%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU646^2 : 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 : n008.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 08:52:33 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU646^2 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n008.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 17:44:33 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (declare-const tptp.emptyset $$unsorted) % 0.39/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.kfst (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.cartprodmempair1 Bool) % 0.39/0.57 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (declare-const tptp.kfstpairEq Bool) % 0.39/0.57 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 0.39/0.57 (define @t1 () (@var "Xy" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.39/0.57 (define @t3 () (_ (_ tptp.kpair @t2) @t1)) % 0.39/0.57 (define @t4 () (@var "Xu" $$unsorted)) % 0.39/0.57 (define @t5 () (= @t4 @t3)) % 0.39/0.57 (define @t6 () (@var "B" $$unsorted)) % 0.39/0.57 (define @t7 () (_ (_ tptp.in @t1) @t6)) % 0.39/0.57 (define @t8 () (and @t7 @t5)) % 0.39/0.57 (define @t9 () (@list @t1)) % 0.39/0.57 (define @t10 () (exists @t9 @t8)) % 0.39/0.57 (define @t11 () (@var "A" $$unsorted)) % 0.39/0.57 (define @t12 () (_ (_ tptp.in @t2) @t11)) % 0.39/0.57 (define @t13 () (and @t12 @t10)) % 0.39/0.57 (define @t14 () (@list @t2)) % 0.39/0.57 (define @t15 () (exists @t14 @t13)) % 0.39/0.57 (define @t16 () (_ (_ tptp.cartprod @t11) @t6)) % 0.39/0.57 (define @t17 () (_ tptp.in @t4)) % 0.39/0.57 (define @t18 () (_ @t17 @t16)) % 0.39/0.57 (define @t19 () (=> @t18 @t15)) % 0.39/0.57 (define @t20 () (@list @t11 @t6 @t4)) % 0.39/0.57 (define @t21 () (forall @t20 @t19)) % 0.39/0.57 (define @t22 () (= tptp.cartprodmempair1 @t21)) % 0.39/0.57 (define @t23 () (= (_ tptp.kfst @t3) @t2)) % 0.39/0.57 (define @t24 () (@list @t2 @t1)) % 0.39/0.57 (define @t25 () (forall @t24 @t23)) % 0.39/0.57 (define @t26 () (= tptp.kfstpairEq @t25)) % 0.39/0.57 (define @t27 () (_ tptp.kfst @t4)) % 0.39/0.57 (define @t28 () (_ (_ tptp.in @t27) @t11)) % 0.39/0.57 (define @t29 () (forall @t20 (=> @t18 @t28))) % 0.39/0.57 (define @t30 () (=> tptp.kfstpairEq @t29)) % 0.39/0.57 (define @t31 () (=> tptp.cartprodmempair1 @t30)) % 0.39/0.57 (define @t32 () (not @t31)) % 0.39/0.57 (define @t33 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.39/0.57 (define @t34 () (_ tptp.setadjoin @t2)) % 0.39/0.57 (define @t35 () (_ @t34 @t33)) % 0.39/0.57 (define @t36 () (_ (_ tptp.setadjoin @t35) tptp.emptyset)) % 0.39/0.57 (define @t37 () (_ @t34 tptp.emptyset)) % 0.39/0.57 (define @t38 () (_ (_ tptp.setadjoin @t37) @t36)) % 0.39/0.57 (define @t39 () (lambda @t24 @t38)) % 0.39/0.57 (define @t40 () (tptp.kfst @t4)) % 0.39/0.57 (define @t41 () (tptp.in @t40 @t11)) % 0.39/0.57 (define @t42 () (tptp.cartprod @t11 @t6)) % 0.39/0.57 (define @t43 () (tptp.in @t4 @t42)) % 0.39/0.57 (define @t44 () (not @t43)) % 0.39/0.57 (define @t45 () (forall @t20 (or @t44 @t41))) % 0.39/0.57 (define @t46 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.39/0.57 (define @t47 () (tptp.setadjoin @t2 @t46)) % 0.39/0.57 (define @t48 () (tptp.setadjoin @t47 tptp.emptyset)) % 0.39/0.57 (define @t49 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.39/0.57 (define @t50 () (tptp.setadjoin @t49 @t48)) % 0.39/0.57 (define @t51 () (tptp.kfst @t50)) % 0.39/0.57 (define @t52 () (_ tptp.kfst @t38)) % 0.39/0.57 (define @t53 () (= @t2 @t52)) % 0.39/0.57 (define @t54 () (lambda @t9 @t38)) % 0.39/0.57 (define @t55 () (_ @t39 @t2)) % 0.39/0.57 (define @t56 () (_ @t55 @t1)) % 0.39/0.57 (define @t57 () (= (_ tptp.kfst @t56) @t2)) % 0.39/0.57 (define @t58 () (forall @t24 @t57)) % 0.39/0.57 (define @t59 () (=> tptp.kfstpairEq @t45)) % 0.39/0.57 (define @t60 () (@var "BOUND_VARIABLE_7527" $$unsorted)) % 0.39/0.57 (define @t61 () (tptp.setadjoin @t49 (tptp.setadjoin (tptp.setadjoin @t2 (tptp.setadjoin @t60 tptp.emptyset)) tptp.emptyset))) % 0.39/0.57 (define @t62 () (not (= @t4 @t61))) % 0.39/0.57 (define @t63 () (not (tptp.in @t60 @t6))) % 0.39/0.57 (define @t64 () (tptp.in @t2 @t11)) % 0.39/0.57 (define @t65 () (not @t64)) % 0.39/0.57 (define @t66 () (or @t65 @t63 @t62)) % 0.39/0.57 (define @t67 () (@list @t2 @t60)) % 0.39/0.57 (define @t68 () (not (forall @t67 @t66))) % 0.39/0.57 (define @t69 () (not @t18)) % 0.39/0.57 (define @t70 () (or @t69 @t68)) % 0.39/0.57 (define @t71 () (or @t63 @t62)) % 0.39/0.57 (define @t72 () (or @t65 @t71)) % 0.39/0.57 (define @t73 () (forall @t67 @t72)) % 0.39/0.57 (define @t74 () (@list @t60)) % 0.39/0.57 (define @t75 () (forall @t74 @t72)) % 0.39/0.57 (define @t76 () (forall @t74 @t71)) % 0.39/0.57 (define @t77 () (or @t65 @t76)) % 0.39/0.57 (define @t78 () (tptp.in @t1 @t6)) % 0.39/0.57 (define @t79 () (not @t78)) % 0.39/0.57 (define @t80 () (forall @t9 (or @t79 (not (= @t4 @t50))))) % 0.39/0.57 (define @t81 () (not @t12)) % 0.39/0.57 (define @t82 () (or @t81 @t80)) % 0.39/0.57 (define @t83 () (not @t80)) % 0.39/0.57 (define @t84 () (and @t12 @t83)) % 0.39/0.57 (define @t85 () (forall @t14 (not @t84))) % 0.39/0.57 (define @t86 () (not @t85)) % 0.39/0.57 (define @t87 () (not (= @t50 @t4))) % 0.39/0.57 (define @t88 () (or @t79 @t87)) % 0.39/0.57 (define @t89 () (= @t38 @t4)) % 0.39/0.57 (define @t90 () (not @t89)) % 0.39/0.57 (define @t91 () (not @t7)) % 0.39/0.57 (define @t92 () (or @t91 @t90)) % 0.39/0.57 (define @t93 () (and @t7 @t89)) % 0.39/0.57 (define @t94 () (forall @t9 (not @t93))) % 0.39/0.57 (define @t95 () (not @t94)) % 0.39/0.57 (define @t96 () (= @t4 @t56)) % 0.39/0.57 (define @t97 () (and @t7 @t96)) % 0.39/0.57 (define @t98 () (exists @t9 @t97)) % 0.39/0.57 (define @t99 () (and @t12 @t98)) % 0.39/0.57 (define @t100 () (exists @t14 @t99)) % 0.39/0.57 (define @t101 () (=> @t18 @t100)) % 0.39/0.57 (define @t102 () (forall @t20 @t101)) % 0.39/0.57 (define @t103 () (=> tptp.cartprodmempair1 @t59)) % 0.39/0.57 (define @t104 () (or @t69 @t28)) % 0.39/0.57 (define @t105 () (@quantifiers_skolemize @t45 2)) % 0.39/0.57 (define @t106 () (not (= @t105 @t61))) % 0.39/0.57 (define @t107 () (@quantifiers_skolemize @t45 1)) % 0.39/0.57 (define @t108 () (not (tptp.in @t60 @t107))) % 0.39/0.57 (define @t109 () (@quantifiers_skolemize @t45 0)) % 0.39/0.57 (define @t110 () (not (tptp.in @t2 @t109))) % 0.39/0.57 (define @t111 () (or @t110 @t108 @t106)) % 0.39/0.57 (define @t112 () (forall @t67 @t111)) % 0.39/0.57 (define @t113 () (not @t112)) % 0.39/0.57 (define @t114 () (tptp.in @t105 (tptp.cartprod @t109 @t107))) % 0.39/0.57 (define @t115 () (not @t114)) % 0.39/0.57 (define @t116 () (or @t115 @t113)) % 0.39/0.57 (define @t117 () (forall @t20 (or @t44 @t68))) % 0.39/0.57 (define @t118 () (forall @t67 (or @t110 @t108 (not (= @t61 @t105))))) % 0.39/0.57 (define @t119 () (not @t118)) % 0.39/0.57 (define @t120 () (or @t115 @t119)) % 0.39/0.57 (define @t121 () (tptp.kfst @t105)) % 0.39/0.57 (define @t122 () (tptp.in @t121 @t109)) % 0.39/0.57 (define @t123 () (or @t115 @t122)) % 0.39/0.57 (define @t124 () (@list true)) % 0.39/0.57 (define @t125 () (@list @t123)) % 0.39/0.57 (define @t126 () (@quantifiers_skolemize @t118 1)) % 0.39/0.57 (define @t127 () (@quantifiers_skolemize @t118 0)) % 0.39/0.57 (define @t128 () (tptp.setadjoin (tptp.setadjoin @t127 tptp.emptyset) (tptp.setadjoin (tptp.setadjoin @t127 (tptp.setadjoin @t126 tptp.emptyset)) tptp.emptyset))) % 0.39/0.57 (define @t129 () (= @t105 @t128)) % 0.39/0.57 (define @t130 () (not @t129)) % 0.39/0.57 (define @t131 () (not (tptp.in @t126 @t107))) % 0.39/0.57 (define @t132 () (tptp.in @t127 @t109)) % 0.39/0.57 (define @t133 () (not @t132)) % 0.39/0.57 (define @t134 () (or @t133 @t131 @t130)) % 0.39/0.57 (define @t135 () (not @t134)) % 0.39/0.57 (define @t136 () (not (= @t128 @t105))) % 0.39/0.57 (define @t137 () (or @t133 @t131 @t136)) % 0.39/0.57 (define @t138 () (not @t137)) % 0.39/0.57 (define @t139 () (@list @t134)) % 0.39/0.57 (assume @p1 @t22) % 0.39/0.57 (assume @p2 @t26) % 0.39/0.57 (assume @p3 @t32) % 0.39/0.57 (assume @p4 true) % 0.39/0.57 (step @p5 (= tptp.kpair @t39) :rule refl :args (@t39)) % 0.39/0.57 (step @p6 :rule evaluate :args ((= false true))) % 0.39/0.57 (step @p7 :rule refl :args (@t45)) % 0.39/0.57 (step @p8 :rule refl :args ((tptp.kfst @t38))) % 0.39/0.57 (step @p9 :rule refl :args ((tptp.setadjoin @t37 @t36))) % 0.39/0.57 (step @p10 :rule refl :args ((tptp.setadjoin @t35 tptp.emptyset))) % 0.39/0.57 (step @p11 :rule refl :args (tptp.emptyset)) % 0.39/0.57 (step @p12 :rule refl :args ((tptp.setadjoin @t2 @t33))) % 0.39/0.57 (step @p13 :rule refl :args (@t46)) % 0.39/0.57 (step @p14 :rule refl :args (@t2)) % 0.39/0.57 (step @p15 :rule cong :premises (@p14 @p13) :args (@t47)) % 0.39/0.57 (step @p16 :rule trans :premises (@p15 @p12)) % 0.39/0.57 (step @p17 :rule cong :premises (@p16 @p11) :args (@t48)) % 0.39/0.57 (step @p18 :rule trans :premises (@p17 @p10)) % 0.39/0.57 (step @p19 :rule refl :args (@t49)) % 0.39/0.57 (step @p20 :rule cong :premises (@p19 @p18) :args (@t50)) % 0.39/0.57 (step @p21 :rule trans :premises (@p20 @p9)) % 0.39/0.57 (step @p22 :rule cong :premises (@p21) :args (@t51)) % 0.39/0.57 (step @p23 :rule trans :premises (@p22 @p8)) % 0.39/0.57 (step @p24 :rule refl :args (tptp.kfst)) % 0.39/0.57 (step @p25 :rule ho_cong :premises (@p24 @p21)) % 0.39/0.57 (step @p26 :rule cong :premises (@p25 @p23) :args ((= (_ tptp.kfst @t50) @t51))) % 0.39/0.57 (step @p27 :rule symm :premises (@p26)) % 0.39/0.57 (step @p28 :rule refl :args (@t52)) % 0.39/0.57 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.39/0.57 (step @p30 :rule refl :args (tptp.setadjoin)) % 0.39/0.57 (step @p31 :rule ho_cong :premises (@p30 @p19)) % 0.39/0.57 (step @p32 :rule ho_cong :premises (@p31 @p18)) % 0.39/0.57 (step @p33 :rule cong :premises (@p32 @p21) :args ((= (_ (_ tptp.setadjoin @t49) @t48) @t50))) % 0.39/0.57 (step @p34 :rule symm :premises (@p33)) % 0.39/0.57 (step @p35 :rule refl :args (@t38)) % 0.39/0.57 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.39/0.57 (step @p37 :rule ho_cong :premises (@p30 @p16)) % 0.39/0.57 (step @p38 :rule ho_cong :premises (@p37 @p11)) % 0.39/0.57 (step @p39 :rule cong :premises (@p38 @p18) :args ((= (_ (_ tptp.setadjoin @t47) tptp.emptyset) @t48))) % 0.39/0.57 (step @p40 :rule symm :premises (@p39)) % 0.39/0.57 (step @p41 :rule refl :args (@t36)) % 0.39/0.57 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.39/0.57 (step @p43 :rule refl :args (@t34)) % 0.39/0.57 (step @p44 :rule ho_cong :premises (@p43 @p13)) % 0.39/0.57 (step @p45 :rule cong :premises (@p44 @p16) :args ((= (_ @t34 @t46) @t47))) % 0.39/0.57 (step @p46 :rule symm :premises (@p45)) % 0.39/0.57 (step @p47 :rule refl :args (@t35)) % 0.39/0.57 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 0.39/0.57 (step @p49 :rule refl :args (@t33)) % 0.39/0.57 (step @p50 :rule cong :premises (@p49 @p13) :args ((= @t33 @t46))) % 0.39/0.57 (step @p51 :rule symm :premises (@p50)) % 0.39/0.57 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.39/0.57 (step @p53 :rule ho_cong :premises (@p43 @p52)) % 0.39/0.57 (step @p54 :rule trans :premises (@p53 @p48)) % 0.39/0.57 (step @p55 :rule ho_cong :premises (@p30 @p54)) % 0.39/0.57 (step @p56 :rule ho_cong :premises (@p55 @p11)) % 0.39/0.57 (step @p57 :rule trans :premises (@p56 @p42)) % 0.39/0.57 (step @p58 :rule refl :args (@t37)) % 0.39/0.57 (step @p59 :rule cong :premises (@p58 @p19) :args ((= @t37 @t49))) % 0.39/0.57 (step @p60 :rule symm :premises (@p59)) % 0.39/0.57 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.39/0.57 (step @p62 :rule ho_cong :premises (@p30 @p61)) % 0.39/0.57 (step @p63 :rule ho_cong :premises (@p62 @p57)) % 0.39/0.57 (step @p64 :rule trans :premises (@p63 @p36)) % 0.39/0.57 (step @p65 :rule ho_cong :premises (@p24 @p64)) % 0.39/0.57 (step @p66 :rule trans :premises (@p65 @p29)) % 0.39/0.57 (step @p67 :rule cong :premises (@p14 @p66) :args (@t53)) % 0.39/0.57 (step @p68 :rule cong :premises (@p67) :args ((forall @t24 @t53))) % 0.39/0.57 (step @p69 :rule eq-symm :args (@t52 @t2)) % 0.39/0.57 (step @p70 :rule refl :args (@t2)) % 0.39/0.57 (step @p71 :rule beta-reduce :args ((= (_ @t54 @t1) @t38))) % 0.39/0.57 (step @p72 :rule refl :args (@t1)) % 0.39/0.57 (step @p73 :rule beta-reduce :args ((= @t55 @t54))) % 0.39/0.57 (step @p74 :rule ho_cong :premises (@p73 @p72)) % 0.39/0.57 (step @p75 :rule trans :premises (@p74 @p71)) % 0.39/0.57 (step @p76 :rule refl :args (tptp.kfst)) % 0.39/0.57 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.39/0.57 (step @p78 :rule cong :premises (@p77 @p70) :args (@t57)) % 0.39/0.57 (step @p79 :rule trans :premises (@p78 @p69)) % 0.39/0.57 (step @p80 :rule cong :premises (@p79) :args (@t58)) % 0.39/0.57 (step @p81 :rule trans :premises (@p80 @p68)) % 0.39/0.57 (step @p82 :rule refl :args (tptp.kfstpairEq)) % 0.39/0.57 (step @p83 :rule cong :premises (@p82 @p81) :args ((= tptp.kfstpairEq @t58))) % 0.39/0.57 (step @p84 :rule ho_cong :premises (@p5 @p70)) % 0.39/0.57 (step @p85 :rule ho_cong :premises (@p84 @p72)) % 0.39/0.57 (step @p86 :rule ho_cong :premises (@p76 @p85)) % 0.39/0.57 (step @p87 :rule cong :premises (@p86 @p70) :args (@t23)) % 0.39/0.57 (step @p88 :rule cong :premises (@p87) :args (@t25)) % 0.39/0.57 (step @p89 :rule cong :premises (@p82 @p88) :args (@t26)) % 0.39/0.57 (step @p90 :rule trans :premises (@p89 @p83)) % 0.39/0.57 (step @p91 :rule eq_resolve :premises (@p2 @p90)) % 0.39/0.57 (step @p92 :rule cong :premises (@p91 @p7) :args (@t59)) % 0.39/0.57 (step @p93 :rule refl :args (@t68)) % 0.39/0.57 (step @p94 :rule refl :args ((tptp.in @t4 @t16))) % 0.39/0.57 (step @p95 :rule refl :args (@t42)) % 0.39/0.57 (step @p96 :rule refl :args (@t4)) % 0.39/0.57 (step @p97 :rule cong :premises (@p96 @p95) :args (@t43)) % 0.39/0.57 (step @p98 :rule trans :premises (@p97 @p94)) % 0.39/0.57 (step @p99 :rule refl :args (@t17)) % 0.39/0.57 (step @p100 :rule ho_cong :premises (@p99 @p95)) % 0.39/0.57 (step @p101 :rule cong :premises (@p100 @p98) :args ((= (_ @t17 @t42) @t43))) % 0.39/0.57 (step @p102 :rule symm :premises (@p101)) % 0.39/0.57 (step @p103 :rule refl :args (@t18)) % 0.39/0.57 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.39/0.57 (step @p105 :rule refl :args (@t16)) % 0.39/0.57 (step @p106 :rule cong :premises (@p105 @p95) :args ((= @t16 @t42))) % 0.39/0.57 (step @p107 :rule symm :premises (@p106)) % 0.39/0.57 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.39/0.57 (step @p109 :rule ho_cong :premises (@p99 @p108)) % 0.39/0.57 (step @p110 :rule trans :premises (@p109 @p104)) % 0.39/0.57 (step @p111 :rule cong :premises (@p110) :args (@t69)) % 0.39/0.57 (step @p112 :rule nary_cong :premises (@p111 @p93) :args (@t70)) % 0.39/0.57 (step @p113 :rule cong :premises (@p112) :args ((forall @t20 @t70))) % 0.39/0.57 (step @p114 :rule bool-impl-elim :args (@t18 @t68)) % 0.39/0.57 (step @p115 :rule cong :premises (@p114) :args ((forall @t20 (=> @t18 @t68)))) % 0.39/0.57 (step @p116 :rule trans :premises (@p115 @p113)) % 0.39/0.57 (step @p117 :rule aci_norm :args ((= @t72 @t66))) % 0.39/0.57 (step @p118 :rule cong :premises (@p117) :args (@t73)) % 0.39/0.57 (step @p119 :rule quant-merge-prenex :args ((= (forall @t14 @t75) @t73))) % 0.39/0.57 (step @p120 :rule alpha_equiv :args (@t76 (@list @t60) (@list @t1))) % 0.39/0.57 (step @p121 :rule refl :args (@t65)) % 0.39/0.57 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t77)) % 0.39/0.57 (step @p123 :rule quant-miniscope-or :args ((= @t75 @t77))) % 0.39/0.57 (step @p124 :rule trans :premises (@p123 @p122)) % 0.39/0.57 (step @p125 :rule symm :premises (@p124)) % 0.39/0.57 (step @p126 :rule cong :premises (@p125) :args ((forall @t14 (or @t65 @t80)))) % 0.39/0.57 (step @p127 :rule trans :premises (@p126 @p119)) % 0.39/0.57 (step @p128 :rule trans :premises (@p127 @p118)) % 0.39/0.57 (step @p129 :rule refl :args (@t80)) % 0.39/0.57 (step @p130 :rule refl :args (@t64)) % 0.39/0.57 (step @p131 :rule refl :args (@t12)) % 0.39/0.57 (step @p132 :rule cong :premises (@p131 @p130) :args ((= @t12 @t64))) % 0.39/0.57 (step @p133 :rule symm :premises (@p132)) % 0.39/0.57 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.39/0.57 (step @p135 :rule cong :premises (@p134) :args (@t81)) % 0.39/0.57 (step @p136 :rule nary_cong :premises (@p135 @p129) :args (@t82)) % 0.39/0.57 (step @p137 :rule cong :premises (@p136) :args ((forall @t14 @t82))) % 0.39/0.57 (step @p138 :rule trans :premises (@p137 @p128)) % 0.39/0.57 (step @p139 :rule bool-double-not-elim :args (@t80)) % 0.39/0.57 (step @p140 :rule refl :args (@t81)) % 0.39/0.57 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or @t81 (not @t83)))) % 0.39/0.57 (step @p142 :rule bool-and-de-morgan :args (@t12 @t83 true)) % 0.39/0.57 (step @p143 :rule trans :premises (@p142 @p141)) % 0.39/0.57 (step @p144 :rule cong :premises (@p143) :args (@t85)) % 0.39/0.57 (step @p145 :rule trans :premises (@p144 @p138)) % 0.39/0.57 (step @p146 :rule cong :premises (@p145) :args (@t86)) % 0.39/0.57 (step @p147 :rule exists-elim :args ((= (exists @t14 @t84) @t86))) % 0.39/0.57 (step @p148 :rule trans :premises (@p147 @p146)) % 0.39/0.57 (step @p149 :rule eq-symm :args (@t50 @t4)) % 0.39/0.57 (step @p150 :rule cong :premises (@p149) :args (@t87)) % 0.39/0.57 (step @p151 :rule refl :args (@t79)) % 0.39/0.57 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t88)) % 0.39/0.57 (step @p153 :rule cong :premises (@p152) :args ((forall @t9 @t88))) % 0.39/0.57 (step @p154 :rule cong :premises (@p64 @p96) :args (@t89)) % 0.39/0.57 (step @p155 :rule cong :premises (@p154) :args (@t90)) % 0.39/0.57 (step @p156 :rule refl :args (@t78)) % 0.39/0.57 (step @p157 :rule refl :args (@t7)) % 0.39/0.57 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t7 @t78))) % 0.39/0.57 (step @p159 :rule symm :premises (@p158)) % 0.39/0.57 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.39/0.57 (step @p161 :rule cong :premises (@p160) :args (@t91)) % 0.39/0.57 (step @p162 :rule nary_cong :premises (@p161 @p155) :args (@t92)) % 0.39/0.57 (step @p163 :rule cong :premises (@p162) :args ((forall @t9 @t92))) % 0.39/0.57 (step @p164 :rule trans :premises (@p163 @p153)) % 0.39/0.57 (step @p165 :rule bool-and-de-morgan :args (@t7 @t89 true)) % 0.39/0.57 (step @p166 :rule cong :premises (@p165) :args (@t94)) % 0.39/0.57 (step @p167 :rule trans :premises (@p166 @p164)) % 0.39/0.57 (step @p168 :rule cong :premises (@p167) :args (@t95)) % 0.39/0.57 (step @p169 :rule exists-elim :args ((= (exists @t9 @t93) @t95))) % 0.39/0.57 (step @p170 :rule trans :premises (@p169 @p168)) % 0.39/0.57 (step @p171 :rule eq-symm :args (@t4 @t38)) % 0.39/0.57 (step @p172 :rule refl :args (@t4)) % 0.39/0.57 (step @p173 :rule cong :premises (@p172 @p75) :args (@t96)) % 0.39/0.57 (step @p174 :rule trans :premises (@p173 @p171)) % 0.39/0.57 (step @p175 :rule refl :args (@t7)) % 0.39/0.57 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t97)) % 0.39/0.57 (step @p177 :rule cong :premises (@p176) :args (@t98)) % 0.39/0.57 (step @p178 :rule trans :premises (@p177 @p170)) % 0.39/0.57 (step @p179 :rule refl :args (@t12)) % 0.39/0.57 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t99)) % 0.39/0.57 (step @p181 :rule cong :premises (@p180) :args (@t100)) % 0.39/0.57 (step @p182 :rule trans :premises (@p181 @p148)) % 0.39/0.57 (step @p183 :rule refl :args (@t18)) % 0.39/0.57 (step @p184 :rule cong :premises (@p183 @p182) :args (@t101)) % 0.39/0.57 (step @p185 :rule cong :premises (@p184) :args (@t102)) % 0.39/0.57 (step @p186 :rule trans :premises (@p185 @p116)) % 0.39/0.57 (step @p187 :rule refl :args (tptp.cartprodmempair1)) % 0.39/0.57 (step @p188 :rule cong :premises (@p187 @p186) :args ((= tptp.cartprodmempair1 @t102))) % 0.39/0.57 (step @p189 :rule cong :premises (@p172 @p85) :args (@t5)) % 0.39/0.57 (step @p190 :rule nary_cong :premises (@p175 @p189) :args (@t8)) % 0.39/0.57 (step @p191 :rule cong :premises (@p190) :args (@t10)) % 0.39/0.57 (step @p192 :rule nary_cong :premises (@p179 @p191) :args (@t13)) % 0.39/0.57 (step @p193 :rule cong :premises (@p192) :args (@t15)) % 0.39/0.57 (step @p194 :rule cong :premises (@p183 @p193) :args (@t19)) % 0.39/0.57 (step @p195 :rule cong :premises (@p194) :args (@t21)) % 0.39/0.57 (step @p196 :rule cong :premises (@p187 @p195) :args (@t22)) % 0.39/0.57 (step @p197 :rule trans :premises (@p196 @p188)) % 0.39/0.57 (step @p198 :rule eq_resolve :premises (@p1 @p197)) % 0.39/0.57 (step @p199 :rule cong :premises (@p198 @p92) :args (@t103)) % 0.39/0.57 (step @p200 :rule cong :premises (@p199) :args ((not @t103))) % 0.39/0.57 (step @p201 :rule refl :args ((tptp.in @t27 @t11))) % 0.39/0.57 (step @p202 :rule refl :args (@t11)) % 0.39/0.57 (step @p203 :rule refl :args (@t40)) % 0.39/0.57 (step @p204 :rule cong :premises (@p203 @p202) :args (@t41)) % 0.39/0.57 (step @p205 :rule trans :premises (@p204 @p201)) % 0.39/0.57 (step @p206 :rule refl :args (tptp.in)) % 0.39/0.57 (step @p207 :rule ho_cong :premises (@p206 @p203)) % 0.39/0.57 (step @p208 :rule ho_cong :premises (@p207 @p202)) % 0.39/0.57 (step @p209 :rule cong :premises (@p208 @p205) :args ((= (_ (_ tptp.in @t40) @t11) @t41))) % 0.39/0.57 (step @p210 :rule symm :premises (@p209)) % 0.39/0.57 (step @p211 :rule refl :args (@t28)) % 0.39/0.57 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 0.39/0.57 (step @p213 :rule refl :args (@t27)) % 0.39/0.57 (step @p214 :rule cong :premises (@p213 @p203) :args ((= @t27 @t40))) % 0.39/0.57 (step @p215 :rule symm :premises (@p214)) % 0.39/0.57 (step @p216 :rule eq_resolve :premises (@p213 @p215)) % 0.39/0.57 (step @p217 :rule ho_cong :premises (@p206 @p216)) % 0.39/0.57 (step @p218 :rule ho_cong :premises (@p217 @p202)) % 0.39/0.57 (step @p219 :rule trans :premises (@p218 @p212)) % 0.39/0.57 (step @p220 :rule nary_cong :premises (@p111 @p219) :args (@t104)) % 0.39/0.57 (step @p221 :rule cong :premises (@p220) :args ((forall @t20 @t104))) % 0.39/0.57 (step @p222 :rule bool-impl-elim :args (@t18 @t28)) % 0.39/0.57 (step @p223 :rule cong :premises (@p222) :args (@t29)) % 0.39/0.57 (step @p224 :rule trans :premises (@p223 @p221)) % 0.39/0.57 (step @p225 :rule cong :premises (@p82 @p224) :args (@t30)) % 0.39/0.57 (step @p226 :rule cong :premises (@p187 @p225) :args (@t31)) % 0.39/0.57 (step @p227 :rule cong :premises (@p226) :args (@t32)) % 0.39/0.57 (step @p228 :rule trans :premises (@p227 @p200)) % 0.39/0.57 (step @p229 :rule eq_resolve :premises (@p3 @p228)) % 0.39/0.57 (step @p230 :rule not_implies_elim1 :premises (@p229)) % 0.39/0.57 (step @p231 :rule eq-symm :args (@t105 @t61)) % 0.39/0.57 (step @p232 :rule cong :premises (@p231) :args (@t106)) % 0.39/0.57 (step @p233 :rule refl :args (@t108)) % 0.39/0.57 (step @p234 :rule refl :args (@t110)) % 0.39/0.57 (step @p235 :rule nary_cong :premises (@p234 @p233 @p232) :args (@t111)) % 0.39/0.57 (step @p236 :rule cong :premises (@p235) :args (@t112)) % 0.39/0.57 (step @p237 :rule cong :premises (@p236) :args (@t113)) % 0.39/0.57 (step @p238 :rule refl :args (@t115)) % 0.39/0.57 (step @p239 :rule nary_cong :premises (@p238 @p237) :args (@t116)) % 0.39/0.57 (step @p240 :rule refl :args (@t117)) % 0.39/0.57 (step @p241 :rule cong :premises (@p240 @p239) :args ((=> @t117 @t116))) % 0.39/0.57 (assume-push @p308 @t117) % 0.39/0.57 (step @p243 :rule instantiate :premises (@p230) :args ((@list @t109 @t107 @t105))) % 0.39/0.57 (step-pop @p309 :rule scope :premises (@p243)) % 0.39/0.57 (step @p244 :rule process_scope :premises (@p309) :args (@t116)) % 0.39/0.57 (step @p246 :rule eq_resolve :premises (@p244 @p241)) % 0.39/0.57 (step @p247 :rule implies_elim :premises (@p246)) % 0.39/0.57 (step @p248 :rule chain_m_resolution :premises (@p247 @p230) :args (@t120 (@list false) (@list @t117))) % 0.39/0.57 (step @p249 :rule not_implies_elim2 :premises (@p229)) % 0.39/0.57 (step @p250 :rule not_implies_elim2 :premises (@p249)) % 0.39/0.57 (step @p251 :rule skolemize :premises (@p250)) % 0.39/0.57 (step @p252 :rule bool-double-not-elim :args (@t114)) % 0.39/0.57 (step @p253 :rule refl :args (@t123)) % 0.39/0.57 (step @p254 :rule nary_cong :premises (@p253 @p252) :args ((or @t123 (not @t115)))) % 0.39/0.57 (step @p255 :rule cnf_or_neg :args (@t123 0)) % 0.39/0.57 (step @p256 :rule eq_resolve :premises (@p255 @p254)) % 0.39/0.57 (step @p257 :rule reordering :premises (@p256) :args ((or @t114 @t123))) % 0.39/0.57 (step @p258 :rule chain_m_resolution :premises (@p257 @p251) :args (@t114 @t124 @t125)) % 0.39/0.57 (step @p259 :rule cnf_or_pos :args (@t120)) % 0.39/0.57 (step @p260 :rule reordering :premises (@p259) :args ((or @t115 @t119 (not @t120)))) % 0.39/0.57 (step @p261 :rule chain_m_resolution :premises (@p260 @p258 @p248) :args (@t119 (@list false false) (@list @t114 @t120))) % 0.39/0.57 (step @p262 :rule refl :args (@t135)) % 0.39/0.57 (step @p263 :rule bool-double-not-elim :args (@t118)) % 0.39/0.57 (step @p264 :rule nary_cong :premises (@p263 @p262) :args ((or (not @t119) @t135))) % 0.39/0.57 (step @p265 :rule eq-symm :args (@t128 @t105)) % 0.39/0.57 (step @p266 :rule cong :premises (@p265) :args (@t136)) % 0.39/0.57 (step @p267 :rule refl :args (@t131)) % 0.39/0.57 (step @p268 :rule refl :args (@t133)) % 0.39/0.57 (step @p269 :rule nary_cong :premises (@p268 @p267 @p266) :args (@t137)) % 0.39/0.57 (step @p270 :rule cong :premises (@p269) :args (@t138)) % 0.39/0.57 (step @p271 :rule refl :args (@t119)) % 0.39/0.57 (step @p272 :rule cong :premises (@p271 @p270) :args ((=> @t119 @t138))) % 0.39/0.57 (assume-push @p310 @t119) % 0.39/0.57 (step @p274 :rule skolemize :premises (@p261)) % 0.39/0.57 (step-pop @p311 :rule scope :premises (@p274)) % 0.39/0.57 (step @p275 :rule process_scope :premises (@p311) :args (@t138)) % 0.39/0.57 (step @p277 :rule eq_resolve :premises (@p275 @p272)) % 0.39/0.57 (step @p278 :rule implies_elim :premises (@p277)) % 0.39/0.57 (step @p279 :rule eq_resolve :premises (@p278 @p264)) % 0.39/0.57 (step @p280 :rule chain_m_resolution :premises (@p279 @p261) :args (@t135 @t124 (@list @t118))) % 0.39/0.57 (step @p281 :rule bool-double-not-elim :args (@t132)) % 0.39/0.57 (step @p282 :rule refl :args (@t134)) % 0.39/0.57 (step @p283 :rule nary_cong :premises (@p282 @p281) :args ((or @t134 (not @t133)))) % 0.39/0.57 (step @p284 :rule cnf_or_neg :args (@t134 0)) % 0.39/0.57 (step @p285 :rule eq_resolve :premises (@p284 @p283)) % 0.39/0.57 (step @p286 :rule reordering :premises (@p285) :args ((or @t132 @t134))) % 0.39/0.57 (step @p287 :rule chain_m_resolution :premises (@p286 @p280) :args (@t132 @t124 @t139)) % 0.39/0.57 (step @p288 :rule true_intro :premises (@p287)) % 0.39/0.57 (step @p289 :rule refl :args (@t109)) % 0.39/0.57 (step @p290 :rule not_implies_elim1 :premises (@p249)) % 0.39/0.57 (step @p291 :rule instantiate :premises (@p290) :args ((@list @t127 @t126))) % 0.39/0.57 (step @p292 :rule symm :premises (@p291)) % 0.39/0.57 (step @p293 :rule bool-double-not-elim :args (@t129)) % 0.39/0.57 (step @p294 :rule nary_cong :premises (@p282 @p293) :args ((or @t134 (not @t130)))) % 0.39/0.57 (step @p295 :rule cnf_or_neg :args (@t134 2)) % 0.39/0.57 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.39/0.57 (step @p297 :rule reordering :premises (@p296) :args ((or @t129 @t134))) % 0.39/0.57 (step @p298 :rule chain_m_resolution :premises (@p297 @p280) :args (@t129 @t124 @t139)) % 0.39/0.57 (step @p299 :rule cong :premises (@p298) :args (@t121)) % 0.39/0.57 (step @p300 :rule trans :premises (@p299 @p292)) % 0.39/0.57 (step @p301 :rule cong :premises (@p300 @p289) :args (@t122)) % 0.39/0.57 (step @p302 :rule cnf_or_neg :args (@t123 1)) % 0.39/0.57 (step @p303 :rule chain_m_resolution :premises (@p302 @p251) :args ((not @t122) @t124 @t125)) % 0.39/0.57 (step @p304 :rule false_intro :premises (@p303)) % 0.39/0.57 (step @p305 :rule symm :premises (@p304)) % 0.39/0.57 (step @p306 :rule trans :premises (@p305 @p301 @p288)) % 0.39/0.57 (step @p307 false :rule eq_resolve :premises (@p306 @p6)) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------