%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU589^2 : 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 : n023.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 08:52:19 AM UTC 2026 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU589^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n023.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:43:13 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.49 %----Proving TH0 % 0.36/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.36/0.57 (declare-const tptp.dsetconstrI Bool) % 0.36/0.57 (define tptp.binintersect () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_2) (_ (_ tptp.in _let_2) _let_1)))))))) % 0.36/0.57 (define @t1 () (@var "Xy" $$unsorted)) % 0.36/0.57 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.36/0.57 (define @t3 () (_ @t2 @t1)) % 0.36/0.57 (define @t4 () (@list @t1)) % 0.36/0.57 (define @t5 () (lambda @t4 @t3)) % 0.36/0.57 (define @t6 () (@var "A" $$unsorted)) % 0.36/0.57 (define @t7 () (_ tptp.dsetconstr @t6)) % 0.36/0.57 (define @t8 () (_ @t7 @t5)) % 0.36/0.57 (define @t9 () (@var "Xx" $$unsorted)) % 0.36/0.57 (define @t10 () (_ tptp.in @t9)) % 0.36/0.57 (define @t11 () (_ @t10 @t8)) % 0.36/0.57 (define @t12 () (_ @t2 @t9)) % 0.36/0.57 (define @t13 () (=> @t12 @t11)) % 0.36/0.57 (define @t14 () (_ @t10 @t6)) % 0.36/0.57 (define @t15 () (@list @t6 @t2 @t9)) % 0.36/0.57 (define @t16 () (forall @t15 (=> @t14 @t13))) % 0.36/0.57 (define @t17 () (= tptp.dsetconstrI @t16)) % 0.36/0.57 (define @t18 () (@var "B" $$unsorted)) % 0.36/0.57 (define @t19 () (_ @t10 @t18)) % 0.36/0.57 (define @t20 () (=> @t19 (_ @t10 (_ (_ tptp.binintersect @t6) @t18)))) % 0.36/0.57 (define @t21 () (=> @t14 @t20)) % 0.36/0.57 (define @t22 () (@list @t6 @t18 @t9)) % 0.36/0.57 (define @t23 () (forall @t22 @t21)) % 0.36/0.57 (define @t24 () (=> tptp.dsetconstrI @t23)) % 0.36/0.57 (define @t25 () (not @t24)) % 0.36/0.57 (define @t26 () (lambda (@list @t9) @t19)) % 0.36/0.57 (define @t27 () (_ @t7 @t26)) % 0.36/0.57 (define @t28 () (lambda (@list @t6 @t18) @t27)) % 0.36/0.57 (define @t29 () (@var "BOUND_VARIABLE_7492" $$unsorted)) % 0.36/0.57 (define @t30 () (tptp.in @t29 @t18)) % 0.36/0.57 (define @t31 () (@list @t29)) % 0.36/0.57 (define @t32 () (lambda @t31 @t30)) % 0.36/0.57 (define @t33 () (tptp.dsetconstr @t6 @t32)) % 0.36/0.57 (define @t34 () (tptp.in @t9 @t33)) % 0.36/0.57 (define @t35 () (tptp.in @t9 @t18)) % 0.36/0.57 (define @t36 () (tptp.in @t9 @t6)) % 0.36/0.57 (define @t37 () (not @t36)) % 0.36/0.57 (define @t38 () (forall @t22 (or @t37 (not @t35) @t34))) % 0.36/0.57 (define @t39 () (_ @t2 @t1)) % 0.36/0.57 (define @t40 () (lambda @t4 @t39)) % 0.36/0.57 (define @t41 () (tptp.dsetconstr @t6 @t40)) % 0.36/0.57 (define @t42 () (tptp.in @t9 @t41)) % 0.36/0.57 (define @t43 () (_ @t2 @t9)) % 0.36/0.57 (define @t44 () (not @t43)) % 0.36/0.57 (define @t45 () (or @t37 @t44 @t42)) % 0.36/0.57 (define @t46 () (not @t12)) % 0.36/0.57 (define @t47 () (not @t14)) % 0.36/0.57 (define @t48 () (or @t47 @t46 @t11)) % 0.36/0.57 (define @t49 () (=> tptp.dsetconstrI @t38)) % 0.36/0.57 (define @t50 () (_ (_ tptp.in @t29) @t18)) % 0.36/0.57 (define @t51 () (lambda @t31 @t50)) % 0.36/0.57 (define @t52 () (_ @t7 @t51)) % 0.36/0.57 (define @t53 () (_ @t10 @t52)) % 0.36/0.57 (define @t54 () (not @t19)) % 0.36/0.57 (define @t55 () (or @t47 @t54 @t53)) % 0.36/0.57 (define @t56 () (=> @t19 @t53)) % 0.36/0.57 (define @t57 () (=> @t19 (_ @t10 @t27))) % 0.36/0.57 (define @t58 () (=> @t14 @t57)) % 0.36/0.57 (define @t59 () (lambda (@list @t18) @t27)) % 0.36/0.57 (define @t60 () (_ @t28 @t6)) % 0.36/0.57 (define @t61 () (=> @t19 (_ @t10 (_ @t60 @t18)))) % 0.36/0.57 (define @t62 () (=> @t14 @t61)) % 0.36/0.57 (define @t63 () (forall @t22 @t62)) % 0.36/0.57 (define @t64 () (=> tptp.dsetconstrI @t63)) % 0.36/0.57 (define @t65 () (@quantifiers_skolemize @t38 1)) % 0.36/0.57 (define @t66 () (tptp.in @t29 @t65)) % 0.36/0.57 (define @t67 () (lambda @t31 @t66)) % 0.36/0.57 (define @t68 () (@purify @t67)) % 0.36/0.57 (define @t69 () (@quantifiers_skolemize @t38 0)) % 0.36/0.57 (define @t70 () (@quantifiers_skolemize @t38 2)) % 0.36/0.57 (define @t71 () (tptp.in @t70 (tptp.dsetconstr @t69 @t68))) % 0.36/0.57 (define @t72 () (tptp.in @t70 @t65)) % 0.36/0.57 (define @t73 () (not @t72)) % 0.36/0.57 (define @t74 () (tptp.in @t70 @t69)) % 0.36/0.57 (define @t75 () (not @t74)) % 0.36/0.57 (define @t76 () (or @t75 @t73 @t71)) % 0.36/0.57 (define @t77 () (not @t76)) % 0.36/0.57 (define @t78 () (not @t38)) % 0.36/0.57 (define @t79 () (tptp.dsetconstr @t69 @t67)) % 0.36/0.57 (define @t80 () (tptp.in @t70 @t79)) % 0.36/0.57 (define @t81 () (or @t75 @t73 @t80)) % 0.36/0.57 (define @t82 () (not @t81)) % 0.36/0.57 (define @t83 () (@list true)) % 0.36/0.57 (define @t84 () (@list @t76)) % 0.36/0.57 (define @t85 () (_ @t68 @t29)) % 0.36/0.57 (define @t86 () (_ @t67 @t29)) % 0.36/0.57 (define @t87 () (= @t85 @t86)) % 0.36/0.57 (define @t88 () (forall @t31 @t87)) % 0.36/0.57 (define @t89 () (_ @t68 @t70)) % 0.36/0.57 (define @t90 () (not @t89)) % 0.36/0.57 (define @t91 () (or @t75 @t90 @t71)) % 0.36/0.57 (define @t92 () (= @t72 @t89)) % 0.36/0.57 (assume @p1 @t17) % 0.36/0.57 (assume @p2 @t25) % 0.36/0.57 (assume @p3 true) % 0.36/0.57 (step @p4 (= tptp.binintersect @t28) :rule refl :args (@t28)) % 0.36/0.57 (step @p5 :rule refl :args (@t38)) % 0.36/0.57 (step @p6 :rule lambda-elim :args ((= @t40 @t2))) % 0.36/0.57 (step @p7 :rule refl :args (@t6)) % 0.36/0.57 (step @p8 :rule cong :premises (@p7 @p6) :args (@t41)) % 0.36/0.57 (step @p9 :rule refl :args (@t9)) % 0.36/0.57 (step @p10 :rule cong :premises (@p9 @p8) :args (@t42)) % 0.36/0.57 (step @p11 :rule refl :args (@t44)) % 0.36/0.57 (step @p12 :rule refl :args (@t37)) % 0.36/0.57 (step @p13 :rule nary_cong :premises (@p12 @p11 @p10) :args (@t45)) % 0.36/0.57 (step @p14 :rule cong :premises (@p13) :args ((forall @t15 @t45))) % 0.36/0.57 (step @p15 :rule refl :args ((tptp.in @t9 @t8))) % 0.36/0.57 (step @p16 :rule refl :args ((tptp.dsetconstr @t6 @t5))) % 0.36/0.57 (step @p17 :rule refl :args (@t39)) % 0.36/0.57 (step @p18 :rule cong :premises (@p17) :args (@t40)) % 0.36/0.57 (step @p19 :rule refl :args (@t6)) % 0.36/0.57 (step @p20 :rule cong :premises (@p19 @p18) :args (@t41)) % 0.36/0.57 (step @p21 :rule trans :premises (@p20 @p16)) % 0.36/0.57 (step @p22 :rule refl :args (@t9)) % 0.36/0.57 (step @p23 :rule cong :premises (@p22 @p21) :args (@t42)) % 0.36/0.57 (step @p24 :rule trans :premises (@p23 @p15)) % 0.36/0.57 (step @p25 :rule refl :args (@t10)) % 0.36/0.57 (step @p26 :rule ho_cong :premises (@p25 @p21)) % 0.36/0.57 (step @p27 :rule cong :premises (@p26 @p24) :args ((= (_ @t10 @t41) @t42))) % 0.36/0.57 (step @p28 :rule symm :premises (@p27)) % 0.36/0.57 (step @p29 :rule refl :args (@t11)) % 0.36/0.57 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.36/0.57 (step @p31 :rule refl :args (@t7)) % 0.36/0.57 (step @p32 :rule ho_cong :premises (@p31 @p18)) % 0.36/0.57 (step @p33 :rule cong :premises (@p32 @p21) :args ((= (_ @t7 @t40) @t41))) % 0.36/0.57 (step @p34 :rule symm :premises (@p33)) % 0.36/0.57 (step @p35 :rule refl :args (@t8)) % 0.36/0.57 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.36/0.57 (step @p37 :rule refl :args (@t3)) % 0.36/0.57 (step @p38 :rule cong :premises (@p37 @p17) :args ((= @t3 @t39))) % 0.36/0.57 (step @p39 :rule symm :premises (@p38)) % 0.36/0.57 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.36/0.57 (step @p41 :rule cong :premises (@p40) :args (@t5)) % 0.36/0.57 (step @p42 :rule ho_cong :premises (@p31 @p41)) % 0.36/0.57 (step @p43 :rule trans :premises (@p42 @p36)) % 0.36/0.57 (step @p44 :rule ho_cong :premises (@p25 @p43)) % 0.36/0.57 (step @p45 :rule trans :premises (@p44 @p30)) % 0.36/0.57 (step @p46 :rule refl :args (@t43)) % 0.36/0.57 (step @p47 :rule refl :args (@t12)) % 0.36/0.57 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t12 @t43))) % 0.36/0.57 (step @p49 :rule symm :premises (@p48)) % 0.36/0.57 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.36/0.57 (step @p51 :rule cong :premises (@p50) :args (@t46)) % 0.36/0.57 (step @p52 :rule refl :args (@t36)) % 0.36/0.57 (step @p53 :rule refl :args (@t14)) % 0.36/0.57 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t14 @t36))) % 0.36/0.57 (step @p55 :rule symm :premises (@p54)) % 0.36/0.57 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.36/0.57 (step @p57 :rule cong :premises (@p56) :args (@t47)) % 0.36/0.57 (step @p58 :rule nary_cong :premises (@p57 @p51 @p45) :args (@t48)) % 0.36/0.57 (step @p59 :rule cong :premises (@p58) :args ((forall @t15 @t48))) % 0.36/0.57 (step @p60 :rule trans :premises (@p59 @p14)) % 0.36/0.57 (step @p61 :rule aci_norm :args ((= (or @t47 (or @t46 @t11)) @t48))) % 0.36/0.57 (step @p62 :rule bool-impl-elim :args (@t12 @t11)) % 0.36/0.57 (step @p63 :rule refl :args (@t47)) % 0.36/0.57 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t47 @t13))) % 0.36/0.57 (step @p65 :rule trans :premises (@p64 @p61)) % 0.36/0.57 (step @p66 :rule bool-impl-elim :args (@t14 @t13)) % 0.36/0.57 (step @p67 :rule trans :premises (@p66 @p65)) % 0.36/0.57 (step @p68 :rule cong :premises (@p67) :args (@t16)) % 0.36/0.57 (step @p69 :rule trans :premises (@p68 @p60)) % 0.36/0.57 (step @p70 :rule refl :args (tptp.dsetconstrI)) % 0.36/0.57 (step @p71 :rule cong :premises (@p70 @p69) :args (@t17)) % 0.36/0.57 (step @p72 :rule eq_resolve :premises (@p1 @p71)) % 0.36/0.57 (step @p73 :rule cong :premises (@p72 @p5) :args (@t49)) % 0.36/0.57 (step @p74 :rule cong :premises (@p73) :args ((not @t49))) % 0.36/0.57 (step @p75 :rule refl :args ((tptp.in @t9 @t52))) % 0.36/0.57 (step @p76 :rule refl :args ((tptp.dsetconstr @t6 @t51))) % 0.36/0.57 (step @p77 :rule refl :args (@t30)) % 0.36/0.57 (step @p78 :rule cong :premises (@p77) :args (@t32)) % 0.36/0.57 (step @p79 :rule cong :premises (@p19 @p78) :args (@t33)) % 0.36/0.57 (step @p80 :rule trans :premises (@p79 @p76)) % 0.36/0.57 (step @p81 :rule cong :premises (@p22 @p80) :args (@t34)) % 0.36/0.57 (step @p82 :rule trans :premises (@p81 @p75)) % 0.36/0.57 (step @p83 :rule ho_cong :premises (@p25 @p80)) % 0.36/0.57 (step @p84 :rule cong :premises (@p83 @p82) :args ((= (_ @t10 @t33) @t34))) % 0.36/0.57 (step @p85 :rule symm :premises (@p84)) % 0.36/0.57 (step @p86 :rule refl :args (@t53)) % 0.36/0.57 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.36/0.57 (step @p88 :rule ho_cong :premises (@p31 @p78)) % 0.36/0.57 (step @p89 :rule cong :premises (@p88 @p80) :args ((= (_ @t7 @t32) @t33))) % 0.36/0.57 (step @p90 :rule symm :premises (@p89)) % 0.36/0.57 (step @p91 :rule refl :args (@t52)) % 0.36/0.57 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.36/0.57 (step @p93 :rule refl :args (@t50)) % 0.36/0.57 (step @p94 :rule cong :premises (@p93 @p77) :args ((= @t50 @t30))) % 0.36/0.57 (step @p95 :rule symm :premises (@p94)) % 0.36/0.57 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.36/0.57 (step @p97 :rule cong :premises (@p96) :args (@t51)) % 0.36/0.57 (step @p98 :rule ho_cong :premises (@p31 @p97)) % 0.36/0.57 (step @p99 :rule trans :premises (@p98 @p92)) % 0.36/0.57 (step @p100 :rule ho_cong :premises (@p25 @p99)) % 0.36/0.57 (step @p101 :rule trans :premises (@p100 @p87)) % 0.36/0.57 (step @p102 :rule refl :args (@t35)) % 0.36/0.57 (step @p103 :rule refl :args (@t19)) % 0.36/0.57 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t19 @t35))) % 0.36/0.57 (step @p105 :rule symm :premises (@p104)) % 0.36/0.57 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.36/0.57 (step @p107 :rule cong :premises (@p106) :args (@t54)) % 0.36/0.57 (step @p108 :rule nary_cong :premises (@p57 @p107 @p101) :args (@t55)) % 0.36/0.57 (step @p109 :rule cong :premises (@p108) :args ((forall @t22 @t55))) % 0.36/0.57 (step @p110 :rule aci_norm :args ((= (or @t47 (or @t54 @t53)) @t55))) % 0.36/0.57 (step @p111 :rule bool-impl-elim :args (@t19 @t53)) % 0.36/0.57 (step @p112 :rule nary_cong :premises (@p63 @p111) :args ((or @t47 @t56))) % 0.36/0.57 (step @p113 :rule trans :premises (@p112 @p110)) % 0.36/0.57 (step @p114 :rule bool-impl-elim :args (@t14 @t56)) % 0.36/0.57 (step @p115 :rule trans :premises (@p114 @p113)) % 0.36/0.57 (step @p116 :rule cong :premises (@p115) :args ((forall @t22 (=> @t14 @t56)))) % 0.36/0.57 (step @p117 :rule trans :premises (@p116 @p109)) % 0.36/0.57 (step @p118 :rule alpha_equiv :args (@t26 (@list @t9) (@list @t29))) % 0.36/0.57 (step @p119 :rule ho_cong :premises (@p31 @p118)) % 0.36/0.57 (step @p120 :rule ho_cong :premises (@p25 @p119)) % 0.36/0.57 (step @p121 :rule cong :premises (@p103 @p120) :args (@t57)) % 0.36/0.57 (step @p122 :rule cong :premises (@p53 @p121) :args (@t58)) % 0.36/0.57 (step @p123 :rule cong :premises (@p122) :args ((forall @t22 @t58))) % 0.36/0.57 (step @p124 :rule trans :premises (@p123 @p117)) % 0.36/0.57 (step @p125 :rule beta-reduce :args ((= (_ @t59 @t18) @t27))) % 0.36/0.57 (step @p126 :rule refl :args (@t18)) % 0.36/0.57 (step @p127 :rule beta-reduce :args ((= @t60 @t59))) % 0.36/0.57 (step @p128 :rule ho_cong :premises (@p127 @p126)) % 0.36/0.57 (step @p129 :rule trans :premises (@p128 @p125)) % 0.36/0.57 (step @p130 :rule refl :args (@t10)) % 0.36/0.57 (step @p131 :rule ho_cong :premises (@p130 @p129)) % 0.36/0.57 (step @p132 :rule refl :args (@t19)) % 0.36/0.57 (step @p133 :rule cong :premises (@p132 @p131) :args (@t61)) % 0.36/0.57 (step @p134 :rule refl :args (@t14)) % 0.36/0.57 (step @p135 :rule cong :premises (@p134 @p133) :args (@t62)) % 0.36/0.57 (step @p136 :rule cong :premises (@p135) :args (@t63)) % 0.36/0.57 (step @p137 :rule trans :premises (@p136 @p124)) % 0.36/0.57 (step @p138 :rule cong :premises (@p70 @p137) :args (@t64)) % 0.36/0.57 (step @p139 :rule cong :premises (@p138) :args ((not @t64))) % 0.36/0.57 (step @p140 :rule ho_cong :premises (@p4 @p7)) % 0.36/0.57 (step @p141 :rule ho_cong :premises (@p140 @p126)) % 0.36/0.57 (step @p142 :rule ho_cong :premises (@p130 @p141)) % 0.36/0.57 (step @p143 :rule cong :premises (@p132 @p142) :args (@t20)) % 0.36/0.57 (step @p144 :rule cong :premises (@p134 @p143) :args (@t21)) % 0.36/0.57 (step @p145 :rule cong :premises (@p144) :args (@t23)) % 0.36/0.57 (step @p146 :rule cong :premises (@p70 @p145) :args (@t24)) % 0.36/0.57 (step @p147 :rule cong :premises (@p146) :args (@t25)) % 0.36/0.57 (step @p148 :rule trans :premises (@p147 @p139)) % 0.36/0.57 (step @p149 :rule trans :premises (@p148 @p74)) % 0.36/0.57 (step @p150 :rule eq_resolve :premises (@p2 @p149)) % 0.36/0.57 (step @p151 :rule not_implies_elim2 :premises (@p150)) % 0.36/0.57 (step @p152 :rule refl :args (@t77)) % 0.36/0.57 (step @p153 :rule bool-double-not-elim :args (@t38)) % 0.36/0.57 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((or (not @t78) @t77))) % 0.36/0.57 (step @p155 :rule eq-refl :args (@t67)) % 0.36/0.57 (step @p156 :rule skolem_intro :args (@t68)) % 0.36/0.57 (step @p157 :rule refl :args (@t67)) % 0.36/0.57 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t67 @t68))) % 0.36/0.57 (step @p159 :rule trans :premises (@p158 @p155)) % 0.36/0.57 (step @p160 :rule true_elim :premises (@p159)) % 0.36/0.57 (step @p161 :rule refl :args (@t69)) % 0.36/0.57 (step @p162 :rule cong :premises (@p161 @p160) :args (@t79)) % 0.36/0.57 (step @p163 :rule refl :args (@t70)) % 0.36/0.57 (step @p164 :rule cong :premises (@p163 @p162) :args (@t80)) % 0.36/0.57 (step @p165 :rule refl :args (@t73)) % 0.36/0.57 (step @p166 :rule refl :args (@t75)) % 0.36/0.57 (step @p167 :rule nary_cong :premises (@p166 @p165 @p164) :args (@t81)) % 0.36/0.57 (step @p168 :rule cong :premises (@p167) :args (@t82)) % 0.36/0.57 (step @p169 :rule refl :args (@t78)) % 0.36/0.57 (step @p170 :rule cong :premises (@p169 @p168) :args ((=> @t78 @t82))) % 0.36/0.57 (assume-push @p221 @t78) % 0.36/0.57 (step @p172 :rule skolemize :premises (@p151)) % 0.36/0.57 (step-pop @p222 :rule scope :premises (@p172)) % 0.36/0.57 (step @p173 :rule process_scope :premises (@p222) :args (@t82)) % 0.36/0.57 (step @p175 :rule eq_resolve :premises (@p173 @p170)) % 0.36/0.57 (step @p176 :rule implies_elim :premises (@p175)) % 0.36/0.57 (step @p177 :rule eq_resolve :premises (@p176 @p154)) % 0.36/0.57 (step @p178 :rule chain_m_resolution :premises (@p177 @p151) :args (@t77 @t83 (@list @t38))) % 0.36/0.57 (step @p179 :rule bool-double-not-elim :args (@t72)) % 0.36/0.57 (step @p180 :rule refl :args (@t76)) % 0.36/0.57 (step @p181 :rule nary_cong :premises (@p180 @p179) :args ((or @t76 (not @t73)))) % 0.36/0.57 (step @p182 :rule cnf_or_neg :args (@t76 1)) % 0.36/0.57 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.36/0.57 (step @p184 :rule reordering :premises (@p183) :args ((or @t72 @t76))) % 0.36/0.57 (step @p185 :rule chain_m_resolution :premises (@p184 @p178) :args (@t72 @t83 @t84)) % 0.36/0.57 (step @p186 :rule eq-symm :args (@t85 @t66)) % 0.36/0.57 (step @p187 :rule beta-reduce :args ((= @t86 @t66))) % 0.36/0.57 (step @p188 :rule refl :args (@t85)) % 0.36/0.57 (step @p189 :rule cong :premises (@p188 @p187) :args (@t87)) % 0.36/0.57 (step @p190 :rule trans :premises (@p189 @p186)) % 0.36/0.57 (step @p191 :rule cong :premises (@p190) :args (@t88)) % 0.36/0.57 (step @p192 :rule quant-unused-vars :args ((= (forall @t31 true) true))) % 0.36/0.57 (step @p193 :rule eq-refl :args (@t86)) % 0.36/0.57 (step @p194 :rule cong :premises (@p193) :args ((forall @t31 (= @t86 @t86)))) % 0.36/0.57 (step @p195 :rule trans :premises (@p194 @p192)) % 0.36/0.57 (step @p196 :rule refl :args (@t86)) % 0.36/0.57 (step @p197 :rule refl :args (@t29)) % 0.36/0.57 (step @p198 :rule ho_cong :premises (@p156 @p197)) % 0.36/0.57 (step @p199 :rule cong :premises (@p198 @p196) :args (@t87)) % 0.36/0.57 (step @p200 :rule cong :premises (@p199) :args (@t88)) % 0.36/0.57 (step @p201 :rule trans :premises (@p200 @p195)) % 0.36/0.57 (step @p202 :rule true_elim :premises (@p201)) % 0.36/0.57 (step @p203 :rule eq_resolve :premises (@p202 @p191)) % 0.36/0.57 (step @p204 :rule instantiate :premises (@p203) :args ((@list @t70))) % 0.36/0.57 (step @p205 :rule not_implies_elim1 :premises (@p150)) % 0.36/0.57 (step @p206 :rule instantiate :premises (@p205) :args ((@list @t69 @t68 @t70))) % 0.36/0.57 (step @p207 :rule cnf_or_neg :args (@t76 2)) % 0.36/0.57 (step @p208 :rule chain_m_resolution :premises (@p207 @p178) :args ((not @t71) @t83 @t84)) % 0.36/0.57 (step @p209 :rule bool-double-not-elim :args (@t74)) % 0.36/0.57 (step @p210 :rule nary_cong :premises (@p180 @p209) :args ((or @t76 (not @t75)))) % 0.36/0.57 (step @p211 :rule cnf_or_neg :args (@t76 0)) % 0.36/0.57 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 0.36/0.57 (step @p213 :rule reordering :premises (@p212) :args ((or @t74 @t76))) % 0.36/0.57 (step @p214 :rule chain_m_resolution :premises (@p213 @p178) :args (@t74 @t83 @t84)) % 0.36/0.57 (step @p215 :rule cnf_or_pos :args (@t91)) % 0.36/0.57 (step @p216 :rule reordering :premises (@p215) :args ((or @t75 @t71 @t90 (not @t91)))) % 0.36/0.57 (step @p217 :rule chain_m_resolution :premises (@p216 @p214 @p208 @p206) :args (@t90 (@list false true false) (@list @t74 @t71 @t91))) % 0.36/0.57 (step @p218 :rule cnf_equiv_pos1 :args (@t92)) % 0.36/0.57 (step @p219 :rule reordering :premises (@p218) :args ((or @t73 @t89 (not @t92)))) % 0.36/0.57 (step @p220 false :rule chain_m_resolution :premises (@p219 @p217 @p204 @p185) :args (false (@list true false false) (@list @t89 @t92 @t72))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------