%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU517^2 : TPTP v9.2.1. Released v3.7.0. % 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 08:52:01 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU517^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n007.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:39:27 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.40/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (declare-const tptp.setext Bool) % 0.40/0.61 (declare-const tptp.dsetconstrEL Bool) % 0.40/0.61 (declare-const tptp.dsetconstrI Bool) % 0.40/0.61 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.61 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.40/0.61 (define @t1 () (@var "Xy" $$unsorted)) % 0.40/0.61 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.40/0.61 (define @t3 () (_ @t2 @t1)) % 0.40/0.61 (define @t4 () (@list @t1)) % 0.40/0.61 (define @t5 () (lambda @t4 @t3)) % 0.40/0.61 (define @t6 () (@var "A" $$unsorted)) % 0.40/0.61 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.40/0.61 (define @t8 () (_ @t7 @t5)) % 0.40/0.61 (define @t9 () (@var "Xx" $$unsorted)) % 0.40/0.61 (define @t10 () (_ tptp.in @t9)) % 0.40/0.61 (define @t11 () (_ @t10 @t8)) % 0.40/0.61 (define @t12 () (_ @t2 @t9)) % 0.40/0.61 (define @t13 () (=> @t12 @t11)) % 0.40/0.61 (define @t14 () (_ @t10 @t6)) % 0.40/0.61 (define @t15 () (@list @t6 @t2 @t9)) % 0.40/0.61 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.40/0.61 (define @t17 () (= tptp.dsetconstrI @t16)) % 0.40/0.61 (define @t18 () (forall @t15 (=> @t11 @t14))) % 0.40/0.61 (define @t19 () (= tptp.dsetconstrEL @t18)) % 0.40/0.61 (define @t20 () (@var "B" $$unsorted)) % 0.40/0.61 (define @t21 () (= @t6 @t20)) % 0.40/0.61 (define @t22 () (_ @t10 @t20)) % 0.40/0.61 (define @t23 () (@list @t9)) % 0.40/0.61 (define @t24 () (forall @t23 (=> @t22 @t14))) % 0.40/0.61 (define @t25 () (=> @t24 @t21)) % 0.40/0.61 (define @t26 () (forall @t23 (=> @t14 @t22))) % 0.40/0.61 (define @t27 () (=> @t26 @t25)) % 0.40/0.61 (define @t28 () (@list @t6 @t20)) % 0.40/0.61 (define @t29 () (forall @t28 @t27)) % 0.40/0.61 (define @t30 () (= tptp.setext @t29)) % 0.40/0.61 (define @t31 () (lambda @t23 true)) % 0.40/0.61 (define @t32 () (= (_ @t7 @t31) @t6)) % 0.40/0.61 (define @t33 () (@list @t6)) % 0.40/0.61 (define @t34 () (forall @t33 @t32)) % 0.40/0.61 (define @t35 () (=> tptp.setext @t34)) % 0.40/0.61 (define @t36 () (=> tptp.dsetconstrEL @t35)) % 0.40/0.61 (define @t37 () (=> tptp.dsetconstrI @t36)) % 0.40/0.61 (define @t38 () (not @t37)) % 0.40/0.61 (define @t39 () (@var "BOUND_VARIABLE_7650" $$unsorted)) % 0.40/0.61 (define @t40 () (lambda (@list @t39) true)) % 0.40/0.61 (define @t41 () (tptp.dsetconstr @t6 @t40)) % 0.40/0.61 (define @t42 () (forall @t33 (= @t6 @t41))) % 0.40/0.61 (define @t43 () (tptp.in @t9 @t6)) % 0.40/0.61 (define @t44 () (tptp.in @t9 @t20)) % 0.40/0.61 (define @t45 () (forall @t23 (or (not @t44) @t43))) % 0.40/0.61 (define @t46 () (not @t45)) % 0.40/0.61 (define @t47 () (not @t43)) % 0.40/0.61 (define @t48 () (forall @t23 (or @t47 @t44))) % 0.40/0.61 (define @t49 () (not @t48)) % 0.40/0.61 (define @t50 () (=> @t45 @t21)) % 0.40/0.61 (define @t51 () (not @t22)) % 0.40/0.61 (define @t52 () (or @t51 @t14)) % 0.40/0.61 (define @t53 () (not @t14)) % 0.40/0.61 (define @t54 () (or @t53 @t22)) % 0.40/0.61 (define @t55 () (=> tptp.setext @t42)) % 0.40/0.61 (define @t56 () (_ @t2 @t1)) % 0.40/0.61 (define @t57 () (lambda @t4 @t56)) % 0.40/0.61 (define @t58 () (tptp.dsetconstr @t6 @t57)) % 0.40/0.61 (define @t59 () (tptp.in @t9 @t58)) % 0.40/0.61 (define @t60 () (not @t59)) % 0.40/0.61 (define @t61 () (or @t60 @t43)) % 0.40/0.61 (define @t62 () (not @t11)) % 0.40/0.61 (define @t63 () (or @t62 @t14)) % 0.40/0.61 (define @t64 () (=> tptp.dsetconstrEL @t55)) % 0.40/0.61 (define @t65 () (_ @t2 @t9)) % 0.40/0.61 (define @t66 () (not @t65)) % 0.40/0.61 (define @t67 () (or @t47 @t66 @t59)) % 0.40/0.61 (define @t68 () (not @t12)) % 0.40/0.61 (define @t69 () (or @t53 @t68 @t11)) % 0.40/0.61 (define @t70 () (=> tptp.dsetconstrI @t64)) % 0.40/0.61 (define @t71 () (_ @t7 @t40)) % 0.40/0.61 (define @t72 () (= @t6 @t71)) % 0.40/0.61 (define @t73 () (@purify @t40)) % 0.40/0.61 (define @t74 () (@quantifiers_skolemize @t42 0)) % 0.40/0.61 (define @t75 () (tptp.dsetconstr @t74 @t73)) % 0.40/0.61 (define @t76 () (tptp.in @t9 @t75)) % 0.40/0.61 (define @t77 () (tptp.in @t9 @t74)) % 0.40/0.61 (define @t78 () (forall @t23 (or (not @t77) @t76))) % 0.40/0.61 (define @t79 () (@quantifiers_skolemize @t78 0)) % 0.40/0.61 (define @t80 () (tptp.in @t79 @t75)) % 0.40/0.61 (define @t81 () (not (tptp.in @t79 @t74))) % 0.40/0.61 (define @t82 () (or @t81 @t80)) % 0.40/0.61 (define @t83 () (_ @t73 @t79)) % 0.40/0.61 (define @t84 () (not @t83)) % 0.40/0.61 (define @t85 () (or @t81 @t84 @t80)) % 0.40/0.61 (define @t86 () (tptp.in @t9 (tptp.dsetconstr @t6 @t2))) % 0.40/0.61 (define @t87 () (forall @t15 (or @t47 @t66 @t86))) % 0.40/0.61 (define @t88 () (@list false)) % 0.40/0.61 (define @t89 () (not @t82)) % 0.40/0.61 (define @t90 () (not @t78)) % 0.40/0.61 (define @t91 () (= @t74 @t75)) % 0.40/0.61 (define @t92 () (not @t91)) % 0.40/0.61 (define @t93 () (not @t42)) % 0.40/0.61 (define @t94 () (tptp.dsetconstr @t74 @t40)) % 0.40/0.61 (define @t95 () (= @t74 @t94)) % 0.40/0.61 (define @t96 () (not @t95)) % 0.40/0.61 (define @t97 () (@list true)) % 0.40/0.61 (define @t98 () (forall @t23 (or (not @t76) @t77))) % 0.40/0.61 (define @t99 () (not @t98)) % 0.40/0.61 (define @t100 () (or @t90 @t99 @t91)) % 0.40/0.61 (define @t101 () (@quantifiers_skolemize @t98 0)) % 0.40/0.61 (define @t102 () (or (not (tptp.in @t101 @t75)) (tptp.in @t101 @t74))) % 0.40/0.61 (define @t103 () (not @t102)) % 0.40/0.61 (define @t104 () (forall @t15 (or (not @t86) @t43))) % 0.40/0.61 (assume @p1 @t17) % 0.40/0.61 (assume @p2 @t19) % 0.40/0.61 (assume @p3 @t30) % 0.40/0.61 (assume @p4 @t38) % 0.40/0.61 (assume @p5 true) % 0.40/0.61 (step @p6 :rule refl :args (@t42)) % 0.40/0.61 (step @p7 :rule aci_norm :args ((= (or @t49 (or @t46 @t21)) (or @t49 @t46 @t21)))) % 0.40/0.61 (step @p8 :rule bool-impl-elim :args (@t45 @t21)) % 0.40/0.61 (step @p9 :rule refl :args (@t49)) % 0.40/0.61 (step @p10 :rule nary_cong :premises (@p9 @p8) :args ((or @t49 @t50))) % 0.40/0.61 (step @p11 :rule trans :premises (@p10 @p7)) % 0.40/0.61 (step @p12 :rule bool-impl-elim :args (@t48 @t50)) % 0.40/0.61 (step @p13 :rule trans :premises (@p12 @p11)) % 0.40/0.61 (step @p14 :rule cong :premises (@p13) :args ((forall @t28 (=> @t48 @t50)))) % 0.40/0.61 (step @p15 :rule refl :args (@t21)) % 0.40/0.61 (step @p16 :rule refl :args (@t43)) % 0.40/0.61 (step @p17 :rule refl :args (@t14)) % 0.40/0.61 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t14 @t43))) % 0.40/0.61 (step @p19 :rule symm :premises (@p18)) % 0.40/0.61 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.40/0.61 (step @p21 :rule refl :args (@t44)) % 0.40/0.61 (step @p22 :rule refl :args (@t22)) % 0.40/0.61 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t22 @t44))) % 0.40/0.61 (step @p24 :rule symm :premises (@p23)) % 0.40/0.61 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.40/0.61 (step @p26 :rule cong :premises (@p25) :args (@t51)) % 0.40/0.61 (step @p27 :rule nary_cong :premises (@p26 @p20) :args (@t52)) % 0.40/0.61 (step @p28 :rule cong :premises (@p27) :args ((forall @t23 @t52))) % 0.40/0.61 (step @p29 :rule bool-impl-elim :args (@t22 @t14)) % 0.40/0.61 (step @p30 :rule cong :premises (@p29) :args (@t24)) % 0.40/0.61 (step @p31 :rule trans :premises (@p30 @p28)) % 0.40/0.61 (step @p32 :rule cong :premises (@p31 @p15) :args (@t25)) % 0.40/0.61 (step @p33 :rule cong :premises (@p20) :args (@t53)) % 0.40/0.61 (step @p34 :rule nary_cong :premises (@p33 @p25) :args (@t54)) % 0.40/0.61 (step @p35 :rule cong :premises (@p34) :args ((forall @t23 @t54))) % 0.40/0.61 (step @p36 :rule bool-impl-elim :args (@t14 @t22)) % 0.40/0.61 (step @p37 :rule cong :premises (@p36) :args (@t26)) % 0.40/0.61 (step @p38 :rule trans :premises (@p37 @p35)) % 0.40/0.61 (step @p39 :rule cong :premises (@p38 @p32) :args (@t27)) % 0.40/0.61 (step @p40 :rule cong :premises (@p39) :args (@t29)) % 0.40/0.61 (step @p41 :rule trans :premises (@p40 @p14)) % 0.40/0.61 (step @p42 :rule refl :args (tptp.setext)) % 0.40/0.61 (step @p43 :rule cong :premises (@p42 @p41) :args (@t30)) % 0.40/0.61 (step @p44 :rule eq_resolve :premises (@p3 @p43)) % 0.40/0.61 (step @p45 :rule cong :premises (@p44 @p6) :args (@t55)) % 0.40/0.61 (step @p46 :rule refl :args (@t43)) % 0.40/0.61 (step @p47 :rule lambda-elim :args ((= @t57 @t2))) % 0.40/0.61 (step @p48 :rule refl :args (@t6)) % 0.40/0.61 (step @p49 :rule cong :premises (@p48 @p47) :args (@t58)) % 0.40/0.61 (step @p50 :rule refl :args (@t9)) % 0.40/0.61 (step @p51 :rule cong :premises (@p50 @p49) :args (@t59)) % 0.40/0.61 (step @p52 :rule cong :premises (@p51) :args (@t60)) % 0.40/0.61 (step @p53 :rule nary_cong :premises (@p52 @p46) :args (@t61)) % 0.40/0.61 (step @p54 :rule cong :premises (@p53) :args ((forall @t15 @t61))) % 0.40/0.61 (step @p55 :rule refl :args ((tptp.in @t9 @t8))) % 0.40/0.61 (step @p56 :rule refl :args ((tptp.dsetconstr @t6 @t5))) % 0.40/0.61 (step @p57 :rule refl :args (@t56)) % 0.40/0.61 (step @p58 :rule cong :premises (@p57) :args (@t57)) % 0.40/0.61 (step @p59 :rule refl :args (@t6)) % 0.40/0.61 (step @p60 :rule cong :premises (@p59 @p58) :args (@t58)) % 0.40/0.61 (step @p61 :rule trans :premises (@p60 @p56)) % 0.40/0.61 (step @p62 :rule refl :args (@t9)) % 0.40/0.61 (step @p63 :rule cong :premises (@p62 @p61) :args (@t59)) % 0.40/0.61 (step @p64 :rule trans :premises (@p63 @p55)) % 0.40/0.61 (step @p65 :rule refl :args (@t10)) % 0.40/0.61 (step @p66 :rule ho_cong :premises (@p65 @p61)) % 0.40/0.61 (step @p67 :rule cong :premises (@p66 @p64) :args ((= (_ @t10 @t58) @t59))) % 0.40/0.61 (step @p68 :rule symm :premises (@p67)) % 0.40/0.61 (step @p69 :rule refl :args (@t11)) % 0.40/0.61 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.40/0.61 (step @p71 :rule refl :args (@t7)) % 0.40/0.61 (step @p72 :rule ho_cong :premises (@p71 @p58)) % 0.40/0.61 (step @p73 :rule cong :premises (@p72 @p61) :args ((= (_ @t7 @t57) @t58))) % 0.40/0.61 (step @p74 :rule symm :premises (@p73)) % 0.40/0.61 (step @p75 :rule refl :args (@t8)) % 0.40/0.61 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.40/0.61 (step @p77 :rule refl :args (@t3)) % 0.40/0.61 (step @p78 :rule cong :premises (@p77 @p57) :args ((= @t3 @t56))) % 0.40/0.61 (step @p79 :rule symm :premises (@p78)) % 0.40/0.61 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.40/0.61 (step @p81 :rule cong :premises (@p80) :args (@t5)) % 0.40/0.61 (step @p82 :rule ho_cong :premises (@p71 @p81)) % 0.40/0.61 (step @p83 :rule trans :premises (@p82 @p76)) % 0.40/0.61 (step @p84 :rule ho_cong :premises (@p65 @p83)) % 0.40/0.61 (step @p85 :rule trans :premises (@p84 @p70)) % 0.40/0.61 (step @p86 :rule cong :premises (@p85) :args (@t62)) % 0.40/0.61 (step @p87 :rule nary_cong :premises (@p86 @p20) :args (@t63)) % 0.40/0.61 (step @p88 :rule cong :premises (@p87) :args ((forall @t15 @t63))) % 0.40/0.61 (step @p89 :rule trans :premises (@p88 @p54)) % 0.40/0.61 (step @p90 :rule bool-impl-elim :args (@t11 @t14)) % 0.40/0.61 (step @p91 :rule cong :premises (@p90) :args (@t18)) % 0.40/0.61 (step @p92 :rule trans :premises (@p91 @p89)) % 0.40/0.61 (step @p93 :rule refl :args (tptp.dsetconstrEL)) % 0.40/0.61 (step @p94 :rule cong :premises (@p93 @p92) :args (@t19)) % 0.40/0.61 (step @p95 :rule eq_resolve :premises (@p2 @p94)) % 0.40/0.61 (step @p96 :rule cong :premises (@p95 @p45) :args (@t64)) % 0.40/0.61 (step @p97 :rule refl :args (@t66)) % 0.40/0.61 (step @p98 :rule refl :args (@t47)) % 0.40/0.61 (step @p99 :rule nary_cong :premises (@p98 @p97 @p51) :args (@t67)) % 0.40/0.61 (step @p100 :rule cong :premises (@p99) :args ((forall @t15 @t67))) % 0.40/0.61 (step @p101 :rule refl :args (@t65)) % 0.40/0.61 (step @p102 :rule refl :args (@t12)) % 0.40/0.61 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t12 @t65))) % 0.40/0.61 (step @p104 :rule symm :premises (@p103)) % 0.40/0.61 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.40/0.61 (step @p106 :rule cong :premises (@p105) :args (@t68)) % 0.40/0.61 (step @p107 :rule nary_cong :premises (@p33 @p106 @p85) :args (@t69)) % 0.40/0.61 (step @p108 :rule cong :premises (@p107) :args ((forall @t15 @t69))) % 0.40/0.61 (step @p109 :rule trans :premises (@p108 @p100)) % 0.40/0.61 (step @p110 :rule aci_norm :args ((= (or @t53 (or @t68 @t11)) @t69))) % 0.40/0.61 (step @p111 :rule bool-impl-elim :args (@t12 @t11)) % 0.40/0.61 (step @p112 :rule refl :args (@t53)) % 0.40/0.61 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or @t53 @t13))) % 0.40/0.61 (step @p114 :rule trans :premises (@p113 @p110)) % 0.40/0.61 (step @p115 :rule bool-impl-elim :args (@t14 @t13)) % 0.40/0.61 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.61 (step @p117 :rule cong :premises (@p116) :args (@t16)) % 0.40/0.61 (step @p118 :rule trans :premises (@p117 @p109)) % 0.40/0.61 (step @p119 :rule refl :args (tptp.dsetconstrI)) % 0.40/0.61 (step @p120 :rule cong :premises (@p119 @p118) :args (@t17)) % 0.40/0.61 (step @p121 :rule eq_resolve :premises (@p1 @p120)) % 0.40/0.61 (step @p122 :rule cong :premises (@p121 @p96) :args (@t70)) % 0.40/0.61 (step @p123 :rule cong :premises (@p122) :args ((not @t70))) % 0.40/0.61 (step @p124 :rule refl :args (@t41)) % 0.40/0.61 (step @p125 :rule refl :args (@t40)) % 0.40/0.61 (step @p126 :rule cong :premises (@p59 @p125) :args (@t41)) % 0.40/0.61 (step @p127 :rule trans :premises (@p126 @p124)) % 0.40/0.61 (step @p128 :rule ho_cong :premises (@p71 @p125)) % 0.40/0.61 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t71 @t41))) % 0.40/0.61 (step @p130 :rule symm :premises (@p129)) % 0.40/0.61 (step @p131 :rule refl :args ((_ @t7 @t40))) % 0.40/0.61 (step @p132 :rule eq_resolve :premises (@p131 @p130)) % 0.40/0.61 (step @p133 :rule cong :premises (@p59 @p132) :args (@t72)) % 0.40/0.61 (step @p134 :rule cong :premises (@p133) :args ((forall @t33 @t72))) % 0.40/0.61 (step @p135 :rule eq-symm :args (@t71 @t6)) % 0.40/0.61 (step @p136 :rule symm :premises (@p125)) % 0.40/0.61 (step @p137 :rule alpha_equiv :args (@t31 (@list @t9) (@list @t39))) % 0.40/0.61 (step @p138 :rule trans :premises (@p137 @p136)) % 0.40/0.61 (step @p139 :rule refl :args (@t7)) % 0.40/0.61 (step @p140 :rule ho_cong :premises (@p139 @p138)) % 0.40/0.61 (step @p141 :rule cong :premises (@p140 @p48) :args (@t32)) % 0.40/0.61 (step @p142 :rule trans :premises (@p141 @p135)) % 0.40/0.61 (step @p143 :rule cong :premises (@p142) :args (@t34)) % 0.40/0.61 (step @p144 :rule trans :premises (@p143 @p134)) % 0.40/0.61 (step @p145 :rule cong :premises (@p42 @p144) :args (@t35)) % 0.40/0.61 (step @p146 :rule cong :premises (@p93 @p145) :args (@t36)) % 0.40/0.61 (step @p147 :rule cong :premises (@p119 @p146) :args (@t37)) % 0.40/0.61 (step @p148 :rule cong :premises (@p147) :args (@t38)) % 0.40/0.61 (step @p149 :rule trans :premises (@p148 @p123)) % 0.40/0.61 (step @p150 :rule eq_resolve :premises (@p4 @p149)) % 0.40/0.61 (step @p151 :rule not_implies_elim2 :premises (@p150)) % 0.40/0.61 (step @p152 :rule not_implies_elim1 :premises (@p151)) % 0.40/0.61 (step @p153 :rule not_implies_elim2 :premises (@p151)) % 0.40/0.61 (step @p154 :rule not_implies_elim1 :premises (@p153)) % 0.40/0.61 (step @p155 :rule instantiate :premises (@p154) :args ((@list @t74 @t75))) % 0.40/0.61 (step @p156 :rule not_implies_elim1 :premises (@p150)) % 0.40/0.61 (step @p157 :rule aci_norm :args ((= (or @t81 false @t80) @t82))) % 0.40/0.61 (step @p158 :rule refl :args (@t80)) % 0.40/0.61 (step @p159 :rule evaluate :args ((not true))) % 0.40/0.61 (step @p160 :rule beta-reduce :args ((= (_ @t40 @t79) true))) % 0.40/0.61 (step @p161 :rule refl :args (@t79)) % 0.40/0.61 (step @p162 :rule skolem_intro :args (@t73)) % 0.40/0.61 (step @p163 :rule ho_cong :premises (@p162 @p161)) % 0.40/0.61 (step @p164 :rule bool-eq-true :args (@t83)) % 0.40/0.61 (step @p165 :rule trans :premises (@p164 @p163 @p160)) % 0.40/0.61 (step @p166 :rule true_elim :premises (@p165)) % 0.40/0.61 (step @p167 :rule cong :premises (@p166) :args (@t84)) % 0.40/0.61 (step @p168 :rule trans :premises (@p167 @p159)) % 0.40/0.61 (step @p169 :rule refl :args (@t81)) % 0.40/0.61 (step @p170 :rule nary_cong :premises (@p169 @p168 @p158) :args (@t85)) % 0.40/0.61 (step @p171 :rule trans :premises (@p170 @p157)) % 0.40/0.61 (step @p172 :rule refl :args (@t87)) % 0.40/0.61 (step @p173 :rule cong :premises (@p172 @p171) :args ((=> @t87 @t85))) % 0.40/0.61 (assume-push @p235 @t87) % 0.40/0.61 (step @p175 :rule instantiate :premises (@p156) :args ((@list @t74 @t73 @t79))) % 0.40/0.61 (step-pop @p236 :rule scope :premises (@p175)) % 0.40/0.61 (step @p176 :rule process_scope :premises (@p236) :args (@t85)) % 0.40/0.61 (step @p178 :rule eq_resolve :premises (@p176 @p173)) % 0.40/0.61 (step @p179 :rule implies_elim :premises (@p178)) % 0.40/0.61 (step @p180 :rule chain_m_resolution :premises (@p179 @p156) :args (@t82 @t88 (@list @t87))) % 0.40/0.61 (step @p181 :rule refl :args (@t89)) % 0.40/0.61 (step @p182 :rule bool-double-not-elim :args (@t78)) % 0.40/0.61 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or (not @t90) @t89))) % 0.40/0.61 (assume-push @p237 @t90) % 0.40/0.61 (step @p185 :rule skolemize :premises (@p237)) % 0.40/0.61 (step-pop @p238 :rule scope :premises (@p185)) % 0.40/0.61 (step @p186 :rule process_scope :premises (@p238) :args (@t89)) % 0.40/0.61 (step @p188 :rule implies_elim :premises (@p186)) % 0.40/0.61 (step @p189 :rule eq_resolve :premises (@p188 @p183)) % 0.40/0.61 (step @p190 :rule chain_m_resolution :premises (@p189 @p180) :args (@t78 @t88 (@list @t82))) % 0.40/0.61 (step @p191 :rule not_implies_elim2 :premises (@p153)) % 0.40/0.61 (step @p192 :rule refl :args (@t92)) % 0.40/0.61 (step @p193 :rule bool-double-not-elim :args (@t42)) % 0.40/0.61 (step @p194 :rule nary_cong :premises (@p193 @p192) :args ((or (not @t93) @t92))) % 0.40/0.61 (step @p195 :rule eq-refl :args (@t40)) % 0.40/0.61 (step @p196 :rule refl :args (@t40)) % 0.40/0.61 (step @p197 :rule cong :premises (@p196 @p136) :args ((= @t40 @t40))) % 0.40/0.61 (step @p198 :rule trans :premises (@p197 @p195)) % 0.40/0.61 (step @p199 :rule cong :premises (@p196 @p162) :args ((= @t40 @t73))) % 0.40/0.61 (step @p200 :rule trans :premises (@p199 @p198)) % 0.40/0.61 (step @p201 :rule true_elim :premises (@p200)) % 0.40/0.61 (step @p202 :rule refl :args (@t74)) % 0.40/0.61 (step @p203 :rule cong :premises (@p202 @p201) :args (@t94)) % 0.40/0.61 (step @p204 :rule cong :premises (@p202 @p203) :args (@t95)) % 0.40/0.61 (step @p205 :rule cong :premises (@p204) :args (@t96)) % 0.40/0.61 (step @p206 :rule refl :args (@t93)) % 0.40/0.61 (step @p207 :rule cong :premises (@p206 @p205) :args ((=> @t93 @t96))) % 0.40/0.61 (assume-push @p239 @t93) % 0.40/0.61 (step @p209 :rule skolemize :premises (@p191)) % 0.40/0.61 (step-pop @p240 :rule scope :premises (@p209)) % 0.40/0.61 (step @p210 :rule process_scope :premises (@p240) :args (@t96)) % 0.40/0.61 (step @p212 :rule eq_resolve :premises (@p210 @p207)) % 0.40/0.61 (step @p213 :rule implies_elim :premises (@p212)) % 0.40/0.61 (step @p214 :rule eq_resolve :premises (@p213 @p194)) % 0.40/0.61 (step @p215 :rule chain_m_resolution :premises (@p214 @p191) :args (@t92 @t97 (@list @t42))) % 0.40/0.61 (step @p216 :rule cnf_or_pos :args (@t100)) % 0.40/0.61 (step @p217 :rule reordering :premises (@p216) :args ((or @t91 @t90 @t99 (not @t100)))) % 0.40/0.61 (step @p218 :rule chain_m_resolution :premises (@p217 @p215 @p190 @p155) :args (@t99 (@list true false false) (@list @t91 @t78 @t100))) % 0.40/0.61 (step @p219 :rule refl :args (@t103)) % 0.40/0.61 (step @p220 :rule bool-double-not-elim :args (@t98)) % 0.40/0.61 (step @p221 :rule nary_cong :premises (@p220 @p219) :args ((or (not @t99) @t103))) % 0.40/0.61 (assume-push @p241 @t99) % 0.40/0.61 (step @p223 :rule skolemize :premises (@p241)) % 0.40/0.61 (step-pop @p242 :rule scope :premises (@p223)) % 0.40/0.61 (step @p224 :rule process_scope :premises (@p242) :args (@t103)) % 0.40/0.61 (step @p226 :rule implies_elim :premises (@p224)) % 0.40/0.61 (step @p227 :rule eq_resolve :premises (@p226 @p221)) % 0.40/0.61 (step @p228 :rule chain_m_resolution :premises (@p227 @p218) :args (@t103 @t97 (@list @t98))) % 0.40/0.61 (assume-push @p243 @t104) % 0.40/0.61 (step @p230 :rule instantiate :premises (@p152) :args ((@list @t74 @t73 @t101))) % 0.40/0.61 (step-pop @p244 :rule scope :premises (@p230)) % 0.40/0.61 (step @p231 :rule process_scope :premises (@p244) :args (@t102)) % 0.40/0.62 (step @p233 :rule implies_elim :premises (@p231)) % 0.40/0.62 (step @p234 false :rule chain_m_resolution :premises (@p233 @p228 @p152) :args (false (@list true false) (@list @t102 @t104))) % 0.40/0.62 ) % 0.40/0.62 % SZS output end Proof % 0.40/0.62 % cvc5 exiting %------------------------------------------------------------------------------