%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM412+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 : n007.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 08:39:19 AM UTC 2026 % Result : Theorem 0.35s 0.61s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM412+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 % 0.17/0.34 % Computer : n007.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 11:16:11 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.35/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.35/0.61 % SZS status Theorem % 0.35/0.61 % SZS output start Proof % 0.35/0.61 ( % 0.35/0.61 (declare-sort $$unsorted 0) % 0.35/0.61 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.35/0.61 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.empty_set $$unsorted) % 0.35/0.61 (declare-const tptp.relation_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.with_non_empty_elements (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.relation_rng (-> $$unsorted $$unsorted)) % 0.35/0.61 (declare-const tptp.tseq_dom_restriction (-> $$unsorted $$unsorted $$unsorted)) % 0.35/0.61 (declare-const tptp.function (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.transfinite_sequence_of (-> $$unsorted $$unsorted Bool)) % 0.35/0.61 (declare-const tptp.transfinite_sequence (-> $$unsorted Bool)) % 0.35/0.61 (define @t1 () (@var "A" $$unsorted)) % 0.35/0.61 (define @t2 () (@var "B" $$unsorted)) % 0.35/0.61 (define @t3 () (tptp.in @t1 @t2)) % 0.35/0.61 (define @t4 () (@list @t1 @t2)) % 0.35/0.61 (define @t5 () (tptp.function @t1)) % 0.35/0.61 (define @t6 () (tptp.empty @t1)) % 0.35/0.61 (define @t7 () (@list @t1)) % 0.35/0.61 (define @t8 () (tptp.epsilon_connected @t1)) % 0.35/0.61 (define @t9 () (tptp.epsilon_transitive @t1)) % 0.35/0.61 (define @t10 () (and @t9 @t8)) % 0.35/0.61 (define @t11 () (tptp.ordinal @t1)) % 0.35/0.61 (define @t12 () (tptp.relation @t1)) % 0.35/0.61 (define @t13 () (tptp.one_to_one @t1)) % 0.35/0.61 (define @t14 () (and @t12 @t5 @t13)) % 0.35/0.61 (define @t15 () (and @t12 @t6 @t5)) % 0.35/0.61 (define @t16 () (and @t9 @t8 @t11)) % 0.35/0.61 (define @t17 () (tptp.transfinite_sequence_of @t2 @t1)) % 0.35/0.61 (define @t18 () (= @t17 (tptp.subset (tptp.relation_rng @t2) @t1))) % 0.35/0.61 (define @t19 () (tptp.transfinite_sequence @t2)) % 0.35/0.61 (define @t20 () (tptp.function @t2)) % 0.35/0.61 (define @t21 () (tptp.relation @t2)) % 0.35/0.61 (define @t22 () (and @t21 @t20 @t19)) % 0.35/0.61 (define @t23 () (forall @t4 (=> @t22 @t18))) % 0.35/0.61 (define @t24 () (tptp.relation_rng @t1)) % 0.35/0.61 (define @t25 () (tptp.tseq_dom_restriction @t1 @t2)) % 0.35/0.61 (define @t26 () (tptp.transfinite_sequence_of @t25 @t24)) % 0.35/0.61 (define @t27 () (tptp.ordinal @t2)) % 0.35/0.61 (define @t28 () (tptp.transfinite_sequence @t1)) % 0.35/0.61 (define @t29 () (and @t12 @t5 @t28 @t27)) % 0.35/0.61 (define @t30 () (forall @t4 (=> @t29 @t26))) % 0.35/0.61 (define @t31 () (tptp.relation_dom_restriction @t1 @t2)) % 0.35/0.61 (define @t32 () (tptp.relation @t31)) % 0.35/0.61 (define @t33 () (forall @t4 (=> @t17 @t22))) % 0.35/0.61 (define @t34 () (@list @t2)) % 0.35/0.61 (define @t35 () (tptp.relation_empty_yielding tptp.empty_set)) % 0.35/0.61 (define @t36 () (tptp.relation tptp.empty_set)) % 0.35/0.61 (define @t37 () (tptp.empty tptp.empty_set)) % 0.35/0.61 (define @t38 () (tptp.relation_empty_yielding @t1)) % 0.35/0.61 (define @t39 () (and @t12 @t38)) % 0.35/0.61 (define @t40 () (and @t12 @t5)) % 0.35/0.61 (define @t41 () (and @t12 (tptp.relation_non_empty @t1) @t5)) % 0.35/0.61 (define @t42 () (tptp.empty @t24)) % 0.35/0.61 (define @t43 () (not @t6)) % 0.35/0.61 (define @t44 () (and @t43 @t12)) % 0.35/0.61 (define @t45 () (tptp.element @t1 @t2)) % 0.35/0.61 (define @t46 () (tptp.empty @t2)) % 0.35/0.61 (define @t47 () (tptp.subset @t1 @t2)) % 0.35/0.61 (define @t48 () (@var "C" $$unsorted)) % 0.35/0.61 (define @t49 () (tptp.transfinite_sequence_of @t48 @t2)) % 0.35/0.61 (define @t50 () (tptp.transfinite_sequence_of @t48 @t1)) % 0.35/0.61 (define @t51 () (@list @t48)) % 0.35/0.61 (define @t52 () (forall @t51 (=> @t50 @t49))) % 0.35/0.61 (define @t53 () (=> @t47 @t52)) % 0.35/0.61 (define @t54 () (forall @t4 @t53)) % 0.35/0.61 (define @t55 () (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction @t2 @t48) @t1)) % 0.35/0.61 (define @t56 () (tptp.ordinal @t48)) % 0.35/0.61 (define @t57 () (forall @t51 (=> @t56 @t55))) % 0.35/0.61 (define @t58 () (=> @t17 @t57)) % 0.35/0.61 (define @t59 () (forall @t4 @t58)) % 0.35/0.61 (define @t60 () (not @t59)) % 0.35/0.61 (define @t61 () (tptp.element @t2 (tptp.powerset @t48))) % 0.35/0.61 (define @t62 () (@list @t1 @t2 @t48)) % 0.35/0.61 (define @t63 () (@var "BOUND_VARIABLE_7799" $$unsorted)) % 0.35/0.61 (define @t64 () (tptp.transfinite_sequence_of @t63 @t2)) % 0.35/0.61 (define @t65 () (not (tptp.transfinite_sequence_of @t63 @t1))) % 0.35/0.61 (define @t66 () (not @t47)) % 0.35/0.61 (define @t67 () (or @t66 @t65 @t64)) % 0.35/0.61 (define @t68 () (or @t65 @t64)) % 0.35/0.61 (define @t69 () (or @t66 @t68)) % 0.35/0.61 (define @t70 () (@list @t1 @t2 @t63)) % 0.35/0.61 (define @t71 () (forall @t70 @t69)) % 0.35/0.61 (define @t72 () (@list @t63)) % 0.35/0.61 (define @t73 () (forall @t72 @t69)) % 0.35/0.61 (define @t74 () (forall @t72 @t68)) % 0.35/0.61 (define @t75 () (@list @t48)) % 0.35/0.61 (define @t76 () (or @t66 @t74)) % 0.35/0.61 (define @t77 () (forall @t51 (or (not @t50) @t49))) % 0.35/0.61 (define @t78 () (not @t27)) % 0.35/0.61 (define @t79 () (not @t28)) % 0.35/0.61 (define @t80 () (not @t5)) % 0.35/0.61 (define @t81 () (not @t12)) % 0.35/0.61 (define @t82 () (or @t81 @t80 @t79 @t78)) % 0.35/0.61 (define @t83 () (@var "BOUND_VARIABLE_7818" $$unsorted)) % 0.35/0.61 (define @t84 () (tptp.transfinite_sequence_of (tptp.tseq_dom_restriction @t2 @t83) @t1)) % 0.35/0.61 (define @t85 () (not (tptp.ordinal @t83))) % 0.35/0.61 (define @t86 () (not @t17)) % 0.35/0.61 (define @t87 () (or @t86 @t85 @t84)) % 0.35/0.61 (define @t88 () (@list @t1 @t2 @t83)) % 0.35/0.61 (define @t89 () (forall @t88 @t87)) % 0.35/0.61 (define @t90 () (@quantifiers_skolemize @t89 2)) % 0.35/0.62 (define @t91 () (@quantifiers_skolemize @t89 1)) % 0.35/0.62 (define @t92 () (@quantifiers_skolemize @t89 0)) % 0.35/0.62 (define @t93 () (@list @t92 @t91)) % 0.35/0.62 (define @t94 () (or @t85 @t84)) % 0.35/0.62 (define @t95 () (or @t86 @t94)) % 0.35/0.62 (define @t96 () (forall @t88 @t95)) % 0.35/0.62 (define @t97 () (@list @t83)) % 0.35/0.62 (define @t98 () (forall @t97 @t95)) % 0.35/0.62 (define @t99 () (forall @t97 @t94)) % 0.35/0.62 (define @t100 () (or @t86 @t99)) % 0.35/0.62 (define @t101 () (forall @t51 (or (not @t56) @t55))) % 0.35/0.62 (define @t102 () (tptp.transfinite_sequence_of @t91 @t92)) % 0.35/0.62 (define @t103 () (tptp.tseq_dom_restriction @t91 @t90)) % 0.35/0.62 (define @t104 () (tptp.transfinite_sequence_of @t103 @t92)) % 0.35/0.62 (define @t105 () (tptp.ordinal @t90)) % 0.35/0.62 (define @t106 () (not @t105)) % 0.35/0.62 (define @t107 () (not @t102)) % 0.35/0.62 (define @t108 () (or @t107 @t106 @t104)) % 0.35/0.62 (define @t109 () (@list true)) % 0.35/0.62 (define @t110 () (@list @t108)) % 0.35/0.62 (define @t111 () (tptp.transfinite_sequence @t91)) % 0.35/0.62 (define @t112 () (tptp.function @t91)) % 0.35/0.62 (define @t113 () (tptp.relation @t91)) % 0.35/0.62 (define @t114 () (and @t113 @t112 @t111)) % 0.35/0.62 (define @t115 () (or @t107 @t114)) % 0.35/0.62 (define @t116 () (@list false false)) % 0.35/0.62 (define @t117 () (not @t114)) % 0.35/0.62 (define @t118 () (@list false)) % 0.35/0.62 (define @t119 () (@list @t114)) % 0.35/0.62 (define @t120 () (tptp.relation_rng @t91)) % 0.35/0.62 (define @t121 () (tptp.transfinite_sequence_of @t103 @t120)) % 0.35/0.62 (define @t122 () (not @t111)) % 0.35/0.62 (define @t123 () (not @t112)) % 0.35/0.62 (define @t124 () (not @t113)) % 0.35/0.62 (define @t125 () (or @t124 @t123 @t122 @t106 @t121)) % 0.35/0.62 (define @t126 () (not @t19)) % 0.35/0.62 (define @t127 () (not @t20)) % 0.35/0.62 (define @t128 () (not @t21)) % 0.35/0.62 (define @t129 () (or @t128 @t127 @t126)) % 0.35/0.62 (define @t130 () (tptp.subset @t120 @t92)) % 0.35/0.62 (define @t131 () (= @t102 @t130)) % 0.35/0.62 (define @t132 () (or @t124 @t123 @t122 @t131)) % 0.35/0.62 (define @t133 () (not @t121)) % 0.35/0.62 (define @t134 () (not @t130)) % 0.35/0.62 (define @t135 () (or @t134 @t133 @t104)) % 0.35/0.62 (define @t136 () (not @t135)) % 0.35/0.62 (define @t137 () (forall @t70 @t67)) % 0.35/0.62 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 0.35/0.62 (assume @p2 (forall @t7 (=> @t6 @t5))) % 0.35/0.62 (assume @p3 (forall @t7 (=> @t11 @t10))) % 0.35/0.62 (assume @p4 (forall @t7 (=> @t6 @t12))) % 0.35/0.62 (assume @p5 (forall @t7 (=> @t15 @t14))) % 0.35/0.62 (assume @p6 (forall @t7 (=> @t10 @t11))) % 0.35/0.62 (assume @p7 (forall @t7 (=> @t6 @t16))) % 0.35/0.62 (assume @p8 @t23) % 0.35/0.62 (assume @p9 @t30) % 0.35/0.62 (assume @p10 (forall @t4 (=> @t12 @t32))) % 0.35/0.62 (assume @p11 @t33) % 0.35/0.62 (assume @p12 (forall @t7 (exists @t34 @t17))) % 0.35/0.62 (assume @p13 (forall @t7 (exists @t34 (tptp.element @t2 @t1)))) % 0.35/0.62 (assume @p14 (and @t37 @t36 @t35)) % 0.35/0.62 (assume @p15 (forall @t4 (=> @t39 (and @t32 (tptp.relation_empty_yielding @t31))))) % 0.35/0.62 (assume @p16 @t37) % 0.35/0.62 (assume @p17 (and @t36 @t35 (tptp.function tptp.empty_set) (tptp.one_to_one tptp.empty_set) @t37 (tptp.epsilon_transitive tptp.empty_set) (tptp.epsilon_connected tptp.empty_set) (tptp.ordinal tptp.empty_set))) % 0.35/0.62 (assume @p18 (forall @t4 (=> @t40 (and @t32 (tptp.function @t31))))) % 0.35/0.62 (assume @p19 (and @t37 @t36)) % 0.35/0.62 (assume @p20 (forall @t7 (=> @t41 (tptp.with_non_empty_elements @t24)))) % 0.35/0.62 (assume @p21 (forall @t7 (=> @t44 (not @t42)))) % 0.35/0.62 (assume @p22 (forall @t7 (=> @t6 (and @t42 (tptp.relation @t24))))) % 0.35/0.62 (assume @p23 (exists @t7 @t40)) % 0.35/0.62 (assume @p24 (exists @t7 @t16)) % 0.35/0.62 (assume @p25 (exists @t7 (and @t6 @t12))) % 0.35/0.62 (assume @p26 (exists @t7 @t6)) % 0.35/0.62 (assume @p27 (exists @t7 @t15)) % 0.35/0.62 (assume @p28 (exists @t7 (and @t12 @t5 @t13 @t6 @t9 @t8 @t11))) % 0.35/0.62 (assume @p29 (exists @t7 @t44)) % 0.35/0.62 (assume @p30 (exists @t7 @t43)) % 0.35/0.62 (assume @p31 (exists @t7 @t14)) % 0.35/0.62 (assume @p32 (exists @t7 (and @t43 @t9 @t8 @t11))) % 0.35/0.62 (assume @p33 (exists @t7 @t39)) % 0.35/0.62 (assume @p34 (exists @t7 (and @t12 @t38 @t5))) % 0.35/0.62 (assume @p35 (exists @t7 (and @t12 @t5 @t28))) % 0.35/0.62 (assume @p36 (exists @t7 @t41)) % 0.35/0.62 (assume @p37 (forall @t4 (=> @t29 (= @t25 @t31)))) % 0.35/0.62 (assume @p38 (forall @t4 (tptp.subset @t1 @t1))) % 0.35/0.62 (assume @p39 (forall @t4 (=> @t3 @t45))) % 0.35/0.62 (assume @p40 (forall @t4 (=> @t45 (or @t46 @t3)))) % 0.35/0.62 (assume @p41 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) @t47))) % 0.35/0.62 (assume @p42 @t54) % 0.35/0.62 (assume @p43 @t60) % 0.35/0.62 (assume @p44 (forall @t62 (=> (and @t3 @t61) (tptp.element @t1 @t48)))) % 0.35/0.62 (assume @p45 (forall @t62 (not (and @t3 @t61 (tptp.empty @t48))))) % 0.35/0.62 (assume @p46 (forall @t7 (=> @t6 (= @t1 tptp.empty_set)))) % 0.35/0.62 (assume @p47 (forall @t4 (not (and @t3 @t46)))) % 0.35/0.62 (assume @p48 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t46)))) % 0.35/0.62 (assume @p49 true) % 0.35/0.62 (step @p50 :rule aci_norm :args ((= @t69 @t67))) % 0.35/0.62 (step @p51 :rule cong :premises (@p50) :args (@t71)) % 0.35/0.62 (step @p52 :rule quant-merge-prenex :args ((= (forall @t4 @t73) @t71))) % 0.35/0.62 (step @p53 :rule alpha_equiv :args (@t74 (@list @t63) @t75)) % 0.35/0.62 (step @p54 :rule refl :args (@t66)) % 0.35/0.62 (step @p55 :rule nary_cong :premises (@p54 @p53) :args (@t76)) % 0.35/0.62 (step @p56 :rule quant-miniscope-or :args ((= @t73 @t76))) % 0.35/0.62 (step @p57 :rule trans :premises (@p56 @p55)) % 0.35/0.62 (step @p58 :rule symm :premises (@p57)) % 0.35/0.62 (step @p59 :rule cong :premises (@p58) :args ((forall @t4 (or @t66 @t77)))) % 0.35/0.62 (step @p60 :rule trans :premises (@p59 @p52)) % 0.35/0.62 (step @p61 :rule trans :premises (@p60 @p51)) % 0.35/0.62 (step @p62 :rule bool-impl-elim :args (@t47 @t77)) % 0.35/0.62 (step @p63 :rule cong :premises (@p62) :args ((forall @t4 (=> @t47 @t77)))) % 0.35/0.62 (step @p64 :rule trans :premises (@p63 @p61)) % 0.35/0.62 (step @p65 :rule bool-impl-elim :args (@t50 @t49)) % 0.35/0.62 (step @p66 :rule cong :premises (@p65) :args (@t52)) % 0.35/0.62 (step @p67 :rule refl :args (@t47)) % 0.35/0.62 (step @p68 :rule cong :premises (@p67 @p66) :args (@t53)) % 0.35/0.62 (step @p69 :rule cong :premises (@p68) :args (@t54)) % 0.35/0.62 (step @p70 :rule trans :premises (@p69 @p64)) % 0.35/0.62 (step @p71 :rule eq_resolve :premises (@p42 @p70)) % 0.35/0.62 (step @p72 :rule aci_norm :args ((= (or @t82 @t26) (or @t81 @t80 @t79 @t78 @t26)))) % 0.35/0.62 (step @p73 :rule refl :args (@t26)) % 0.35/0.62 (step @p74 :rule aci_norm :args ((= (or @t81 (or @t80 (or @t79 @t78))) @t82))) % 0.35/0.62 (step @p75 :rule bool-and-de-morgan :args (@t28 @t27 true)) % 0.35/0.62 (step @p76 :rule refl :args (@t80)) % 0.35/0.62 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t80 (not (and @t28 @t27))))) % 0.35/0.62 (step @p78 :rule bool-and-de-morgan :args (@t5 @t28 (and @t27))) % 0.35/0.62 (step @p79 :rule trans :premises (@p78 @p77)) % 0.35/0.62 (step @p80 :rule refl :args (@t81)) % 0.35/0.62 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t81 (not (and @t5 @t28 @t27))))) % 0.35/0.62 (step @p82 :rule bool-and-de-morgan :args (@t12 @t5 (and @t28 @t27))) % 0.35/0.62 (step @p83 :rule trans :premises (@p82 @p81)) % 0.35/0.62 (step @p84 :rule trans :premises (@p83 @p74)) % 0.35/0.62 (step @p85 :rule nary_cong :premises (@p84 @p73) :args ((or (not @t29) @t26))) % 0.35/0.62 (step @p86 :rule trans :premises (@p85 @p72)) % 0.35/0.62 (step @p87 :rule bool-impl-elim :args (@t29 @t26)) % 0.35/0.62 (step @p88 :rule trans :premises (@p87 @p86)) % 0.35/0.62 (step @p89 :rule cong :premises (@p88) :args (@t30)) % 0.35/0.62 (step @p90 :rule eq_resolve :premises (@p9 @p89)) % 0.35/0.62 (step @p91 :rule instantiate :premises (@p90) :args ((@list @t91 @t90))) % 0.35/0.62 (step @p92 :rule bool-impl-elim :args (@t17 @t22)) % 0.35/0.62 (step @p93 :rule cong :premises (@p92) :args (@t33)) % 0.35/0.62 (step @p94 :rule eq_resolve :premises (@p11 @p93)) % 0.35/0.62 (step @p95 :rule instantiate :premises (@p94) :args (@t93)) % 0.35/0.62 (step @p96 :rule aci_norm :args ((= @t95 @t87))) % 0.35/0.62 (step @p97 :rule cong :premises (@p96) :args (@t96)) % 0.35/0.62 (step @p98 :rule quant-merge-prenex :args ((= (forall @t4 @t98) @t96))) % 0.35/0.62 (step @p99 :rule alpha_equiv :args (@t99 (@list @t83) @t75)) % 0.35/0.62 (step @p100 :rule refl :args (@t86)) % 0.35/0.62 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t100)) % 0.35/0.62 (step @p102 :rule quant-miniscope-or :args ((= @t98 @t100))) % 0.35/0.62 (step @p103 :rule trans :premises (@p102 @p101)) % 0.35/0.62 (step @p104 :rule symm :premises (@p103)) % 0.35/0.62 (step @p105 :rule cong :premises (@p104) :args ((forall @t4 (or @t86 @t101)))) % 0.35/0.62 (step @p106 :rule trans :premises (@p105 @p98)) % 0.35/0.62 (step @p107 :rule trans :premises (@p106 @p97)) % 0.35/0.62 (step @p108 :rule bool-impl-elim :args (@t17 @t101)) % 0.35/0.62 (step @p109 :rule cong :premises (@p108) :args ((forall @t4 (=> @t17 @t101)))) % 0.35/0.62 (step @p110 :rule trans :premises (@p109 @p107)) % 0.35/0.62 (step @p111 :rule bool-impl-elim :args (@t56 @t55)) % 0.35/0.62 (step @p112 :rule cong :premises (@p111) :args (@t57)) % 0.35/0.62 (step @p113 :rule refl :args (@t17)) % 0.35/0.62 (step @p114 :rule cong :premises (@p113 @p112) :args (@t58)) % 0.35/0.62 (step @p115 :rule cong :premises (@p114) :args (@t59)) % 0.35/0.62 (step @p116 :rule trans :premises (@p115 @p110)) % 0.35/0.62 (step @p117 :rule cong :premises (@p116) :args (@t60)) % 0.35/0.62 (step @p118 :rule eq_resolve :premises (@p43 @p117)) % 0.35/0.62 (step @p119 :rule skolemize :premises (@p118)) % 0.35/0.62 (step @p120 :rule bool-double-not-elim :args (@t102)) % 0.35/0.62 (step @p121 :rule refl :args (@t108)) % 0.35/0.62 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or @t108 (not @t107)))) % 0.35/0.62 (step @p123 :rule cnf_or_neg :args (@t108 0)) % 0.35/0.62 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 0.35/0.62 (step @p125 :rule reordering :premises (@p124) :args ((or @t102 @t108))) % 0.35/0.62 (step @p126 :rule chain_m_resolution :premises (@p125 @p119) :args (@t102 @t109 @t110)) % 0.35/0.62 (step @p127 :rule cnf_or_pos :args (@t115)) % 0.35/0.62 (step @p128 :rule reordering :premises (@p127) :args ((or @t107 @t114 (not @t115)))) % 0.35/0.62 (step @p129 :rule chain_m_resolution :premises (@p128 @p126 @p95) :args (@t114 @t116 (@list @t102 @t115))) % 0.35/0.62 (step @p130 :rule cnf_and_pos :args (@t114 2)) % 0.35/0.62 (step @p131 :rule reordering :premises (@p130) :args ((or @t111 @t117))) % 0.35/0.62 (step @p132 :rule chain_m_resolution :premises (@p131 @p129) :args (@t111 @t118 @t119)) % 0.35/0.62 (step @p133 :rule cnf_and_pos :args (@t114 1)) % 0.35/0.62 (step @p134 :rule reordering :premises (@p133) :args ((or @t112 @t117))) % 0.35/0.62 (step @p135 :rule chain_m_resolution :premises (@p134 @p129) :args (@t112 @t118 @t119)) % 0.35/0.62 (step @p136 :rule cnf_and_pos :args (@t114 0)) % 0.35/0.62 (step @p137 :rule reordering :premises (@p136) :args ((or @t113 @t117))) % 0.35/0.62 (step @p138 :rule chain_m_resolution :premises (@p137 @p129) :args (@t113 @t118 @t119)) % 0.35/0.62 (step @p139 :rule bool-double-not-elim :args (@t105)) % 0.35/0.62 (step @p140 :rule nary_cong :premises (@p121 @p139) :args ((or @t108 (not @t106)))) % 0.35/0.62 (step @p141 :rule cnf_or_neg :args (@t108 1)) % 0.35/0.62 (step @p142 :rule eq_resolve :premises (@p141 @p140)) % 0.35/0.62 (step @p143 :rule reordering :premises (@p142) :args ((or @t105 @t108))) % 0.35/0.62 (step @p144 :rule chain_m_resolution :premises (@p143 @p119) :args (@t105 @t109 @t110)) % 0.35/0.62 (step @p145 :rule cnf_or_pos :args (@t125)) % 0.35/0.62 (step @p146 :rule reordering :premises (@p145) :args ((or @t106 @t124 @t123 @t122 @t121 (not @t125)))) % 0.35/0.62 (step @p147 :rule chain_m_resolution :premises (@p146 @p144 @p138 @p135 @p132 @p91) :args (@t121 (@list false false false false false) (@list @t105 @t113 @t112 @t111 @t125))) % 0.35/0.62 (step @p148 :rule aci_norm :args ((= (or @t129 @t18) (or @t128 @t127 @t126 @t18)))) % 0.35/0.62 (step @p149 :rule refl :args (@t18)) % 0.35/0.62 (step @p150 :rule aci_norm :args ((= (or @t128 (or @t127 @t126)) @t129))) % 0.35/0.62 (step @p151 :rule bool-and-de-morgan :args (@t20 @t19 true)) % 0.35/0.62 (step @p152 :rule refl :args (@t128)) % 0.35/0.62 (step @p153 :rule nary_cong :premises (@p152 @p151) :args ((or @t128 (not (and @t20 @t19))))) % 0.35/0.62 (step @p154 :rule bool-and-de-morgan :args (@t21 @t20 (and @t19))) % 0.35/0.62 (step @p155 :rule trans :premises (@p154 @p153)) % 0.35/0.62 (step @p156 :rule trans :premises (@p155 @p150)) % 0.35/0.62 (step @p157 :rule nary_cong :premises (@p156 @p149) :args ((or (not @t22) @t18))) % 0.35/0.62 (step @p158 :rule trans :premises (@p157 @p148)) % 0.35/0.62 (step @p159 :rule bool-impl-elim :args (@t22 @t18)) % 0.35/0.62 (step @p160 :rule trans :premises (@p159 @p158)) % 0.35/0.62 (step @p161 :rule cong :premises (@p160) :args (@t23)) % 0.35/0.62 (step @p162 :rule eq_resolve :premises (@p8 @p161)) % 0.35/0.62 (step @p163 :rule instantiate :premises (@p162) :args (@t93)) % 0.35/0.62 (step @p164 :rule cnf_or_pos :args (@t132)) % 0.35/0.62 (step @p165 :rule reordering :premises (@p164) :args ((or @t124 @t123 @t122 @t131 (not @t132)))) % 0.35/0.62 (step @p166 :rule chain_m_resolution :premises (@p165 @p138 @p135 @p132 @p163) :args (@t131 (@list false false false false) (@list @t113 @t112 @t111 @t132))) % 0.35/0.62 (step @p167 :rule cnf_equiv_pos1 :args (@t131)) % 0.35/0.62 (step @p168 :rule reordering :premises (@p167) :args ((or @t107 @t130 (not @t131)))) % 0.35/0.62 (step @p169 :rule chain_m_resolution :premises (@p168 @p126 @p166) :args (@t130 @t116 (@list @t102 @t131))) % 0.35/0.62 (step @p170 :rule cnf_or_neg :args (@t108 2)) % 0.35/0.62 (step @p171 :rule chain_m_resolution :premises (@p170 @p119) :args ((not @t104) @t109 @t110)) % 0.35/0.62 (step @p172 :rule cnf_or_pos :args (@t135)) % 0.35/0.62 (step @p173 :rule reordering :premises (@p172) :args ((or @t104 @t134 @t133 @t136))) % 0.35/0.62 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p169 @p147) :args (@t136 (@list true false false) (@list @t104 @t130 @t121))) % 0.35/0.62 (assume-push @p181 @t137) % 0.35/0.62 (step @p176 :rule instantiate :premises (@p71) :args ((@list @t120 @t92 @t103))) % 0.35/0.62 (step-pop @p182 :rule scope :premises (@p176)) % 0.35/0.62 (step @p177 :rule process_scope :premises (@p182) :args (@t135)) % 0.35/0.62 (step @p179 :rule implies_elim :premises (@p177)) % 0.35/0.62 (step @p180 false :rule chain_m_resolution :premises (@p179 @p174 @p71) :args (false (@list true false) (@list @t135 @t137))) % 0.35/0.62 ) % 0.35/0.62 % SZS output end Proof % 0.35/0.62 % cvc5 exiting %------------------------------------------------------------------------------