%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU191+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.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 08:50:54 AM UTC 2026 % Result : Theorem 135.73s 135.92s % Output : Proof 135.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU191+1 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n001.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 16:36:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 135.73/135.92 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 135.73/135.92 --- Run --no-e-matching --full-saturate-quant at 6... % 135.73/135.92 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 135.73/135.92 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 135.73/135.92 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 135.73/135.92 --- Run --trigger-sel=max --full-saturate-quant at 15... % 135.73/135.92 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 135.73/135.92 --- Run --multi-trigger-cache --full-saturate-quant at 15... % 135.73/135.92 --- Run --prenex-quant=none --full-saturate-quant at 30... % 135.73/135.92 % SZS status Theorem % 135.73/135.92 % SZS output start Proof % 135.73/135.92 ( % 135.73/135.92 (declare-sort $$unsorted 0) % 135.73/135.92 (declare-const tptp.empty_set $$unsorted) % 135.73/135.92 (declare-const tptp.relation_composition (-> $$unsorted $$unsorted $$unsorted)) % 135.73/135.92 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 135.73/135.92 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 135.73/135.92 (declare-const tptp.ordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 135.73/135.92 (declare-const tptp.empty (-> $$unsorted Bool)) % 135.73/135.92 (declare-const tptp.identity_relation (-> $$unsorted $$unsorted)) % 135.73/135.92 (declare-const tptp.relation (-> $$unsorted Bool)) % 135.73/135.92 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 135.73/135.92 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 135.73/135.92 (define @t1 () (@var "A" $$unsorted)) % 135.73/135.92 (define @t2 () (@var "B" $$unsorted)) % 135.73/135.92 (define @t3 () (tptp.in @t1 @t2)) % 135.73/135.92 (define @t4 () (@list @t1 @t2)) % 135.73/135.92 (define @t5 () (tptp.relation @t1)) % 135.73/135.92 (define @t6 () (tptp.empty @t1)) % 135.73/135.92 (define @t7 () (@list @t1)) % 135.73/135.92 (define @t8 () (tptp.unordered_pair @t1 @t2)) % 135.73/135.92 (define @t9 () (@var "D" $$unsorted)) % 135.73/135.92 (define @t10 () (@var "C" $$unsorted)) % 135.73/135.92 (define @t11 () (= @t10 @t9)) % 135.73/135.92 (define @t12 () (tptp.ordered_pair @t10 @t9)) % 135.73/135.92 (define @t13 () (@list @t10 @t9)) % 135.73/135.92 (define @t14 () (tptp.identity_relation @t1)) % 135.73/135.92 (define @t15 () (= (= @t2 @t14) (forall @t13 (= (tptp.in @t12 @t2) (and (tptp.in @t10 @t1) @t11))))) % 135.73/135.92 (define @t16 () (tptp.relation @t2)) % 135.73/135.92 (define @t17 () (forall @t4 (=> @t16 @t15))) % 135.73/135.92 (define @t18 () (tptp.singleton @t1)) % 135.73/135.92 (define @t19 () (tptp.ordered_pair @t1 @t2)) % 135.73/135.92 (define @t20 () (@var "E" $$unsorted)) % 135.73/135.92 (define @t21 () (@var "F" $$unsorted)) % 135.73/135.92 (define @t22 () (tptp.ordered_pair @t21 @t20)) % 135.73/135.92 (define @t23 () (tptp.in @t22 @t2)) % 135.73/135.92 (define @t24 () (tptp.ordered_pair @t9 @t21)) % 135.73/135.92 (define @t25 () (tptp.in @t24 @t1)) % 135.73/135.92 (define @t26 () (and @t25 @t23)) % 135.73/135.92 (define @t27 () (@list @t21)) % 135.73/135.92 (define @t28 () (exists @t27 @t26)) % 135.73/135.92 (define @t29 () (tptp.ordered_pair @t9 @t20)) % 135.73/135.92 (define @t30 () (tptp.in @t29 @t10)) % 135.73/135.92 (define @t31 () (= @t30 @t28)) % 135.73/135.92 (define @t32 () (@list @t9 @t20)) % 135.73/135.92 (define @t33 () (forall @t32 @t31)) % 135.73/135.92 (define @t34 () (tptp.relation_composition @t1 @t2)) % 135.73/135.92 (define @t35 () (= @t10 @t34)) % 135.73/135.92 (define @t36 () (= @t35 @t33)) % 135.73/135.92 (define @t37 () (tptp.relation @t10)) % 135.73/135.92 (define @t38 () (=> @t37 @t36)) % 135.73/135.92 (define @t39 () (@list @t10)) % 135.73/135.92 (define @t40 () (forall @t39 @t38)) % 135.73/135.92 (define @t41 () (=> @t16 @t40)) % 135.73/135.92 (define @t42 () (@list @t2)) % 135.73/135.92 (define @t43 () (forall @t42 @t41)) % 135.73/135.92 (define @t44 () (=> @t5 @t43)) % 135.73/135.92 (define @t45 () (forall @t7 @t44)) % 135.73/135.92 (define @t46 () (tptp.relation @t34)) % 135.73/135.92 (define @t47 () (and @t5 @t16)) % 135.73/135.92 (define @t48 () (forall @t4 (=> @t47 @t46))) % 135.73/135.92 (define @t49 () (tptp.relation_composition @t2 @t1)) % 135.73/135.92 (define @t50 () (and @t6 @t16)) % 135.73/135.92 (define @t51 () (tptp.empty tptp.empty_set)) % 135.73/135.92 (define @t52 () (not @t6)) % 135.73/135.92 (define @t53 () (tptp.element @t1 @t2)) % 135.73/135.92 (define @t54 () (tptp.empty @t2)) % 135.73/135.92 (define @t55 () (= (tptp.in @t19 (tptp.relation_composition (tptp.identity_relation @t10) @t9)) (and (tptp.in @t1 @t10) (tptp.in @t19 @t9)))) % 135.73/135.92 (define @t56 () (tptp.relation @t9)) % 135.73/135.92 (define @t57 () (@list @t1 @t2 @t10 @t9)) % 135.73/135.92 (define @t58 () (forall @t57 (=> @t56 @t55))) % 135.73/135.92 (define @t59 () (not @t58)) % 135.73/135.92 (define @t60 () (forall @t57 (or (not @t56) @t55))) % 135.73/135.92 (define @t61 () (@quantifiers_skolemize @t60 2)) % 135.73/135.92 (define @t62 () (tptp.identity_relation @t61)) % 135.73/135.92 (define @t63 () (tptp.in @t12 @t62)) % 135.73/135.92 (define @t64 () (and (tptp.in @t10 @t61) @t11)) % 135.73/135.92 (define @t65 () (forall @t13 (= @t64 @t63))) % 135.73/135.92 (define @t66 () (forall @t13 (= @t63 @t64))) % 135.73/135.92 (define @t67 () (= (= @t62 @t62) @t66)) % 135.73/135.92 (define @t68 () (tptp.relation @t62)) % 135.73/135.92 (define @t69 () (not @t68)) % 135.73/135.92 (define @t70 () (or @t69 @t67)) % 135.73/135.92 (define @t71 () (not @t16)) % 135.73/135.92 (define @t72 () (forall @t4 (or @t71 @t15))) % 135.73/135.92 (define @t73 () (or @t69 @t65)) % 135.73/135.92 (define @t74 () (@list false)) % 135.73/135.92 (define @t75 () (@list false false)) % 135.73/135.92 (define @t76 () (not @t23)) % 135.73/135.92 (define @t77 () (= @t35 (forall @t32 (= @t30 (not (forall @t27 (or (not @t25) @t76))))))) % 135.73/135.92 (define @t78 () (not @t37)) % 135.73/135.92 (define @t79 () (forall @t39 (or @t78 @t77))) % 135.73/135.92 (define @t80 () (forall @t42 (or @t71 @t79))) % 135.73/135.92 (define @t81 () (forall @t27 (not @t26))) % 135.73/135.92 (define @t82 () (not @t81)) % 135.73/135.92 (define @t83 () (not (tptp.in @t24 @t62))) % 135.73/135.92 (define @t84 () (forall @t42 (or @t71 (forall @t39 (or @t78 (= (= @t10 (tptp.relation_composition @t62 @t2)) (forall @t32 (= @t30 (not (forall @t27 (or @t83 @t76))))))))))) % 135.73/135.92 (define @t85 () (or @t69 @t84)) % 135.73/135.92 (define @t86 () (@quantifiers_skolemize @t60 3)) % 135.73/135.92 (define @t87 () (tptp.relation @t86)) % 135.73/135.92 (define @t88 () (@quantifiers_skolemize @t60 1)) % 135.73/135.92 (define @t89 () (@quantifiers_skolemize @t60 0)) % 135.73/135.92 (define @t90 () (tptp.ordered_pair @t89 @t88)) % 135.73/135.92 (define @t91 () (tptp.in @t90 @t86)) % 135.73/135.92 (define @t92 () (tptp.in @t89 @t61)) % 135.73/135.92 (define @t93 () (and @t92 @t91)) % 135.73/135.92 (define @t94 () (tptp.relation_composition @t62 @t86)) % 135.73/135.92 (define @t95 () (tptp.in @t90 @t94)) % 135.73/135.92 (define @t96 () (= @t95 @t93)) % 135.73/135.92 (define @t97 () (not @t87)) % 135.73/135.92 (define @t98 () (or @t97 @t96)) % 135.73/135.92 (define @t99 () (@list true)) % 135.73/135.92 (define @t100 () (@list @t98)) % 135.73/135.92 (define @t101 () (not (forall @t27 (or @t83 (not (tptp.in @t22 @t86)))))) % 135.73/135.92 (define @t102 () (forall @t39 (or @t78 (= (= @t10 @t94) (forall @t32 (= @t30 @t101)))))) % 135.73/135.92 (define @t103 () (or @t97 @t102)) % 135.73/135.92 (define @t104 () (tptp.in @t29 @t94)) % 135.73/135.92 (define @t105 () (forall @t32 (= @t101 @t104))) % 135.73/135.92 (define @t106 () (forall @t32 (= @t104 @t101))) % 135.73/135.92 (define @t107 () (= (= @t94 @t94) @t106)) % 135.73/135.92 (define @t108 () (tptp.relation @t94)) % 135.73/135.92 (define @t109 () (not @t108)) % 135.73/135.92 (define @t110 () (or @t109 @t107)) % 135.73/135.92 (define @t111 () (or @t109 @t105)) % 135.73/135.92 (define @t112 () (not @t5)) % 135.73/135.92 (define @t113 () (or @t69 @t97 @t108)) % 135.73/135.92 (define @t114 () (forall @t27 (or (not (tptp.in (tptp.ordered_pair @t89 @t21) @t62)) (not (tptp.in (tptp.ordered_pair @t21 @t88) @t86))))) % 135.73/135.92 (define @t115 () (not @t114)) % 135.73/135.92 (define @t116 () (= @t115 @t95)) % 135.73/135.92 (define @t117 () (= @t95 @t115)) % 135.73/135.92 (define @t118 () (not @t117)) % 135.73/135.92 (define @t119 () (not @t95)) % 135.73/135.92 (define @t120 () (@quantifiers_skolemize @t114 0)) % 135.73/135.92 (define @t121 () (tptp.in (tptp.ordered_pair @t120 @t88) @t86)) % 135.73/135.92 (define @t122 () (not @t121)) % 135.73/135.92 (define @t123 () (tptp.in (tptp.ordered_pair @t89 @t120) @t62)) % 135.73/135.92 (define @t124 () (not @t123)) % 135.73/135.92 (define @t125 () (or @t124 @t122)) % 135.73/135.92 (define @t126 () (not @t125)) % 135.73/135.92 (define @t127 () (not @t115)) % 135.73/135.92 (define @t128 () (= @t89 @t120)) % 135.73/135.92 (define @t129 () (and @t92 @t128)) % 135.73/135.92 (define @t130 () (= @t129 @t123)) % 135.73/135.92 (define @t131 () (= @t123 @t129)) % 135.73/135.92 (define @t132 () (not @t129)) % 135.73/135.92 (define @t133 () (and @t121 @t128)) % 135.73/135.92 (define @t134 () (@list true false)) % 135.73/135.92 (define @t135 () (not @t91)) % 135.73/135.92 (define @t136 () (tptp.in (tptp.ordered_pair @t89 @t89) @t62)) % 135.73/135.92 (define @t137 () (not @t136)) % 135.73/135.92 (define @t138 () (or @t137 @t135)) % 135.73/135.92 (define @t139 () (not @t93)) % 135.73/135.92 (define @t140 () (@list @t93)) % 135.73/135.92 (define @t141 () (= @t92 @t136)) % 135.73/135.92 (define @t142 () (not @t141)) % 135.73/135.92 (define @t143 () (and @t92 (= @t89 @t89))) % 135.73/135.92 (define @t144 () (= @t143 @t136)) % 135.73/135.92 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 135.73/135.92 (assume @p2 (forall @t7 (=> @t6 @t5))) % 135.73/135.92 (assume @p3 (forall @t4 (= @t8 (tptp.unordered_pair @t2 @t1)))) % 135.73/135.92 (assume @p4 @t17) % 135.73/135.92 (assume @p5 (forall @t4 (= @t19 (tptp.unordered_pair @t8 @t18)))) % 135.73/135.92 (assume @p6 @t45) % 135.73/135.92 (assume @p7 true) % 135.73/135.92 (assume @p8 @t48) % 135.73/135.92 (assume @p9 (forall @t7 (tptp.relation @t14))) % 135.73/135.92 (assume @p10 (forall @t7 (exists @t42 (tptp.element @t2 @t1)))) % 135.73/135.92 (assume @p11 (forall @t4 (=> @t50 (and (tptp.empty @t49) (tptp.relation @t49))))) % 135.73/135.92 (assume @p12 @t51) % 135.73/135.92 (assume @p13 (forall @t4 (not (tptp.empty @t19)))) % 135.73/135.92 (assume @p14 (forall @t7 (not (tptp.empty @t18)))) % 135.73/135.92 (assume @p15 (forall @t4 (not (tptp.empty @t8)))) % 135.73/135.92 (assume @p16 (and @t51 (tptp.relation tptp.empty_set))) % 135.73/135.92 (assume @p17 (forall @t4 (=> @t50 (and (tptp.empty @t34) @t46)))) % 135.73/135.92 (assume @p18 (exists @t7 (and @t6 @t5))) % 135.73/135.92 (assume @p19 (exists @t7 @t6)) % 135.73/135.92 (assume @p20 (exists @t7 (and @t52 @t5))) % 135.73/135.92 (assume @p21 (exists @t7 @t52)) % 135.73/135.92 (assume @p22 (forall @t4 (=> @t3 @t53))) % 135.73/135.92 (assume @p23 (forall @t4 (=> @t53 (or @t54 @t3)))) % 135.73/135.92 (assume @p24 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 135.73/135.92 (assume @p25 @t59) % 135.73/135.92 (assume @p26 (forall @t4 (not (and @t3 @t54)))) % 135.73/135.92 (assume @p27 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t54)))) % 135.73/135.92 (step @p28 :rule bool-impl-elim :args (@t16 @t15)) % 135.73/135.92 (step @p29 :rule cong :premises (@p28) :args (@t17)) % 135.73/135.92 (step @p30 :rule eq_resolve :premises (@p4 @p29)) % 135.73/135.92 (step @p31 :rule bool-eq-true :args (@t65)) % 135.73/135.92 (step @p32 :rule eq-symm :args (true @t65)) % 135.73/135.92 (step @p33 :rule trans :premises (@p32 @p31)) % 135.73/135.92 (step @p34 :rule eq-symm :args (@t63 @t64)) % 135.73/135.92 (step @p35 :rule cong :premises (@p34) :args (@t66)) % 135.73/135.92 (step @p36 :rule eq-refl :args (@t62)) % 135.73/135.92 (step @p37 :rule cong :premises (@p36 @p35) :args (@t67)) % 135.73/135.92 (step @p38 :rule trans :premises (@p37 @p33)) % 135.73/135.92 (step @p39 :rule refl :args (@t69)) % 135.73/135.92 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t70)) % 135.73/135.92 (step @p41 :rule refl :args (@t72)) % 135.73/135.92 (step @p42 :rule cong :premises (@p41 @p40) :args ((=> @t72 @t70))) % 135.73/135.92 (assume-push @p261 @t72) % 135.73/135.92 (step @p44 :rule instantiate :premises (@p30) :args ((@list @t61 @t62))) % 135.73/135.92 (step-pop @p262 :rule scope :premises (@p44)) % 135.73/135.92 (step @p45 :rule process_scope :premises (@p262) :args (@t70)) % 135.73/135.92 (step @p47 :rule eq_resolve :premises (@p45 @p42)) % 135.73/135.92 (step @p48 :rule implies_elim :premises (@p47)) % 135.73/135.92 (step @p49 :rule chain_m_resolution :premises (@p48 @p30) :args (@t73 @t74 (@list @t72))) % 135.73/135.92 (step @p50 :rule instantiate :premises (@p9) :args ((@list @t61))) % 135.73/135.92 (step @p51 :rule cnf_or_pos :args (@t73)) % 135.73/135.92 (step @p52 :rule reordering :premises (@p51) :args ((or @t69 @t65 (not @t73)))) % 135.73/135.92 (step @p53 :rule chain_m_resolution :premises (@p52 @p50 @p49) :args (@t65 @t75 (@list @t68 @t73))) % 135.73/135.92 (step @p54 :rule bool-impl-elim :args (@t5 @t80)) % 135.73/135.92 (step @p55 :rule cong :premises (@p54) :args ((forall @t7 (=> @t5 @t80)))) % 135.73/135.92 (step @p56 :rule bool-impl-elim :args (@t16 @t79)) % 135.73/135.92 (step @p57 :rule cong :premises (@p56) :args ((forall @t42 (=> @t16 @t79)))) % 135.73/135.92 (step @p58 :rule bool-impl-elim :args (@t37 @t77)) % 135.73/135.92 (step @p59 :rule cong :premises (@p58) :args ((forall @t39 (=> @t37 @t77)))) % 135.73/135.92 (step @p60 :rule bool-and-de-morgan :args (@t25 @t23 true)) % 135.73/135.92 (step @p61 :rule cong :premises (@p60) :args (@t81)) % 135.73/135.92 (step @p62 :rule cong :premises (@p61) :args (@t82)) % 135.73/135.92 (step @p63 :rule exists-elim :args ((= @t28 @t82))) % 135.73/135.92 (step @p64 :rule trans :premises (@p63 @p62)) % 135.73/135.92 (step @p65 :rule refl :args (@t30)) % 135.73/135.92 (step @p66 :rule cong :premises (@p65 @p64) :args (@t31)) % 135.73/135.92 (step @p67 :rule cong :premises (@p66) :args (@t33)) % 135.73/135.92 (step @p68 :rule refl :args (@t35)) % 135.73/135.92 (step @p69 :rule cong :premises (@p68 @p67) :args (@t36)) % 135.73/135.92 (step @p70 :rule refl :args (@t37)) % 135.73/135.92 (step @p71 :rule cong :premises (@p70 @p69) :args (@t38)) % 135.73/135.92 (step @p72 :rule cong :premises (@p71) :args (@t40)) % 135.73/135.92 (step @p73 :rule trans :premises (@p72 @p59)) % 135.73/135.92 (step @p74 :rule refl :args (@t16)) % 135.73/135.92 (step @p75 :rule cong :premises (@p74 @p73) :args (@t41)) % 135.73/135.92 (step @p76 :rule cong :premises (@p75) :args (@t43)) % 135.73/135.92 (step @p77 :rule trans :premises (@p76 @p57)) % 135.73/135.92 (step @p78 :rule refl :args (@t5)) % 135.73/135.92 (step @p79 :rule cong :premises (@p78 @p77) :args (@t44)) % 135.73/135.92 (step @p80 :rule cong :premises (@p79) :args (@t45)) % 135.73/135.92 (step @p81 :rule trans :premises (@p80 @p55)) % 135.73/135.92 (step @p82 :rule eq_resolve :premises (@p6 @p81)) % 135.73/135.92 (step @p83 :rule instantiate :premises (@p82) :args ((@list @t62))) % 135.73/135.92 (step @p84 :rule cnf_or_pos :args (@t85)) % 135.73/135.92 (step @p85 :rule reordering :premises (@p84) :args ((or @t69 @t84 (not @t85)))) % 135.73/135.92 (step @p86 :rule chain_m_resolution :premises (@p85 @p50 @p83) :args (@t84 @t75 (@list @t68 @t85))) % 135.73/135.92 (step @p87 :rule instantiate :premises (@p86) :args ((@list @t86))) % 135.73/135.92 (step @p88 :rule bool-impl-elim :args (@t56 @t55)) % 135.73/135.92 (step @p89 :rule cong :premises (@p88) :args (@t58)) % 135.73/135.92 (step @p90 :rule cong :premises (@p89) :args (@t59)) % 135.73/135.92 (step @p91 :rule eq_resolve :premises (@p25 @p90)) % 135.73/135.92 (step @p92 :rule skolemize :premises (@p91)) % 135.73/135.92 (step @p93 :rule bool-double-not-elim :args (@t87)) % 135.73/135.92 (step @p94 :rule refl :args (@t98)) % 135.73/135.92 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or @t98 (not @t97)))) % 135.73/135.92 (step @p96 :rule cnf_or_neg :args (@t98 0)) % 135.73/135.92 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 135.73/135.92 (step @p98 :rule reordering :premises (@p97) :args ((or @t87 @t98))) % 135.73/135.92 (step @p99 :rule chain_m_resolution :premises (@p98 @p92) :args (@t87 @t99 @t100)) % 135.73/135.92 (step @p100 :rule cnf_or_pos :args (@t103)) % 135.73/135.92 (step @p101 :rule reordering :premises (@p100) :args ((or @t97 @t102 (not @t103)))) % 135.73/135.92 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p87) :args (@t102 @t75 (@list @t87 @t103))) % 135.73/135.92 (step @p103 :rule bool-eq-true :args (@t105)) % 135.73/135.92 (step @p104 :rule eq-symm :args (true @t105)) % 135.73/135.92 (step @p105 :rule trans :premises (@p104 @p103)) % 135.73/135.92 (step @p106 :rule eq-symm :args (@t104 @t101)) % 135.73/135.92 (step @p107 :rule cong :premises (@p106) :args (@t106)) % 135.73/135.92 (step @p108 :rule eq-refl :args (@t94)) % 135.73/135.92 (step @p109 :rule cong :premises (@p108 @p107) :args (@t107)) % 135.73/135.92 (step @p110 :rule trans :premises (@p109 @p105)) % 135.73/135.92 (step @p111 :rule refl :args (@t109)) % 135.73/135.92 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t110)) % 135.73/135.92 (step @p113 :rule refl :args (@t102)) % 135.73/135.92 (step @p114 :rule cong :premises (@p113 @p112) :args ((=> @t102 @t110))) % 135.73/135.92 (assume-push @p263 @t102) % 135.73/135.92 (step @p116 :rule instantiate :premises (@p102) :args ((@list @t94))) % 135.73/135.92 (step-pop @p264 :rule scope :premises (@p116)) % 135.73/135.92 (step @p117 :rule process_scope :premises (@p264) :args (@t110)) % 135.73/135.92 (step @p119 :rule eq_resolve :premises (@p117 @p114)) % 135.73/135.92 (step @p120 :rule implies_elim :premises (@p119)) % 135.73/135.92 (step @p121 :rule chain_m_resolution :premises (@p120 @p102) :args (@t111 @t74 (@list @t102))) % 135.73/135.92 (step @p122 :rule aci_norm :args ((= (or (or @t112 @t71) @t46) (or @t112 @t71 @t46)))) % 135.73/135.92 (step @p123 :rule refl :args (@t46)) % 135.73/135.92 (step @p124 :rule bool-and-de-morgan :args (@t5 @t16 true)) % 135.73/135.92 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or (not @t47) @t46))) % 135.73/135.92 (step @p126 :rule trans :premises (@p125 @p122)) % 135.73/135.92 (step @p127 :rule bool-impl-elim :args (@t47 @t46)) % 135.73/135.92 (step @p128 :rule trans :premises (@p127 @p126)) % 135.73/135.92 (step @p129 :rule cong :premises (@p128) :args (@t48)) % 135.73/135.92 (step @p130 :rule eq_resolve :premises (@p8 @p129)) % 135.73/135.92 (step @p131 :rule instantiate :premises (@p130) :args ((@list @t62 @t86))) % 135.73/135.92 (step @p132 :rule cnf_or_pos :args (@t113)) % 135.73/135.92 (step @p133 :rule reordering :premises (@p132) :args ((or @t97 @t69 @t108 (not @t113)))) % 135.73/135.92 (step @p134 :rule chain_m_resolution :premises (@p133 @p99 @p50 @p131) :args (@t108 (@list false false false) (@list @t87 @t68 @t113))) % 135.73/135.92 (step @p135 :rule cnf_or_pos :args (@t111)) % 135.73/135.92 (step @p136 :rule reordering :premises (@p135) :args ((or @t109 @t105 (not @t111)))) % 135.73/135.92 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p121) :args (@t105 @t75 (@list @t108 @t111))) % 135.73/135.92 (step @p138 :rule eq-symm :args (@t115 @t95)) % 135.73/135.92 (step @p139 :rule refl :args (@t105)) % 135.73/135.92 (step @p140 :rule cong :premises (@p139 @p138) :args ((=> @t105 @t116))) % 135.73/135.92 (assume-push @p265 @t105) % 135.73/135.92 (step @p142 :rule instantiate :premises (@p137) :args ((@list @t89 @t88))) % 135.73/135.92 (step-pop @p266 :rule scope :premises (@p142)) % 135.73/135.92 (step @p143 :rule process_scope :premises (@p266) :args (@t116)) % 135.73/135.92 (step @p145 :rule eq_resolve :premises (@p143 @p140)) % 135.73/135.92 (step @p146 :rule implies_elim :premises (@p145)) % 135.73/135.92 (step @p147 :rule chain_m_resolution :premises (@p146 @p137) :args (@t117 @t74 (@list @t105))) % 135.73/135.92 (step @p148 :rule cnf_or_neg :args (@t98 1)) % 135.73/135.92 (step @p149 :rule chain_m_resolution :premises (@p148 @p92) :args ((not @t96) @t99 @t100)) % 135.73/135.92 (step @p150 :rule cnf_equiv_neg2 :args (@t96)) % 135.73/135.92 (step @p151 :rule cnf_equiv_pos1 :args (@t117)) % 135.73/135.92 (step @p152 :rule reordering :premises (@p151) :args ((or @t119 @t115 @t118))) % 135.73/135.92 (step @p153 :rule refl :args (@t126)) % 135.73/135.92 (step @p154 :rule bool-double-not-elim :args (@t114)) % 135.73/135.92 (step @p155 :rule nary_cong :premises (@p154 @p153) :args ((or @t127 @t126))) % 135.73/135.92 (assume-push @p267 @t115) % 135.73/135.92 (step @p157 :rule skolemize :premises (@p267)) % 135.73/135.92 (step-pop @p268 :rule scope :premises (@p157)) % 135.73/135.92 (step @p158 :rule process_scope :premises (@p268) :args (@t126)) % 135.73/135.92 (step @p160 :rule implies_elim :premises (@p158)) % 135.73/135.92 (step @p161 :rule eq_resolve :premises (@p160 @p155)) % 135.73/135.92 (step @p162 :rule bool-double-not-elim :args (@t123)) % 135.73/135.92 (step @p163 :rule refl :args (@t125)) % 135.73/135.92 (step @p164 :rule nary_cong :premises (@p163 @p162) :args ((or @t125 (not @t124)))) % 135.73/135.92 (step @p165 :rule cnf_or_neg :args (@t125 0)) % 135.73/135.92 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 135.73/135.92 (step @p167 :rule reordering :premises (@p166) :args ((or @t123 @t125))) % 135.73/135.92 (step @p168 :rule bool-double-not-elim :args (@t121)) % 135.73/135.92 (step @p169 :rule nary_cong :premises (@p163 @p168) :args ((or @t125 (not @t122)))) % 135.73/135.92 (step @p170 :rule cnf_or_neg :args (@t125 1)) % 135.73/135.92 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 135.73/135.92 (step @p172 :rule reordering :premises (@p171) :args ((or @t121 @t125))) % 135.73/135.92 (step @p173 :rule eq-symm :args (@t129 @t123)) % 135.73/135.92 (step @p174 :rule refl :args (@t65)) % 135.73/135.92 (step @p175 :rule cong :premises (@p174 @p173) :args ((=> @t65 @t130))) % 135.73/135.92 (assume-push @p269 @t65) % 135.73/135.92 (step @p177 :rule instantiate :premises (@p53) :args ((@list @t89 @t120))) % 135.73/135.92 (step-pop @p270 :rule scope :premises (@p177)) % 135.73/135.92 (step @p178 :rule process_scope :premises (@p270) :args (@t130)) % 135.73/135.92 (step @p180 :rule eq_resolve :premises (@p178 @p175)) % 135.73/135.92 (step @p181 :rule implies_elim :premises (@p180)) % 135.73/135.92 (step @p182 :rule chain_m_resolution :premises (@p181 @p53) :args (@t131 @t74 (@list @t65))) % 135.73/135.92 (step @p183 :rule cnf_equiv_pos1 :args (@t131)) % 135.73/135.92 (step @p184 :rule reordering :premises (@p183) :args ((or @t124 @t129 (not @t131)))) % 135.73/135.92 (step @p185 :rule cnf_and_pos :args (@t129 0)) % 135.73/135.92 (step @p186 :rule reordering :premises (@p185) :args ((or @t92 @t132))) % 135.73/135.92 (step @p187 :rule cnf_and_pos :args (@t129 1)) % 135.73/135.92 (step @p188 :rule reordering :premises (@p187) :args ((or @t128 @t132))) % 135.73/135.92 (step @p189 :rule cnf_and_neg :args (@t93)) % 135.73/135.92 (assume-push @p271 @t121) % 135.73/135.92 (assume-push @p272 @t128) % 135.73/135.92 (assume-push @p273 @t121) % 135.73/135.92 (assume-push @p274 @t128) % 135.73/135.92 (step @p194 :rule true_intro :premises (@p271)) % 135.73/135.92 (step @p195 :rule refl :args (@t86)) % 135.73/135.92 (step @p196 :rule refl :args (@t88)) % 135.73/135.92 (step @p197 :rule cong :premises (@p272 @p196) :args (@t90)) % 135.73/135.92 (step @p198 :rule cong :premises (@p197 @p195) :args (@t91)) % 135.73/135.92 (step @p199 :rule trans :premises (@p198 @p194)) % 135.73/135.92 (step @p200 :rule true_elim :premises (@p199)) % 135.73/135.92 (step-pop @p275 :rule scope :premises (@p200)) % 135.73/135.92 (step-pop @p276 :rule scope :premises (@p275)) % 135.73/135.92 (step @p201 :rule process_scope :premises (@p276) :args (@t91)) % 135.73/135.92 (step @p204 :rule and_intro :premises (@p271 @p272)) % 135.73/135.92 (step @p205 :rule modus_ponens :premises (@p204 @p201)) % 135.73/135.92 (step-pop @p277 :rule scope :premises (@p205)) % 135.73/135.92 (step-pop @p278 :rule scope :premises (@p277)) % 135.73/135.92 (step @p206 :rule process_scope :premises (@p278) :args (@t91)) % 135.73/135.92 (step @p209 :rule implies_elim :premises (@p206)) % 135.73/135.92 (step @p210 :rule cnf_and_neg :args (@t133)) % 135.73/135.92 (step @p211 :rule resolution :premises (@p210 @p209) :args (true @t133)) % 135.73/135.92 (step @p212 :rule reordering :premises (@p211) :args ((or @t91 @t122 (not @t128)))) % 135.73/135.92 (step @p213 :rule chain_m_resolution :premises (@p212 @p189 @p188 @p186 @p184 @p182 @p172 @p167 @p161 @p152 @p147 @p150 @p149) :args (@t119 (@list true false false false false false false true true false true true) (@list @t91 @t128 @t92 @t129 @t131 @t121 @t123 @t125 @t114 @t117 @t93 @t96))) % 135.73/135.92 (step @p214 :rule refl :args (@t95)) % 135.73/135.92 (step @p215 :rule refl :args (@t118)) % 135.73/135.92 (step @p216 :rule nary_cong :premises (@p215 @p214 @p154) :args ((or @t118 @t95 @t127))) % 135.73/135.92 (step @p217 :rule cnf_equiv_pos2 :args (@t117)) % 135.73/135.92 (step @p218 :rule eq_resolve :premises (@p217 @p216)) % 135.73/135.92 (step @p219 :rule reordering :premises (@p218) :args ((or @t95 @t114 @t118))) % 135.73/135.92 (step @p220 :rule chain_m_resolution :premises (@p219 @p213 @p147) :args (@t114 @t134 (@list @t95 @t117))) % 135.73/135.92 (assume-push @p279 @t114) % 135.73/135.92 (step @p222 :rule instantiate :premises (@p279) :args ((@list @t89))) % 135.73/135.92 (step-pop @p280 :rule scope :premises (@p222)) % 135.73/135.92 (step @p223 :rule process_scope :premises (@p280) :args (@t138)) % 135.73/135.92 (step @p225 :rule implies_elim :premises (@p223)) % 135.73/135.92 (step @p226 :rule chain_m_resolution :premises (@p225 @p220) :args (@t138 @t74 (@list @t114))) % 135.73/135.92 (step @p227 :rule cnf_equiv_neg1 :args (@t96)) % 135.73/135.92 (step @p228 :rule reordering :premises (@p227) :args ((or @t95 @t93 @t96))) % 135.73/135.92 (step @p229 :rule chain_m_resolution :premises (@p228 @p213 @p149) :args (@t93 (@list true true) (@list @t95 @t96))) % 135.73/135.92 (step @p230 :rule cnf_and_pos :args (@t93 1)) % 135.73/135.92 (step @p231 :rule reordering :premises (@p230) :args ((or @t91 @t139))) % 135.73/135.92 (step @p232 :rule chain_m_resolution :premises (@p231 @p229) :args (@t91 @t74 @t140)) % 135.73/135.92 (step @p233 :rule cnf_or_pos :args (@t138)) % 135.73/135.92 (step @p234 :rule reordering :premises (@p233) :args ((or @t135 @t137 (not @t138)))) % 135.73/135.94 (step @p235 :rule chain_m_resolution :premises (@p234 @p232 @p226) :args (@t137 @t75 (@list @t91 @t138))) % 135.73/135.94 (step @p236 :rule cnf_and_pos :args (@t93 0)) % 135.73/135.94 (step @p237 :rule reordering :premises (@p236) :args ((or @t92 @t139))) % 135.73/135.94 (step @p238 :rule chain_m_resolution :premises (@p237 @p229) :args (@t92 @t74 @t140)) % 135.73/135.94 (step @p239 :rule cnf_equiv_pos1 :args (@t141)) % 135.73/135.94 (step @p240 :rule reordering :premises (@p239) :args ((or (not @t92) @t136 @t142))) % 135.73/135.94 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p235) :args (@t142 (@list false true) (@list @t92 @t136))) % 135.73/135.94 (step @p242 :rule eq-symm :args (@t136 @t92)) % 135.73/135.94 (step @p243 :rule aci_norm :args ((= (and @t92 true) @t92))) % 135.73/135.94 (step @p244 :rule eq-refl :args (@t89)) % 135.73/135.94 (step @p245 :rule refl :args (@t92)) % 135.73/135.94 (step @p246 :rule nary_cong :premises (@p245 @p244) :args (@t143)) % 135.73/135.94 (step @p247 :rule trans :premises (@p246 @p243)) % 135.73/135.94 (step @p248 :rule refl :args (@t136)) % 135.73/135.94 (step @p249 :rule cong :premises (@p248 @p247) :args ((= @t136 @t143))) % 135.73/135.94 (step @p250 :rule trans :premises (@p249 @p242)) % 135.73/135.94 (step @p251 :rule eq-symm :args (@t143 @t136)) % 135.73/135.94 (step @p252 :rule trans :premises (@p251 @p250)) % 135.73/135.94 (step @p253 :rule cong :premises (@p174 @p252) :args ((=> @t65 @t144))) % 135.73/135.94 (assume-push @p281 @t65) % 135.73/135.94 (step @p255 :rule instantiate :premises (@p53) :args ((@list @t89 @t89))) % 135.73/135.94 (step-pop @p282 :rule scope :premises (@p255)) % 135.73/135.94 (step @p256 :rule process_scope :premises (@p282) :args (@t144)) % 135.73/135.94 (step @p258 :rule eq_resolve :premises (@p256 @p253)) % 135.73/135.94 (step @p259 :rule implies_elim :premises (@p258)) % 135.73/135.94 (step @p260 false :rule chain_m_resolution :premises (@p259 @p241 @p53) :args (false @t134 (@list @t141 @t65))) % 135.73/135.94 ) % 135.73/135.94 % SZS output end Proof % 135.73/135.94 % cvc5 exiting %------------------------------------------------------------------------------