%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM394+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 : n018.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 08:39:18 AM UTC 2026 % Result : Theorem 0.40s 0.60s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM394+1 : TPTP v9.2.1. Released v3.2.0. % 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 : n018.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 11:16:05 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.60 % SZS status Theorem % 0.40/0.60 % SZS output start Proof % 0.40/0.60 ( % 0.40/0.60 (declare-sort $$unsorted 0) % 0.40/0.60 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.epsilon_transitive (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.empty_set $$unsorted) % 0.40/0.60 (declare-const tptp.function (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.epsilon_connected (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.relation (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.ordinal_subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.ordinal (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.relation_non_empty (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.60 (define @t2 () (@var "B" $$unsorted)) % 0.40/0.60 (define @t3 () (tptp.in @t2 @t1)) % 0.40/0.60 (define @t4 () (not @t3)) % 0.40/0.60 (define @t5 () (tptp.in @t1 @t2)) % 0.40/0.60 (define @t6 () (@list @t1 @t2)) % 0.40/0.60 (define @t7 () (tptp.function @t1)) % 0.40/0.60 (define @t8 () (tptp.empty @t1)) % 0.40/0.60 (define @t9 () (@list @t1)) % 0.40/0.60 (define @t10 () (tptp.epsilon_connected @t1)) % 0.40/0.60 (define @t11 () (tptp.epsilon_transitive @t1)) % 0.40/0.60 (define @t12 () (and @t11 @t10)) % 0.40/0.60 (define @t13 () (tptp.ordinal @t1)) % 0.40/0.60 (define @t14 () (forall @t9 (=> @t13 @t12))) % 0.40/0.60 (define @t15 () (tptp.relation @t1)) % 0.40/0.60 (define @t16 () (and @t15 @t7 (tptp.one_to_one @t1))) % 0.40/0.60 (define @t17 () (and @t15 @t8 @t7)) % 0.40/0.60 (define @t18 () (tptp.ordinal_subset @t2 @t1)) % 0.40/0.60 (define @t19 () (tptp.ordinal_subset @t1 @t2)) % 0.40/0.60 (define @t20 () (or @t19 @t18)) % 0.40/0.60 (define @t21 () (tptp.ordinal @t2)) % 0.40/0.60 (define @t22 () (and @t13 @t21)) % 0.40/0.60 (define @t23 () (forall @t6 (=> @t22 @t20))) % 0.40/0.60 (define @t24 () (tptp.subset @t2 @t1)) % 0.40/0.60 (define @t25 () (@list @t2)) % 0.40/0.60 (define @t26 () (forall @t25 (=> @t3 @t24))) % 0.40/0.60 (define @t27 () (= @t11 @t26)) % 0.40/0.60 (define @t28 () (forall @t9 @t27)) % 0.40/0.60 (define @t29 () (tptp.relation tptp.empty_set)) % 0.40/0.60 (define @t30 () (tptp.empty tptp.empty_set)) % 0.40/0.60 (define @t31 () (not @t8)) % 0.40/0.60 (define @t32 () (tptp.relation_empty_yielding @t1)) % 0.40/0.60 (define @t33 () (tptp.subset @t1 @t2)) % 0.40/0.60 (define @t34 () (= @t19 @t33)) % 0.40/0.60 (define @t35 () (forall @t6 (=> @t22 @t34))) % 0.40/0.60 (define @t36 () (tptp.element @t1 @t2)) % 0.40/0.60 (define @t37 () (= @t1 @t2)) % 0.40/0.60 (define @t38 () (not @t37)) % 0.40/0.60 (define @t39 () (not @t5)) % 0.40/0.60 (define @t40 () (not (and @t39 @t38 @t4))) % 0.40/0.60 (define @t41 () (forall @t25 (=> @t21 @t40))) % 0.40/0.60 (define @t42 () (=> @t13 @t41)) % 0.40/0.60 (define @t43 () (forall @t9 @t42)) % 0.40/0.60 (define @t44 () (or @t19 @t3)) % 0.40/0.60 (define @t45 () (forall @t25 (=> @t21 @t44))) % 0.40/0.60 (define @t46 () (=> @t13 @t45)) % 0.40/0.60 (define @t47 () (forall @t9 @t46)) % 0.40/0.60 (define @t48 () (not @t47)) % 0.40/0.60 (define @t49 () (tptp.empty @t2)) % 0.40/0.60 (define @t50 () (@var "C" $$unsorted)) % 0.40/0.60 (define @t51 () (tptp.element @t2 (tptp.powerset @t50))) % 0.40/0.60 (define @t52 () (@list @t1 @t2 @t50)) % 0.40/0.60 (define @t53 () (@var "BOUND_VARIABLE_7710" $$unsorted)) % 0.40/0.60 (define @t54 () (tptp.in @t53 @t1)) % 0.40/0.60 (define @t55 () (tptp.ordinal_subset @t1 @t53)) % 0.40/0.60 (define @t56 () (not (tptp.ordinal @t53))) % 0.40/0.60 (define @t57 () (not @t13)) % 0.40/0.60 (define @t58 () (or @t57 @t56 @t55 @t54)) % 0.40/0.60 (define @t59 () (@list @t1 @t53)) % 0.40/0.60 (define @t60 () (forall @t59 @t58)) % 0.40/0.60 (define @t61 () (@quantifiers_skolemize @t60 1)) % 0.40/0.60 (define @t62 () (@list @t61)) % 0.40/0.60 (define @t63 () (or @t56 @t55 @t54)) % 0.40/0.60 (define @t64 () (or @t57 @t63)) % 0.40/0.60 (define @t65 () (forall @t59 @t64)) % 0.40/0.60 (define @t66 () (@list @t53)) % 0.40/0.60 (define @t67 () (forall @t66 @t64)) % 0.40/0.60 (define @t68 () (forall @t66 @t63)) % 0.40/0.60 (define @t69 () (@list @t2)) % 0.40/0.60 (define @t70 () (or @t57 @t68)) % 0.40/0.60 (define @t71 () (not @t21)) % 0.40/0.60 (define @t72 () (or @t71 @t19 @t3)) % 0.40/0.60 (define @t73 () (forall @t25 @t72)) % 0.40/0.60 (define @t74 () (tptp.ordinal @t61)) % 0.40/0.60 (define @t75 () (@quantifiers_skolemize @t60 0)) % 0.40/0.60 (define @t76 () (tptp.in @t61 @t75)) % 0.40/0.60 (define @t77 () (tptp.ordinal_subset @t75 @t61)) % 0.40/0.60 (define @t78 () (not @t74)) % 0.40/0.60 (define @t79 () (tptp.ordinal @t75)) % 0.40/0.60 (define @t80 () (not @t79)) % 0.40/0.60 (define @t81 () (or @t80 @t78 @t77 @t76)) % 0.40/0.60 (define @t82 () (@list true)) % 0.40/0.60 (define @t83 () (@list @t81)) % 0.40/0.60 (define @t84 () (tptp.epsilon_transitive @t61)) % 0.40/0.60 (define @t85 () (and @t84 (tptp.epsilon_connected @t61))) % 0.40/0.60 (define @t86 () (or @t78 @t85)) % 0.40/0.60 (define @t87 () (@list false false)) % 0.40/0.60 (define @t88 () (@list false)) % 0.40/0.60 (define @t89 () (forall @t25 (or (not (tptp.in @t2 @t61)) (tptp.subset @t2 @t61)))) % 0.40/0.60 (define @t90 () (= @t84 @t89)) % 0.40/0.60 (define @t91 () (@var "BOUND_VARIABLE_7690" $$unsorted)) % 0.40/0.60 (define @t92 () (tptp.in @t91 @t1)) % 0.40/0.60 (define @t93 () (= @t1 @t91)) % 0.40/0.60 (define @t94 () (tptp.in @t1 @t91)) % 0.40/0.60 (define @t95 () (not (tptp.ordinal @t91))) % 0.40/0.60 (define @t96 () (or @t57 @t95 @t94 @t93 @t92)) % 0.40/0.60 (define @t97 () (or @t95 @t94 @t93 @t92)) % 0.40/0.60 (define @t98 () (or @t57 @t97)) % 0.40/0.60 (define @t99 () (@list @t1 @t91)) % 0.40/0.60 (define @t100 () (forall @t99 @t98)) % 0.40/0.60 (define @t101 () (@list @t91)) % 0.40/0.60 (define @t102 () (forall @t101 @t98)) % 0.40/0.60 (define @t103 () (forall @t101 @t97)) % 0.40/0.60 (define @t104 () (or @t57 @t103)) % 0.40/0.60 (define @t105 () (or @t71 @t5 @t37 @t3)) % 0.40/0.60 (define @t106 () (forall @t25 @t105)) % 0.40/0.60 (define @t107 () (not @t4)) % 0.40/0.60 (define @t108 () (not @t38)) % 0.40/0.60 (define @t109 () (not @t39)) % 0.40/0.60 (define @t110 () (or @t109 @t108 @t107)) % 0.40/0.60 (define @t111 () (tptp.in @t75 @t61)) % 0.40/0.60 (define @t112 () (or @t78 @t80 @t76 (= @t61 @t75) @t111)) % 0.40/0.60 (define @t113 () (forall @t99 @t96)) % 0.40/0.60 (define @t114 () (= @t75 @t61)) % 0.40/0.60 (define @t115 () (or @t78 @t80 @t76 @t114 @t111)) % 0.40/0.60 (define @t116 () (or @t57 @t71)) % 0.40/0.60 (define @t117 () (not @t22)) % 0.40/0.60 (define @t118 () (@list @t75 @t61)) % 0.40/0.60 (define @t119 () (not @t77)) % 0.40/0.60 (define @t120 () (tptp.ordinal_subset @t61 @t75)) % 0.40/0.60 (define @t121 () (or @t80 @t78 @t77 @t120)) % 0.40/0.60 (define @t122 () (not @t114)) % 0.40/0.60 (define @t123 () (not @t120)) % 0.40/0.60 (define @t124 () (and @t120 @t114 @t119)) % 0.40/0.60 (define @t125 () (@list true false)) % 0.40/0.60 (define @t126 () (tptp.subset @t75 @t61)) % 0.40/0.60 (define @t127 () (= @t77 @t126)) % 0.40/0.60 (define @t128 () (or @t80 @t78 @t127)) % 0.40/0.60 (define @t129 () (not @t126)) % 0.40/0.60 (define @t130 () (not @t111)) % 0.40/0.60 (define @t131 () (or @t130 @t126)) % 0.40/0.60 (define @t132 () (not @t131)) % 0.40/0.60 (assume @p1 (forall @t6 (=> @t5 @t4))) % 0.40/0.60 (assume @p2 (forall @t9 (=> @t8 @t7))) % 0.40/0.60 (assume @p3 @t14) % 0.40/0.60 (assume @p4 (forall @t9 (=> @t8 @t15))) % 0.40/0.60 (assume @p5 (forall @t9 (=> @t17 @t16))) % 0.40/0.60 (assume @p6 (forall @t9 (=> @t12 @t13))) % 0.40/0.60 (assume @p7 @t23) % 0.40/0.60 (assume @p8 @t28) % 0.40/0.60 (assume @p9 (forall @t9 (exists @t25 (tptp.element @t2 @t1)))) % 0.40/0.60 (assume @p10 (and @t30 @t29 (tptp.relation_empty_yielding tptp.empty_set))) % 0.40/0.60 (assume @p11 @t30) % 0.40/0.60 (assume @p12 (and @t30 @t29)) % 0.40/0.60 (assume @p13 (exists @t9 (and @t15 @t7))) % 0.40/0.60 (assume @p14 (exists @t9 (and @t11 @t10 @t13))) % 0.40/0.60 (assume @p15 (exists @t9 (and @t8 @t15))) % 0.40/0.60 (assume @p16 (exists @t9 @t8)) % 0.40/0.60 (assume @p17 (exists @t9 @t17)) % 0.40/0.60 (assume @p18 (exists @t9 (and @t31 @t15))) % 0.40/0.60 (assume @p19 (exists @t9 @t31)) % 0.40/0.60 (assume @p20 (exists @t9 @t16)) % 0.40/0.60 (assume @p21 (exists @t9 (and @t15 @t32))) % 0.40/0.60 (assume @p22 (exists @t9 (and @t15 @t32 @t7))) % 0.40/0.60 (assume @p23 (exists @t9 (and @t15 (tptp.relation_non_empty @t1) @t7))) % 0.40/0.60 (assume @p24 @t35) % 0.40/0.60 (assume @p25 (forall @t6 (=> @t22 (tptp.ordinal_subset @t1 @t1)))) % 0.40/0.60 (assume @p26 (forall @t6 (tptp.subset @t1 @t1))) % 0.40/0.60 (assume @p27 (forall @t6 (=> @t5 @t36))) % 0.40/0.60 (assume @p28 @t43) % 0.40/0.60 (assume @p29 @t48) % 0.40/0.60 (assume @p30 (forall @t6 (=> @t36 (or @t49 @t5)))) % 0.40/0.60 (assume @p31 (forall @t6 (= (tptp.element @t1 (tptp.powerset @t2)) @t33))) % 0.40/0.60 (assume @p32 (forall @t52 (=> (and @t5 @t51) (tptp.element @t1 @t50)))) % 0.40/0.60 (assume @p33 (forall @t52 (not (and @t5 @t51 (tptp.empty @t50))))) % 0.40/0.60 (assume @p34 (forall @t9 (=> @t8 (= @t1 tptp.empty_set)))) % 0.40/0.60 (assume @p35 (forall @t6 (not (and @t5 @t49)))) % 0.40/0.60 (assume @p36 (forall @t6 (not (and @t8 @t38 @t49)))) % 0.40/0.60 (assume @p37 true) % 0.40/0.60 (step @p38 :rule bool-impl-elim :args (@t3 @t24)) % 0.40/0.60 (step @p39 :rule cong :premises (@p38) :args (@t26)) % 0.40/0.60 (step @p40 :rule refl :args (@t11)) % 0.40/0.60 (step @p41 :rule cong :premises (@p40 @p39) :args (@t27)) % 0.40/0.60 (step @p42 :rule cong :premises (@p41) :args (@t28)) % 0.40/0.60 (step @p43 :rule eq_resolve :premises (@p8 @p42)) % 0.40/0.60 (step @p44 :rule instantiate :premises (@p43) :args (@t62)) % 0.40/0.60 (step @p45 :rule bool-impl-elim :args (@t13 @t12)) % 0.40/0.60 (step @p46 :rule cong :premises (@p45) :args (@t14)) % 0.40/0.60 (step @p47 :rule eq_resolve :premises (@p3 @p46)) % 0.40/0.60 (step @p48 :rule instantiate :premises (@p47) :args (@t62)) % 0.40/0.60 (step @p49 :rule aci_norm :args ((= @t64 @t58))) % 0.40/0.60 (step @p50 :rule cong :premises (@p49) :args (@t65)) % 0.40/0.60 (step @p51 :rule quant-merge-prenex :args ((= (forall @t9 @t67) @t65))) % 0.40/0.60 (step @p52 :rule alpha_equiv :args (@t68 (@list @t53) @t69)) % 0.40/0.60 (step @p53 :rule refl :args (@t57)) % 0.40/0.60 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t70)) % 0.40/0.60 (step @p55 :rule quant-miniscope-or :args ((= @t67 @t70))) % 0.40/0.60 (step @p56 :rule trans :premises (@p55 @p54)) % 0.40/0.60 (step @p57 :rule symm :premises (@p56)) % 0.40/0.60 (step @p58 :rule cong :premises (@p57) :args ((forall @t9 (or @t57 @t73)))) % 0.40/0.60 (step @p59 :rule trans :premises (@p58 @p51)) % 0.40/0.60 (step @p60 :rule trans :premises (@p59 @p50)) % 0.40/0.60 (step @p61 :rule bool-impl-elim :args (@t13 @t73)) % 0.40/0.60 (step @p62 :rule cong :premises (@p61) :args ((forall @t9 (=> @t13 @t73)))) % 0.40/0.60 (step @p63 :rule trans :premises (@p62 @p60)) % 0.40/0.60 (step @p64 :rule aci_norm :args ((= (or @t71 @t44) @t72))) % 0.40/0.60 (step @p65 :rule bool-impl-elim :args (@t21 @t44)) % 0.40/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.40/0.60 (step @p67 :rule cong :premises (@p66) :args (@t45)) % 0.40/0.60 (step @p68 :rule refl :args (@t13)) % 0.40/0.60 (step @p69 :rule cong :premises (@p68 @p67) :args (@t46)) % 0.40/0.60 (step @p70 :rule cong :premises (@p69) :args (@t47)) % 0.40/0.60 (step @p71 :rule trans :premises (@p70 @p63)) % 0.40/0.60 (step @p72 :rule cong :premises (@p71) :args (@t48)) % 0.40/0.60 (step @p73 :rule eq_resolve :premises (@p29 @p72)) % 0.40/0.60 (step @p74 :rule skolemize :premises (@p73)) % 0.40/0.60 (step @p75 :rule bool-double-not-elim :args (@t74)) % 0.40/0.60 (step @p76 :rule refl :args (@t81)) % 0.40/0.60 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or @t81 (not @t78)))) % 0.40/0.60 (step @p78 :rule cnf_or_neg :args (@t81 1)) % 0.40/0.60 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 0.40/0.60 (step @p80 :rule reordering :premises (@p79) :args ((or @t74 @t81))) % 0.40/0.60 (step @p81 :rule chain_m_resolution :premises (@p80 @p74) :args (@t74 @t82 @t83)) % 0.40/0.60 (step @p82 :rule cnf_or_pos :args (@t86)) % 0.40/0.60 (step @p83 :rule reordering :premises (@p82) :args ((or @t78 @t85 (not @t86)))) % 0.40/0.60 (step @p84 :rule chain_m_resolution :premises (@p83 @p81 @p48) :args (@t85 @t87 (@list @t74 @t86))) % 0.40/0.60 (step @p85 :rule cnf_and_pos :args (@t85 0)) % 0.40/0.60 (step @p86 :rule reordering :premises (@p85) :args ((or @t84 (not @t85)))) % 0.40/0.60 (step @p87 :rule chain_m_resolution :premises (@p86 @p84) :args (@t84 @t88 (@list @t85))) % 0.40/0.60 (step @p88 :rule cnf_equiv_pos1 :args (@t90)) % 0.40/0.60 (step @p89 :rule reordering :premises (@p88) :args ((or (not @t84) @t89 (not @t90)))) % 0.40/0.60 (step @p90 :rule chain_m_resolution :premises (@p89 @p87 @p44) :args (@t89 @t87 (@list @t84 @t90))) % 0.40/0.60 (step @p91 :rule aci_norm :args ((= @t98 @t96))) % 0.40/0.60 (step @p92 :rule cong :premises (@p91) :args (@t100)) % 0.40/0.60 (step @p93 :rule quant-merge-prenex :args ((= (forall @t9 @t102) @t100))) % 0.40/0.60 (step @p94 :rule alpha_equiv :args (@t103 (@list @t91) @t69)) % 0.40/0.60 (step @p95 :rule nary_cong :premises (@p53 @p94) :args (@t104)) % 0.40/0.60 (step @p96 :rule quant-miniscope-or :args ((= @t102 @t104))) % 0.40/0.60 (step @p97 :rule trans :premises (@p96 @p95)) % 0.40/0.60 (step @p98 :rule symm :premises (@p97)) % 0.40/0.60 (step @p99 :rule cong :premises (@p98) :args ((forall @t9 (or @t57 @t106)))) % 0.40/0.60 (step @p100 :rule trans :premises (@p99 @p93)) % 0.40/0.60 (step @p101 :rule trans :premises (@p100 @p92)) % 0.40/0.60 (step @p102 :rule bool-impl-elim :args (@t13 @t106)) % 0.40/0.60 (step @p103 :rule cong :premises (@p102) :args ((forall @t9 (=> @t13 @t106)))) % 0.40/0.60 (step @p104 :rule trans :premises (@p103 @p101)) % 0.40/0.60 (step @p105 :rule aci_norm :args ((= (or @t71 (or @t5 @t37 @t3)) @t105))) % 0.40/0.60 (step @p106 :rule bool-double-not-elim :args (@t3)) % 0.40/0.60 (step @p107 :rule bool-double-not-elim :args (@t37)) % 0.40/0.60 (step @p108 :rule bool-double-not-elim :args (@t5)) % 0.40/0.60 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106) :args (@t110)) % 0.40/0.60 (step @p110 :rule aci_norm :args ((= (or @t109 (or @t108 @t107)) @t110))) % 0.40/0.60 (step @p111 :rule trans :premises (@p110 @p109)) % 0.40/0.60 (step @p112 :rule bool-and-de-morgan :args (@t38 @t4 true)) % 0.40/0.60 (step @p113 :rule refl :args (@t109)) % 0.40/0.60 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or @t109 (not (and @t38 @t4))))) % 0.40/0.60 (step @p115 :rule bool-and-de-morgan :args (@t39 @t38 (and @t4))) % 0.40/0.60 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.60 (step @p117 :rule trans :premises (@p116 @p111)) % 0.40/0.60 (step @p118 :rule refl :args (@t71)) % 0.40/0.60 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or @t71 @t40))) % 0.40/0.60 (step @p120 :rule trans :premises (@p119 @p105)) % 0.40/0.60 (step @p121 :rule bool-impl-elim :args (@t21 @t40)) % 0.40/0.60 (step @p122 :rule trans :premises (@p121 @p120)) % 0.40/0.60 (step @p123 :rule cong :premises (@p122) :args (@t41)) % 0.40/0.60 (step @p124 :rule cong :premises (@p68 @p123) :args (@t42)) % 0.40/0.60 (step @p125 :rule cong :premises (@p124) :args (@t43)) % 0.40/0.60 (step @p126 :rule trans :premises (@p125 @p104)) % 0.40/0.60 (step @p127 :rule eq_resolve :premises (@p28 @p126)) % 0.40/0.60 (step @p128 :rule refl :args (@t111)) % 0.40/0.60 (step @p129 :rule eq-symm :args (@t61 @t75)) % 0.40/0.60 (step @p130 :rule refl :args (@t76)) % 0.40/0.60 (step @p131 :rule refl :args (@t80)) % 0.40/0.60 (step @p132 :rule refl :args (@t78)) % 0.40/0.60 (step @p133 :rule nary_cong :premises (@p132 @p131 @p130 @p129 @p128) :args (@t112)) % 0.40/0.60 (step @p134 :rule refl :args (@t113)) % 0.40/0.60 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t113 @t112))) % 0.40/0.60 (assume-push @p225 @t113) % 0.40/0.60 (step @p137 :rule instantiate :premises (@p127) :args ((@list @t61 @t75))) % 0.40/0.60 (step-pop @p226 :rule scope :premises (@p137)) % 0.40/0.60 (step @p138 :rule process_scope :premises (@p226) :args (@t112)) % 0.40/0.60 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 0.40/0.60 (step @p141 :rule implies_elim :premises (@p140)) % 0.40/0.60 (step @p142 :rule chain_m_resolution :premises (@p141 @p127) :args (@t115 @t88 (@list @t113))) % 0.40/0.60 (step @p143 :rule aci_norm :args ((= (or @t116 @t20) (or @t57 @t71 @t19 @t18)))) % 0.40/0.60 (step @p144 :rule refl :args (@t20)) % 0.40/0.60 (step @p145 :rule bool-and-de-morgan :args (@t13 @t21 true)) % 0.40/0.60 (step @p146 :rule nary_cong :premises (@p145 @p144) :args ((or @t117 @t20))) % 0.40/0.60 (step @p147 :rule trans :premises (@p146 @p143)) % 0.40/0.60 (step @p148 :rule bool-impl-elim :args (@t22 @t20)) % 0.40/0.60 (step @p149 :rule trans :premises (@p148 @p147)) % 0.40/0.60 (step @p150 :rule cong :premises (@p149) :args (@t23)) % 0.40/0.60 (step @p151 :rule eq_resolve :premises (@p7 @p150)) % 0.40/0.60 (step @p152 :rule instantiate :premises (@p151) :args (@t118)) % 0.40/0.60 (step @p153 :rule cnf_or_neg :args (@t81 2)) % 0.40/0.60 (step @p154 :rule chain_m_resolution :premises (@p153 @p74) :args (@t119 @t82 @t83)) % 0.40/0.60 (step @p155 :rule bool-double-not-elim :args (@t79)) % 0.40/0.60 (step @p156 :rule nary_cong :premises (@p76 @p155) :args ((or @t81 (not @t80)))) % 0.40/0.60 (step @p157 :rule cnf_or_neg :args (@t81 0)) % 0.40/0.60 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.40/0.60 (step @p159 :rule reordering :premises (@p158) :args ((or @t79 @t81))) % 0.40/0.60 (step @p160 :rule chain_m_resolution :premises (@p159 @p74) :args (@t79 @t82 @t83)) % 0.40/0.60 (step @p161 :rule cnf_or_pos :args (@t121)) % 0.40/0.60 (step @p162 :rule reordering :premises (@p161) :args ((or @t80 @t78 @t77 @t120 (not @t121)))) % 0.40/0.60 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p81 @p154 @p152) :args (@t120 (@list false false true false) (@list @t79 @t74 @t77 @t121))) % 0.40/0.60 (step @p164 :rule refl :args (@t122)) % 0.40/0.60 (step @p165 :rule refl :args (@t123)) % 0.40/0.60 (step @p166 :rule bool-double-not-elim :args (@t77)) % 0.40/0.60 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164) :args ((or (not @t119) @t123 @t122))) % 0.40/0.60 (assume-push @p227 @t120) % 0.40/0.60 (assume-push @p228 @t114) % 0.40/0.60 (assume-push @p229 @t119) % 0.40/0.60 (step @p171 :rule evaluate :args ((= false true))) % 0.40/0.60 (step @p172 :rule true_intro :premises (@p163)) % 0.40/0.60 (step @p173 :rule symm :premises (@p228)) % 0.40/0.60 (step @p174 :rule cong :premises (@p228 @p173) :args (@t77)) % 0.40/0.60 (step @p175 :rule false_intro :premises (@p154)) % 0.40/0.60 (step @p176 :rule symm :premises (@p175)) % 0.40/0.60 (step @p177 :rule trans :premises (@p176 @p174 @p172)) % 0.40/0.60 (step @p178 false :rule eq_resolve :premises (@p177 @p171)) % 0.40/0.60 (step-pop @p230 :rule scope :premises (@p178)) % 0.40/0.60 (step-pop @p231 :rule scope :premises (@p230)) % 0.40/0.60 (step-pop @p232 :rule scope :premises (@p231)) % 0.40/0.60 (step @p179 :rule process_scope :premises (@p232) :args (false)) % 0.40/0.60 (assume-push @p233 @t119) % 0.40/0.60 (assume-push @p234 @t120) % 0.40/0.60 (assume-push @p235 @t114) % 0.40/0.60 (step @p186 :rule and_intro :premises (@p163 @p235 @p154)) % 0.40/0.60 (step-pop @p236 :rule scope :premises (@p186)) % 0.40/0.60 (step-pop @p237 :rule scope :premises (@p236)) % 0.40/0.60 (step-pop @p238 :rule scope :premises (@p237)) % 0.40/0.60 (step @p187 :rule process_scope :premises (@p238) :args (@t124)) % 0.40/0.60 (step @p191 :rule implies_elim :premises (@p187)) % 0.40/0.60 (step @p192 :rule resolution :premises (@p191 @p179) :args (true @t124)) % 0.40/0.60 (step @p193 :rule not_and :premises (@p192)) % 0.40/0.60 (step @p194 :rule eq_resolve :premises (@p193 @p167)) % 0.40/0.60 (step @p195 :rule chain_m_resolution :premises (@p194 @p154 @p163) :args (@t122 @t125 (@list @t77 @t120))) % 0.40/0.60 (step @p196 :rule cnf_or_neg :args (@t81 3)) % 0.40/0.60 (step @p197 :rule chain_m_resolution :premises (@p196 @p74) :args ((not @t76) @t82 @t83)) % 0.40/0.60 (step @p198 :rule cnf_or_pos :args (@t115)) % 0.40/0.60 (step @p199 :rule reordering :premises (@p198) :args ((or @t80 @t78 @t76 @t111 @t114 (not @t115)))) % 0.40/0.60 (step @p200 :rule chain_m_resolution :premises (@p199 @p160 @p81 @p197 @p195 @p142) :args (@t111 (@list false false true true false) (@list @t79 @t74 @t76 @t114 @t115))) % 0.40/0.60 (step @p201 :rule aci_norm :args ((= (or @t116 @t34) (or @t57 @t71 @t34)))) % 0.40/0.60 (step @p202 :rule refl :args (@t34)) % 0.40/0.60 (step @p203 :rule nary_cong :premises (@p145 @p202) :args ((or @t117 @t34))) % 0.40/0.60 (step @p204 :rule trans :premises (@p203 @p201)) % 0.40/0.60 (step @p205 :rule bool-impl-elim :args (@t22 @t34)) % 0.40/0.60 (step @p206 :rule trans :premises (@p205 @p204)) % 0.40/0.60 (step @p207 :rule cong :premises (@p206) :args (@t35)) % 0.40/0.60 (step @p208 :rule eq_resolve :premises (@p24 @p207)) % 0.40/0.60 (step @p209 :rule instantiate :premises (@p208) :args (@t118)) % 0.40/0.60 (step @p210 :rule cnf_or_pos :args (@t128)) % 0.40/0.60 (step @p211 :rule reordering :premises (@p210) :args ((or @t80 @t78 @t127 (not @t128)))) % 0.40/0.60 (step @p212 :rule chain_m_resolution :premises (@p211 @p160 @p81 @p209) :args (@t127 (@list false false false) (@list @t79 @t74 @t128))) % 0.40/0.60 (step @p213 :rule cnf_equiv_pos2 :args (@t127)) % 0.40/0.60 (step @p214 :rule reordering :premises (@p213) :args ((or @t77 @t129 (not @t127)))) % 0.40/0.60 (step @p215 :rule chain_m_resolution :premises (@p214 @p154 @p212) :args (@t129 @t125 (@list @t77 @t127))) % 0.40/0.60 (step @p216 :rule cnf_or_pos :args (@t131)) % 0.40/0.60 (step @p217 :rule reordering :premises (@p216) :args ((or @t126 @t130 @t132))) % 0.40/0.60 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p200) :args (@t132 @t125 (@list @t126 @t111))) % 0.40/0.60 (assume-push @p239 @t89) % 0.40/0.60 (step @p220 :rule instantiate :premises (@p90) :args ((@list @t75))) % 0.40/0.60 (step-pop @p240 :rule scope :premises (@p220)) % 0.40/0.60 (step @p221 :rule process_scope :premises (@p240) :args (@t131)) % 0.40/0.60 (step @p223 :rule implies_elim :premises (@p221)) % 0.40/0.60 (step @p224 false :rule chain_m_resolution :premises (@p223 @p218 @p90) :args (false @t125 (@list @t131 @t89))) % 0.40/0.60 ) % 0.40/0.60 % SZS output end Proof % 0.40/0.60 % cvc5 exiting %------------------------------------------------------------------------------