.77 (step @p143 :rule chain_m_resolution :premises (@p142 @p141) :args ((not @t81) @t99 @t105)) % 34.54/34.77 (step @p144 :rule cnf_equiv_pos2 :args (@t85)) % 34.54/34.77 (step @p145 :rule reordering :premises (@p144) :args ((or @t81 @t106 (not @t85)))) % 34.54/34.77 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p102) :args (@t106 @t94 (@list @t81 @t85))) % 34.54/34.77 (step @p147 :rule false_intro :premises (@p146)) % 34.54/34.77 (step @p148 :rule bool-impl-elim :args (@t28 @t107)) % 34.54/34.77 (step @p149 :rule cong :premises (@p148) :args ((forall @t3 (=> @t28 @t107)))) % 34.54/34.77 (step @p150 :rule eq-symm :args (@t6 @t1)) % 34.54/34.77 (step @p151 :rule cong :premises (@p127 @p150) :args (@t44)) % 34.54/34.77 (step @p152 :rule cong :premises (@p151) :args (@t45)) % 34.54/34.77 (step @p153 :rule trans :premises (@p152 @p149)) % 34.54/34.77 (step @p154 :rule eq_resolve :premises (@p20 @p153)) % 34.54/34.77 (step @p155 :rule instantiate :premises (@p154) :args (@t72)) % 34.54/34.77 (step @p156 :rule bool-eq-true :args (@t108)) % 34.54/34.77 (step @p157 :rule eq-symm :args (true @t108)) % 34.54/34.77 (step @p158 :rule trans :premises (@p157 @p156)) % 34.54/34.77 (step @p159 :rule refl :args (@t108)) % 34.54/34.77 (step @p160 :rule eq-refl :args (@t65)) % 34.54/34.77 (step @p161 :rule cong :premises (@p160 @p159) :args (@t109)) % 34.54/34.77 (step @p162 :rule trans :premises (@p161 @p158)) % 34.54/34.77 (step @p163 :rule cong :premises (@p33 @p162) :args ((=> @t16 @t109))) % 34.54/34.77 (assume-push @p286 @t16) % 34.54/34.77 (step @p165 :rule instantiate :premises (@p5) :args ((@list @t61 @t65))) % 34.54/34.77 (step-pop @p287 :rule scope :premises (@p165)) % 34.54/34.77 (step @p166 :rule process_scope :premises (@p287) :args (@t109)) % 34.54/34.77 (step @p168 :rule eq_resolve :premises (@p166 @p163)) % 34.54/34.77 (step @p169 :rule implies_elim :premises (@p168)) % 34.54/34.77 (step @p170 :rule chain_m_resolution :premises (@p169 @p5) :args (@t108 @t56 @t57)) % 34.54/34.77 (step @p171 :rule instantiate :premises (@p170) :args (@t83)) % 34.54/34.77 (step @p172 :rule bool-double-not-elim :args (@t96)) % 34.54/34.77 (step @p173 :rule refl :args (@t98)) % 34.54/34.77 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or @t98 (not @t97)))) % 34.54/34.77 (step @p175 :rule cnf_or_neg :args (@t98 0)) % 34.54/34.77 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 34.54/34.77 (step @p177 :rule reordering :premises (@p176) :args ((or @t96 @t98))) % 34.54/34.77 (step @p178 :rule chain_m_resolution :premises (@p177 @p136) :args (@t96 @t99 @t100)) % 34.54/34.77 (step @p179 :rule cnf_equiv_pos1 :args (@t111)) % 34.54/34.77 (step @p180 :rule reordering :premises (@p179) :args ((or @t97 @t110 (not @t111)))) % 34.54/34.77 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p171) :args (@t110 @t112 (@list @t96 @t111))) % 34.54/34.77 (step @p182 :rule cnf_or_pos :args (@t115)) % 34.54/34.77 (step @p183 :rule reordering :premises (@p182) :args ((or @t114 @t113 (not @t115)))) % 34.54/34.77 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p155) :args (@t113 @t112 (@list @t110 @t115))) % 34.54/34.77 (step @p185 :rule symm :premises (@p184)) % 34.54/34.77 (step @p186 :rule refl :args (tptp.empty_set)) % 34.54/34.77 (step @p187 :rule cong :premises (@p186 @p185) :args (@t73)) % 34.54/34.77 (step @p188 :rule trans :premises (@p187 @p147)) % 34.54/34.77 (step @p189 :rule false_elim :premises (@p188)) % 34.54/34.77 (step @p190 :rule cnf_equiv_pos1 :args (@t74)) % 34.54/34.77 (step @p191 :rule reordering :premises (@p190) :args ((or @t73 @t116 (not @t74)))) % 34.54/34.77 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p63) :args (@t116 @t94 (@list @t73 @t74))) % 34.54/34.77 (step @p193 :rule bool-impl-elim :args (@t33 @t38)) % 34.54/34.77 (step @p194 :rule cong :premises (@p193) :args (@t39)) % 34.54/34.77 (step @p195 :rule eq_resolve :premises (@p18 @p194)) % 34.54/34.77 (step @p196 :rule instantiate :premises (@p195) :args ((@list @t61 @t52))) % 34.54/34.77 (step @p197 :rule instantiate :premises (@p23) :args (@t117)) % 34.54/34.77 (step @p198 :rule cnf_or_pos :args (@t121)) % 34.54/34.77 (step @p199 :rule reordering :premises (@p198) :args ((or @t120 @t118 (not @t121)))) % 34.54/34.77 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p196) :args (@t118 @t112 (@list @t119 @t121))) % 34.54/34.77 (step @p201 :rule cnf_or_pos :args (@t125)) % 34.54/34.77 (step @p202 :rule reordering :premises (@p201) :args ((or @t122 @t70 @t124 (not @t125)))) % 34.54/34.77 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p192 @p51) :args (@t124 (@list false true false) (@list @t118 @t70 @t125))) % 34.54/34.77 (step @p204 :rule bool-eq-true :args (@t126)) % 34.54/34.77 (step @p205 :rule eq-symm :args (true @t126)) % 34.54/34.77 (step @p206 :rule trans :premises (@p205 @p204)) % 34.54/34.77 (step @p207 :rule refl :args (@t126)) % 34.54/34.77 (step @p208 :rule eq-refl :args (@t62)) % 34.54/34.77 (step @p209 :rule cong :premises (@p208 @p207) :args (@t127)) % 34.54/34.77 (step @p210 :rule trans :premises (@p209 @p206)) % 34.54/34.77 (step @p211 :rule cong :premises (@p33 @p210) :args ((=> @t16 @t127))) % 34.54/34.77 (assume-push @p288 @t16) % 34.54/34.77 (step @p213 :rule instantiate :premises (@p5) :args ((@list @t60 @t62))) % 34.54/34.77 (step-pop @p289 :rule scope :premises (@p213)) % 34.54/34.77 (step @p214 :rule process_scope :premises (@p289) :args (@t127)) % 34.54/34.77 (step @p216 :rule eq_resolve :premises (@p214 @p211)) % 34.54/34.77 (step @p217 :rule implies_elim :premises (@p216)) % 34.54/34.77 (step @p218 :rule chain_m_resolution :premises (@p217 @p5) :args (@t126 @t56 @t57)) % 34.54/34.77 (step @p219 :rule instantiate :premises (@p218) :args (@t83)) % 34.54/34.77 (step @p220 :rule aci_norm :args ((= (or (or @t59 @t128) @t40) (or @t59 @t128 @t40)))) % 34.54/34.77 (step @p221 :rule refl :args (@t40)) % 34.54/34.77 (step @p222 :rule bool-and-de-morgan :args (@t28 @t41 true)) % 34.54/34.77 (step @p223 :rule nary_cong :premises (@p222 @p221) :args ((or (not @t42) @t40))) % 34.54/34.77 (step @p224 :rule trans :premises (@p223 @p220)) % 34.54/34.77 (step @p225 :rule bool-impl-elim :args (@t42 @t40)) % 34.54/34.77 (step @p226 :rule trans :premises (@p225 @p224)) % 34.54/34.77 (step @p227 :rule cong :premises (@p226) :args (@t43)) % 34.54/34.77 (step @p228 :rule eq_resolve :premises (@p19 @p227)) % 34.54/34.77 (step @p229 :rule instantiate :premises (@p228) :args ((@list @t68 @t61 @t60))) % 34.54/34.77 (step @p230 :rule instantiate :premises (@p21) :args (@t117)) % 34.54/34.77 (step @p231 :rule cnf_or_pos :args (@t132)) % 34.54/34.77 (step @p232 :rule reordering :premises (@p231) :args ((or @t131 @t114 @t129 (not @t132)))) % 34.54/34.77 (step @p233 :rule chain_m_resolution :premises (@p232 @p230 @p181 @p229) :args (@t129 (@list false false false) (@list @t130 @t110 @t132))) % 34.54/34.77 (step @p234 :rule cnf_equiv_pos2 :args (@t134)) % 34.54/34.77 (step @p235 :rule reordering :premises (@p234) :args ((or @t133 (not @t129) (not @t134)))) % 34.54/34.77 (step @p236 :rule chain_m_resolution :premises (@p235 @p233 @p219) :args (@t133 @t112 (@list @t129 @t134))) % 34.54/34.77 (step @p237 :rule bool-eq-true :args (@t135)) % 34.54/34.77 (step @p238 :rule eq-symm :args (true @t135)) % 34.54/34.77 (step @p239 :rule trans :premises (@p238 @p237)) % 34.54/34.77 (step @p240 :rule refl :args (@t135)) % 34.54/34.77 (step @p241 :rule eq-refl :args (@t63)) % 34.54/34.77 (step @p242 :rule cong :premises (@p241 @p240) :args (@t136)) % 34.54/34.77 (step @p243 :rule trans :premises (@p242 @p239)) % 34.54/34.77 (step @p244 :rule refl :args (@t32)) % 34.54/34.77 (step @p245 :rule cong :premises (@p244 @p243) :args ((=> @t32 @t136))) % 34.54/34.77 (assume-push @p290 @t32) % 34.54/34.77 (step @p247 :rule instantiate :premises (@p8) :args ((@list @t62 @t53 @t63))) % 34.54/34.77 (step-pop @p291 :rule scope :premises (@p247)) % 34.54/34.77 (step @p248 :rule process_scope :premises (@p291) :args (@t136)) % 34.54/34.77 (step @p250 :rule eq_resolve :premises (@p248 @p245)) % 34.54/34.77 (step @p251 :rule implies_elim :premises (@p250)) % 34.54/34.77 (step @p252 :rule chain_m_resolution :premises (@p251 @p8) :args (@t135 @t56 (@list @t32))) % 34.54/34.77 (step @p253 :rule instantiate :premises (@p252) :args (@t83)) % 34.54/34.77 (step @p254 :rule cnf_or_neg :args (@t102 1)) % 34.54/34.77 (step @p255 :rule chain_m_resolution :premises (@p254 @p141) :args ((not @t101) @t99 @t105)) % 34.54/34.77 (step @p256 :rule cnf_equiv_pos2 :args (@t140)) % 34.54/34.77 (step @p257 :rule reordering :premises (@p256) :args ((or @t101 @t141 (not @t140)))) % 34.54/34.77 (step @p258 :rule chain_m_resolution :premises (@p257 @p255 @p253) :args (@t141 @t94 (@list @t101 @t140))) % 34.54/34.77 (step @p259 :rule bool-double-not-elim :args (@t137)) % 34.54/34.77 (step @p260 :rule refl :args (@t142)) % 34.54/34.77 (step @p261 :rule refl :args (@t139)) % 34.54/34.77 (step @p262 :rule nary_cong :premises (@p261 @p260 @p259) :args ((or @t139 @t142 (not @t138)))) % 34.54/34.77 (step @p263 :rule cnf_and_neg :args (@t139)) % 34.54/34.77 (step @p264 :rule eq_resolve :premises (@p263 @p262)) % 34.54/34.77 (step @p265 :rule reordering :premises (@p264) :args ((or @t137 @t139 @t142))) % 34.54/34.77 (step @p266 :rule chain_m_resolution :premises (@p265 @p258 @p236) :args (@t137 @t94 (@list @t139 @t133))) % 34.54/34.77 (step @p267 :rule cnf_equiv_pos1 :args (@t143)) % 34.54/34.77 (step @p268 :rule reordering :premises (@p267) :args ((or @t138 @t123 @t144))) % 34.54/34.77 (step @p269 :rule chain_m_resolution :premises (@p268 @p266 @p203) :args (@t144 (@list false true) (@list @t137 @t123))) % 34.54/34.77 (assume-push @p292 @t54) % 34.54/34.77 (step @p271 :rule instantiate :premises (@p41) :args (@t83)) % 34.54/34.77 (step-pop @p293 :rule scope :premises (@p271)) % 34.54/34.77 (step @p272 :rule process_scope :premises (@p293) :args (@t143)) % 34.54/34.77 (step @p274 :rule implies_elim :premises (@p272)) % 34.54/34.77 (step @p275 false :rule chain_m_resolution :premises (@p274 @p269 @p41) :args (false @t94 (@list @t143 @t54))) % 34.54/34.77 ) % 34.54/34.77 % SZS output end Proof % 34.54/34.77 % cvc5 exiting %------------------------------------------------------------------------------