%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU638^2 : 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 : n017.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 08:52:31 AM UTC 2026 % Result : Theorem 0.40s 0.58s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU638^2 : 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 : n017.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 17:42:46 EDT 2026 % 0.16/0.35 % CPUTime : % 0.34/0.50 %----Proving TH0 % 0.40/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.58 % SZS status Theorem % 0.40/0.58 % SZS output start Proof % 0.40/0.58 ( % 0.40/0.58 (declare-sort $$unsorted 0) % 0.40/0.58 (declare-const tptp.emptyset $$unsorted) % 0.40/0.58 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.40/0.58 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.40/0.58 (declare-const tptp.dsetconstrER Bool) % 0.40/0.58 (declare-const tptp.dsetconstrEL Bool) % 0.40/0.58 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.40/0.58 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.40/0.58 (define @t1 () (@var "A" $$unsorted)) % 0.40/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.40/0.58 (define @t3 () (_ tptp.in @t2)) % 0.40/0.58 (define @t4 () (_ @t3 @t1)) % 0.40/0.58 (define @t5 () (@var "Xy" $$unsorted)) % 0.40/0.58 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.40/0.58 (define @t7 () (_ @t6 @t5)) % 0.40/0.58 (define @t8 () (@list @t5)) % 0.40/0.58 (define @t9 () (lambda @t8 @t7)) % 0.40/0.58 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.40/0.58 (define @t11 () (_ @t10 @t9)) % 0.40/0.58 (define @t12 () (_ @t3 @t11)) % 0.40/0.58 (define @t13 () (@list @t1 @t6 @t2)) % 0.40/0.58 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.40/0.58 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.40/0.58 (define @t16 () (_ @t6 @t2)) % 0.40/0.58 (define @t17 () (forall @t13 (=> @t12 @t16))) % 0.40/0.58 (define @t18 () (= tptp.dsetconstrER @t17)) % 0.40/0.58 (define @t19 () (and @t4 @t16)) % 0.40/0.58 (define @t20 () (@list @t2)) % 0.40/0.58 (define @t21 () (exists @t20 @t19)) % 0.40/0.58 (define @t22 () (lambda @t20 @t16)) % 0.40/0.58 (define @t23 () (=> (_ (_ tptp.ex1 @t1) @t22) @t21)) % 0.40/0.58 (define @t24 () (@list @t1 @t6)) % 0.40/0.58 (define @t25 () (forall @t24 @t23)) % 0.40/0.58 (define @t26 () (=> tptp.dsetconstrER @t25)) % 0.40/0.58 (define @t27 () (=> tptp.dsetconstrEL @t26)) % 0.40/0.58 (define @t28 () (not @t27)) % 0.40/0.58 (define @t29 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.40/0.58 (define @t30 () (= @t1 @t29)) % 0.40/0.58 (define @t31 () (and @t4 @t30)) % 0.40/0.58 (define @t32 () (exists @t20 @t31)) % 0.40/0.58 (define @t33 () (@list @t1)) % 0.40/0.58 (define @t34 () (lambda @t33 @t32)) % 0.40/0.58 (define @t35 () (_ @t10 @t22)) % 0.40/0.58 (define @t36 () (lambda @t24 (_ tptp.singleton @t35))) % 0.40/0.58 (define @t37 () (@var "BOUND_VARIABLE_7623" $$unsorted)) % 0.40/0.58 (define @t38 () (tptp.setadjoin @t37 tptp.emptyset)) % 0.40/0.58 (define @t39 () (tptp.dsetconstr @t1 @t6)) % 0.40/0.58 (define @t40 () (not (tptp.in @t37 @t39))) % 0.40/0.58 (define @t41 () (_ @t6 @t2)) % 0.40/0.58 (define @t42 () (tptp.in @t2 @t1)) % 0.40/0.58 (define @t43 () (not @t42)) % 0.40/0.58 (define @t44 () (not (forall @t20 (or @t43 (not @t41))))) % 0.40/0.58 (define @t45 () (@list @t1 @t6 @t37)) % 0.40/0.58 (define @t46 () (forall @t45 (or @t44 @t40 (not (= @t39 @t38))))) % 0.40/0.58 (define @t47 () (_ @t6 @t5)) % 0.40/0.58 (define @t48 () (lambda @t8 @t47)) % 0.40/0.58 (define @t49 () (tptp.dsetconstr @t1 @t48)) % 0.40/0.58 (define @t50 () (tptp.in @t2 @t49)) % 0.40/0.58 (define @t51 () (not @t50)) % 0.40/0.58 (define @t52 () (or @t51 @t41)) % 0.40/0.58 (define @t53 () (not @t12)) % 0.40/0.58 (define @t54 () (or @t53 @t16)) % 0.40/0.58 (define @t55 () (=> tptp.dsetconstrER @t46)) % 0.40/0.58 (define @t56 () (or @t51 @t42)) % 0.40/0.58 (define @t57 () (or @t53 @t4)) % 0.40/0.58 (define @t58 () (=> tptp.dsetconstrEL @t55)) % 0.40/0.58 (define @t59 () (not (= @t38 @t39))) % 0.40/0.58 (define @t60 () (or @t44 @t40 @t59)) % 0.40/0.58 (define @t61 () (or @t40 @t59)) % 0.40/0.58 (define @t62 () (or @t61 @t44)) % 0.40/0.58 (define @t63 () (forall @t45 @t62)) % 0.40/0.58 (define @t64 () (@list @t37)) % 0.40/0.58 (define @t65 () (forall @t64 @t62)) % 0.40/0.58 (define @t66 () (forall @t64 @t61)) % 0.40/0.58 (define @t67 () (@list @t2)) % 0.40/0.58 (define @t68 () (or @t66 @t44)) % 0.40/0.58 (define @t69 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.40/0.58 (define @t70 () (forall @t20 (or (not (tptp.in @t2 @t39)) (not (= @t69 @t39))))) % 0.40/0.58 (define @t71 () (not @t70)) % 0.40/0.58 (define @t72 () (not @t16)) % 0.40/0.58 (define @t73 () (not @t4)) % 0.40/0.58 (define @t74 () (or @t73 @t72)) % 0.40/0.58 (define @t75 () (forall @t20 (not @t19))) % 0.40/0.58 (define @t76 () (not @t75)) % 0.40/0.58 (define @t77 () (@var "BOUND_VARIABLE_7588" $$unsorted)) % 0.40/0.58 (define @t78 () (_ @t6 @t77)) % 0.40/0.58 (define @t79 () (@list @t77)) % 0.40/0.58 (define @t80 () (lambda @t79 @t78)) % 0.40/0.58 (define @t81 () (tptp.dsetconstr @t1 @t80)) % 0.40/0.58 (define @t82 () (= @t69 @t81)) % 0.40/0.58 (define @t83 () (not @t82)) % 0.40/0.58 (define @t84 () (tptp.in @t2 @t81)) % 0.40/0.58 (define @t85 () (not @t84)) % 0.40/0.58 (define @t86 () (or @t85 @t83)) % 0.40/0.58 (define @t87 () (_ @t6 @t77)) % 0.40/0.58 (define @t88 () (lambda @t79 @t87)) % 0.40/0.58 (define @t89 () (tptp.dsetconstr @t1 @t88)) % 0.40/0.58 (define @t90 () (= @t69 @t89)) % 0.40/0.58 (define @t91 () (not @t90)) % 0.40/0.58 (define @t92 () (tptp.in @t2 @t89)) % 0.40/0.58 (define @t93 () (not @t92)) % 0.40/0.58 (define @t94 () (or @t93 @t91)) % 0.40/0.58 (define @t95 () (tptp.dsetconstr @t1 @t22)) % 0.40/0.58 (define @t96 () (= @t69 @t95)) % 0.40/0.58 (define @t97 () (not @t96)) % 0.40/0.58 (define @t98 () (tptp.in @t2 @t95)) % 0.40/0.58 (define @t99 () (not @t98)) % 0.40/0.58 (define @t100 () (or @t99 @t97)) % 0.40/0.58 (define @t101 () (forall @t20 @t100)) % 0.40/0.58 (define @t102 () (not @t101)) % 0.40/0.58 (define @t103 () (lambda (@list @t6) @t71)) % 0.40/0.58 (define @t104 () (_ (lambda @t24 @t71) @t1)) % 0.40/0.58 (define @t105 () (=> (_ @t104 @t22) @t21)) % 0.40/0.58 (define @t106 () (forall @t24 @t105)) % 0.40/0.58 (define @t107 () (=> tptp.dsetconstrER @t106)) % 0.40/0.58 (define @t108 () (=> tptp.dsetconstrEL @t107)) % 0.40/0.58 (define @t109 () (@var "BOUND_VARIABLE_7490" $$unsorted)) % 0.40/0.58 (define @t110 () (_ @t6 @t109)) % 0.40/0.58 (define @t111 () (@list @t109)) % 0.40/0.58 (define @t112 () (lambda @t111 @t110)) % 0.40/0.58 (define @t113 () (tptp.dsetconstr @t1 @t112)) % 0.40/0.58 (define @t114 () (= @t69 @t113)) % 0.40/0.58 (define @t115 () (not @t114)) % 0.40/0.58 (define @t116 () (tptp.in @t2 @t113)) % 0.40/0.58 (define @t117 () (not @t116)) % 0.40/0.58 (define @t118 () (or @t117 @t115)) % 0.40/0.58 (define @t119 () (_ @t6 @t109)) % 0.40/0.58 (define @t120 () (lambda @t111 @t119)) % 0.40/0.58 (define @t121 () (_ @t10 @t120)) % 0.40/0.58 (define @t122 () (= @t69 @t121)) % 0.40/0.58 (define @t123 () (not @t122)) % 0.40/0.58 (define @t124 () (tptp.in @t2 @t121)) % 0.40/0.58 (define @t125 () (not @t124)) % 0.40/0.58 (define @t126 () (or @t125 @t123)) % 0.40/0.58 (define @t127 () (= @t69 @t35)) % 0.40/0.58 (define @t128 () (not @t127)) % 0.40/0.58 (define @t129 () (tptp.in @t2 @t35)) % 0.40/0.58 (define @t130 () (not @t129)) % 0.40/0.58 (define @t131 () (or @t130 @t128)) % 0.40/0.58 (define @t132 () (not (= @t35 @t69))) % 0.40/0.58 (define @t133 () (or @t130 @t132)) % 0.40/0.58 (define @t134 () (forall @t20 @t133)) % 0.40/0.58 (define @t135 () (not @t134)) % 0.40/0.58 (define @t136 () (not @t30)) % 0.40/0.58 (define @t137 () (or @t73 @t136)) % 0.40/0.58 (define @t138 () (forall @t20 (not @t31))) % 0.40/0.58 (define @t139 () (not @t138)) % 0.40/0.58 (define @t140 () (@quantifiers_skolemize @t46 1)) % 0.40/0.58 (define @t141 () (@quantifiers_skolemize @t46 0)) % 0.40/0.58 (define @t142 () (forall @t20 (or (not (tptp.in @t2 @t141)) (not (_ @t140 @t2))))) % 0.40/0.58 (define @t143 () (@quantifiers_skolemize @t46 2)) % 0.40/0.58 (define @t144 () (tptp.dsetconstr @t141 @t140)) % 0.40/0.58 (define @t145 () (tptp.in @t143 @t144)) % 0.40/0.58 (define @t146 () (not @t145)) % 0.40/0.58 (define @t147 () (not @t142)) % 0.40/0.58 (define @t148 () (or @t147 @t146 (not (= @t144 (tptp.setadjoin @t143 tptp.emptyset))))) % 0.40/0.58 (define @t149 () (@list true)) % 0.40/0.58 (define @t150 () (@list @t148)) % 0.40/0.58 (define @t151 () (@list @t141 @t140 @t143)) % 0.40/0.58 (define @t152 () (_ @t140 @t143)) % 0.40/0.58 (define @t153 () (or @t146 @t152)) % 0.40/0.58 (define @t154 () (@list false false)) % 0.40/0.58 (define @t155 () (tptp.in @t143 @t141)) % 0.40/0.58 (define @t156 () (or @t146 @t155)) % 0.40/0.58 (define @t157 () (not @t152)) % 0.40/0.58 (define @t158 () (not @t155)) % 0.40/0.58 (define @t159 () (or @t158 @t157)) % 0.40/0.58 (define @t160 () (not @t159)) % 0.40/0.58 (assume @p1 @t15) % 0.40/0.58 (assume @p2 @t18) % 0.40/0.58 (assume @p3 @t28) % 0.40/0.58 (assume @p4 true) % 0.40/0.58 (step @p5 (= tptp.singleton @t34) :rule refl :args (@t34)) % 0.40/0.58 (step @p6 (= tptp.ex1 @t36) :rule refl :args (@t36)) % 0.40/0.58 (step @p7 :rule refl :args (@t46)) % 0.40/0.58 (step @p8 :rule refl :args (@t41)) % 0.40/0.58 (step @p9 :rule lambda-elim :args ((= @t48 @t6))) % 0.40/0.58 (step @p10 :rule refl :args (@t1)) % 0.40/0.58 (step @p11 :rule cong :premises (@p10 @p9) :args (@t49)) % 0.40/0.58 (step @p12 :rule refl :args (@t2)) % 0.40/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args (@t50)) % 0.40/0.58 (step @p14 :rule cong :premises (@p13) :args (@t51)) % 0.40/0.58 (step @p15 :rule nary_cong :premises (@p14 @p8) :args (@t52)) % 0.40/0.58 (step @p16 :rule cong :premises (@p15) :args ((forall @t13 @t52))) % 0.40/0.58 (step @p17 :rule refl :args (@t41)) % 0.40/0.58 (step @p18 :rule refl :args (@t16)) % 0.40/0.58 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t16 @t41))) % 0.40/0.58 (step @p20 :rule symm :premises (@p19)) % 0.40/0.58 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.40/0.58 (step @p22 :rule refl :args ((tptp.in @t2 @t11))) % 0.40/0.58 (step @p23 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.40/0.58 (step @p24 :rule refl :args (@t47)) % 0.40/0.58 (step @p25 :rule cong :premises (@p24) :args (@t48)) % 0.40/0.58 (step @p26 :rule refl :args (@t1)) % 0.40/0.58 (step @p27 :rule cong :premises (@p26 @p25) :args (@t49)) % 0.40/0.58 (step @p28 :rule trans :premises (@p27 @p23)) % 0.40/0.58 (step @p29 :rule refl :args (@t2)) % 0.40/0.58 (step @p30 :rule cong :premises (@p29 @p28) :args (@t50)) % 0.40/0.58 (step @p31 :rule trans :premises (@p30 @p22)) % 0.40/0.58 (step @p32 :rule refl :args (@t3)) % 0.40/0.58 (step @p33 :rule ho_cong :premises (@p32 @p28)) % 0.40/0.58 (step @p34 :rule cong :premises (@p33 @p31) :args ((= (_ @t3 @t49) @t50))) % 0.40/0.58 (step @p35 :rule symm :premises (@p34)) % 0.40/0.58 (step @p36 :rule refl :args (@t12)) % 0.40/0.58 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.40/0.58 (step @p38 :rule refl :args (@t10)) % 0.40/0.58 (step @p39 :rule ho_cong :premises (@p38 @p25)) % 0.40/0.58 (step @p40 :rule cong :premises (@p39 @p28) :args ((= (_ @t10 @t48) @t49))) % 0.40/0.58 (step @p41 :rule symm :premises (@p40)) % 0.40/0.58 (step @p42 :rule refl :args (@t11)) % 0.40/0.58 (step @p43 :rule eq_resolve :premises (@p42 @p41)) % 0.40/0.58 (step @p44 :rule refl :args (@t7)) % 0.40/0.58 (step @p45 :rule cong :premises (@p44 @p24) :args ((= @t7 @t47))) % 0.40/0.58 (step @p46 :rule symm :premises (@p45)) % 0.40/0.58 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.40/0.58 (step @p48 :rule cong :premises (@p47) :args (@t9)) % 0.40/0.58 (step @p49 :rule ho_cong :premises (@p38 @p48)) % 0.40/0.58 (step @p50 :rule trans :premises (@p49 @p43)) % 0.40/0.58 (step @p51 :rule ho_cong :premises (@p32 @p50)) % 0.40/0.58 (step @p52 :rule trans :premises (@p51 @p37)) % 0.40/0.58 (step @p53 :rule cong :premises (@p52) :args (@t53)) % 0.40/0.58 (step @p54 :rule nary_cong :premises (@p53 @p21) :args (@t54)) % 0.40/0.58 (step @p55 :rule cong :premises (@p54) :args ((forall @t13 @t54))) % 0.40/0.58 (step @p56 :rule trans :premises (@p55 @p16)) % 0.40/0.58 (step @p57 :rule bool-impl-elim :args (@t12 @t16)) % 0.40/0.58 (step @p58 :rule cong :premises (@p57) :args (@t17)) % 0.40/0.58 (step @p59 :rule trans :premises (@p58 @p56)) % 0.40/0.58 (step @p60 :rule refl :args (tptp.dsetconstrER)) % 0.40/0.58 (step @p61 :rule cong :premises (@p60 @p59) :args (@t18)) % 0.40/0.58 (step @p62 :rule eq_resolve :premises (@p2 @p61)) % 0.40/0.58 (step @p63 :rule cong :premises (@p62 @p7) :args (@t55)) % 0.40/0.58 (step @p64 :rule refl :args (@t42)) % 0.40/0.58 (step @p65 :rule nary_cong :premises (@p14 @p64) :args (@t56)) % 0.40/0.58 (step @p66 :rule cong :premises (@p65) :args ((forall @t13 @t56))) % 0.40/0.58 (step @p67 :rule refl :args (@t42)) % 0.40/0.58 (step @p68 :rule refl :args (@t4)) % 0.40/0.58 (step @p69 :rule cong :premises (@p68 @p67) :args ((= @t4 @t42))) % 0.40/0.58 (step @p70 :rule symm :premises (@p69)) % 0.40/0.58 (step @p71 :rule eq_resolve :premises (@p68 @p70)) % 0.40/0.58 (step @p72 :rule nary_cong :premises (@p53 @p71) :args (@t57)) % 0.40/0.58 (step @p73 :rule cong :premises (@p72) :args ((forall @t13 @t57))) % 0.40/0.58 (step @p74 :rule trans :premises (@p73 @p66)) % 0.40/0.58 (step @p75 :rule bool-impl-elim :args (@t12 @t4)) % 0.40/0.58 (step @p76 :rule cong :premises (@p75) :args (@t14)) % 0.40/0.58 (step @p77 :rule trans :premises (@p76 @p74)) % 0.40/0.58 (step @p78 :rule refl :args (tptp.dsetconstrEL)) % 0.40/0.58 (step @p79 :rule cong :premises (@p78 @p77) :args (@t15)) % 0.40/0.58 (step @p80 :rule eq_resolve :premises (@p1 @p79)) % 0.40/0.58 (step @p81 :rule cong :premises (@p80 @p63) :args (@t58)) % 0.40/0.58 (step @p82 :rule cong :premises (@p81) :args ((not @t58))) % 0.40/0.58 (step @p83 :rule eq-symm :args (@t38 @t39)) % 0.40/0.58 (step @p84 :rule cong :premises (@p83) :args (@t59)) % 0.40/0.58 (step @p85 :rule refl :args (@t40)) % 0.40/0.58 (step @p86 :rule refl :args (@t44)) % 0.40/0.58 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84) :args (@t60)) % 0.40/0.58 (step @p88 :rule aci_norm :args ((= @t62 @t60))) % 0.40/0.58 (step @p89 :rule trans :premises (@p88 @p87)) % 0.40/0.58 (step @p90 :rule cong :premises (@p89) :args (@t63)) % 0.40/0.58 (step @p91 :rule quant-merge-prenex :args ((= (forall @t24 @t65) @t63))) % 0.40/0.58 (step @p92 :rule refl :args (@t44)) % 0.40/0.58 (step @p93 :rule alpha_equiv :args (@t66 (@list @t37) @t67)) % 0.40/0.58 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t68)) % 0.40/0.58 (step @p95 :rule quant-miniscope-or :args ((= @t65 @t68))) % 0.40/0.58 (step @p96 :rule trans :premises (@p95 @p94)) % 0.40/0.58 (step @p97 :rule symm :premises (@p96)) % 0.40/0.58 (step @p98 :rule cong :premises (@p97) :args ((forall @t24 (or @t70 @t44)))) % 0.40/0.58 (step @p99 :rule trans :premises (@p98 @p91)) % 0.40/0.58 (step @p100 :rule trans :premises (@p99 @p90)) % 0.40/0.58 (step @p101 :rule bool-double-not-elim :args (@t70)) % 0.40/0.58 (step @p102 :rule nary_cong :premises (@p101 @p92) :args ((or (not @t71) @t44))) % 0.40/0.58 (step @p103 :rule bool-impl-elim :args (@t71 @t44)) % 0.40/0.58 (step @p104 :rule trans :premises (@p103 @p102)) % 0.40/0.58 (step @p105 :rule cong :premises (@p104) :args ((forall @t24 (=> @t71 @t44)))) % 0.40/0.58 (step @p106 :rule trans :premises (@p105 @p100)) % 0.40/0.58 (step @p107 :rule cong :premises (@p21) :args (@t72)) % 0.40/0.58 (step @p108 :rule cong :premises (@p71) :args (@t73)) % 0.40/0.58 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t74)) % 0.40/0.58 (step @p110 :rule cong :premises (@p109) :args ((forall @t20 @t74))) % 0.40/0.58 (step @p111 :rule bool-and-de-morgan :args (@t4 @t16 true)) % 0.40/0.58 (step @p112 :rule cong :premises (@p111) :args (@t75)) % 0.40/0.58 (step @p113 :rule trans :premises (@p112 @p110)) % 0.40/0.58 (step @p114 :rule cong :premises (@p113) :args (@t76)) % 0.40/0.58 (step @p115 :rule exists-elim :args ((= @t21 @t76))) % 0.40/0.58 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.58 (step @p117 :rule lambda-elim :args ((= @t80 @t6))) % 0.40/0.58 (step @p118 :rule cong :premises (@p10 @p117) :args (@t81)) % 0.40/0.58 (step @p119 :rule refl :args (@t69)) % 0.40/0.58 (step @p120 :rule cong :premises (@p119 @p118) :args (@t82)) % 0.40/0.58 (step @p121 :rule cong :premises (@p120) :args (@t83)) % 0.40/0.58 (step @p122 :rule cong :premises (@p12 @p118) :args (@t84)) % 0.40/0.58 (step @p123 :rule cong :premises (@p122) :args (@t85)) % 0.40/0.58 (step @p124 :rule nary_cong :premises (@p123 @p121) :args (@t86)) % 0.40/0.58 (step @p125 :rule cong :premises (@p124) :args ((forall @t20 @t86))) % 0.40/0.58 (step @p126 :rule refl :args (@t78)) % 0.40/0.58 (step @p127 :rule refl :args (@t87)) % 0.40/0.58 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t87 @t78))) % 0.40/0.58 (step @p129 :rule symm :premises (@p128)) % 0.40/0.58 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.40/0.58 (step @p131 :rule cong :premises (@p130) :args (@t88)) % 0.40/0.58 (step @p132 :rule cong :premises (@p26 @p131) :args (@t89)) % 0.40/0.58 (step @p133 :rule refl :args (@t69)) % 0.40/0.58 (step @p134 :rule cong :premises (@p133 @p132) :args (@t90)) % 0.40/0.58 (step @p135 :rule cong :premises (@p134) :args (@t91)) % 0.40/0.58 (step @p136 :rule cong :premises (@p29 @p132) :args (@t92)) % 0.40/0.58 (step @p137 :rule cong :premises (@p136) :args (@t93)) % 0.40/0.58 (step @p138 :rule nary_cong :premises (@p137 @p135) :args (@t94)) % 0.40/0.58 (step @p139 :rule cong :premises (@p138) :args ((forall @t20 @t94))) % 0.40/0.58 (step @p140 :rule trans :premises (@p139 @p125)) % 0.40/0.58 (step @p141 :rule alpha_equiv :args (@t22 @t67 (@list @t77))) % 0.40/0.58 (step @p142 :rule cong :premises (@p26 @p141) :args (@t95)) % 0.40/0.58 (step @p143 :rule cong :premises (@p133 @p142) :args (@t96)) % 0.40/0.58 (step @p144 :rule cong :premises (@p143) :args (@t97)) % 0.40/0.58 (step @p145 :rule cong :premises (@p29 @p142) :args (@t98)) % 0.40/0.58 (step @p146 :rule cong :premises (@p145) :args (@t99)) % 0.40/0.58 (step @p147 :rule nary_cong :premises (@p146 @p144) :args (@t100)) % 0.40/0.58 (step @p148 :rule cong :premises (@p147) :args (@t101)) % 0.40/0.58 (step @p149 :rule trans :premises (@p148 @p140)) % 0.40/0.58 (step @p150 :rule cong :premises (@p149) :args (@t102)) % 0.40/0.58 (step @p151 :rule beta-reduce :args ((= (_ @t103 @t22) @t102))) % 0.40/0.58 (step @p152 :rule trans :premises (@p151 @p150)) % 0.40/0.58 (step @p153 :rule refl :args (@t22)) % 0.40/0.58 (step @p154 :rule beta-reduce :args ((= @t104 @t103))) % 0.40/0.58 (step @p155 :rule ho_cong :premises (@p154 @p153)) % 0.40/0.58 (step @p156 :rule trans :premises (@p155 @p152)) % 0.40/0.58 (step @p157 :rule cong :premises (@p156 @p116) :args (@t105)) % 0.40/0.58 (step @p158 :rule cong :premises (@p157) :args (@t106)) % 0.40/0.58 (step @p159 :rule trans :premises (@p158 @p106)) % 0.40/0.58 (step @p160 :rule cong :premises (@p60 @p159) :args (@t107)) % 0.40/0.58 (step @p161 :rule cong :premises (@p78 @p160) :args (@t108)) % 0.40/0.58 (step @p162 :rule cong :premises (@p161) :args ((not @t108))) % 0.40/0.58 (step @p163 :rule refl :args (@t21)) % 0.40/0.58 (step @p164 :rule lambda-elim :args ((= @t112 @t6))) % 0.40/0.58 (step @p165 :rule cong :premises (@p10 @p164) :args (@t113)) % 0.40/0.58 (step @p166 :rule cong :premises (@p119 @p165) :args (@t114)) % 0.40/0.58 (step @p167 :rule cong :premises (@p166) :args (@t115)) % 0.40/0.58 (step @p168 :rule cong :premises (@p12 @p165) :args (@t116)) % 0.40/0.58 (step @p169 :rule cong :premises (@p168) :args (@t117)) % 0.40/0.58 (step @p170 :rule nary_cong :premises (@p169 @p167) :args (@t118)) % 0.40/0.58 (step @p171 :rule cong :premises (@p170) :args ((forall @t20 @t118))) % 0.40/0.58 (step @p172 :rule refl :args ((tptp.dsetconstr @t1 @t120))) % 0.40/0.58 (step @p173 :rule refl :args (@t110)) % 0.40/0.58 (step @p174 :rule cong :premises (@p173) :args (@t112)) % 0.40/0.58 (step @p175 :rule cong :premises (@p26 @p174) :args (@t113)) % 0.40/0.58 (step @p176 :rule trans :premises (@p175 @p172)) % 0.40/0.58 (step @p177 :rule ho_cong :premises (@p38 @p174)) % 0.40/0.58 (step @p178 :rule cong :premises (@p177 @p176) :args ((= (_ @t10 @t112) @t113))) % 0.40/0.58 (step @p179 :rule symm :premises (@p178)) % 0.40/0.58 (step @p180 :rule refl :args (@t121)) % 0.40/0.58 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 0.40/0.58 (step @p182 :rule refl :args (@t119)) % 0.40/0.58 (step @p183 :rule cong :premises (@p182 @p173) :args ((= @t119 @t110))) % 0.40/0.58 (step @p184 :rule symm :premises (@p183)) % 0.40/0.58 (step @p185 :rule eq_resolve :premises (@p182 @p184)) % 0.40/0.58 (step @p186 :rule cong :premises (@p185) :args (@t120)) % 0.40/0.58 (step @p187 :rule ho_cong :premises (@p38 @p186)) % 0.40/0.58 (step @p188 :rule trans :premises (@p187 @p181)) % 0.40/0.58 (step @p189 :rule cong :premises (@p133 @p188) :args (@t122)) % 0.40/0.58 (step @p190 :rule cong :premises (@p189) :args (@t123)) % 0.40/0.58 (step @p191 :rule cong :premises (@p29 @p188) :args (@t124)) % 0.40/0.58 (step @p192 :rule cong :premises (@p191) :args (@t125)) % 0.40/0.58 (step @p193 :rule nary_cong :premises (@p192 @p190) :args (@t126)) % 0.40/0.58 (step @p194 :rule cong :premises (@p193) :args ((forall @t20 @t126))) % 0.40/0.58 (step @p195 :rule trans :premises (@p194 @p171)) % 0.40/0.58 (step @p196 :rule alpha_equiv :args (@t22 @t67 (@list @t109))) % 0.40/0.58 (step @p197 :rule ho_cong :premises (@p38 @p196)) % 0.40/0.58 (step @p198 :rule cong :premises (@p133 @p197) :args (@t127)) % 0.40/0.58 (step @p199 :rule cong :premises (@p198) :args (@t128)) % 0.40/0.58 (step @p200 :rule cong :premises (@p29 @p197) :args (@t129)) % 0.40/0.58 (step @p201 :rule cong :premises (@p200) :args (@t130)) % 0.40/0.58 (step @p202 :rule nary_cong :premises (@p201 @p199) :args (@t131)) % 0.40/0.58 (step @p203 :rule cong :premises (@p202) :args ((forall @t20 @t131))) % 0.40/0.58 (step @p204 :rule trans :premises (@p203 @p195)) % 0.40/0.58 (step @p205 :rule eq-symm :args (@t35 @t69)) % 0.40/0.58 (step @p206 :rule cong :premises (@p205) :args (@t132)) % 0.40/0.58 (step @p207 :rule refl :args (@t130)) % 0.40/0.58 (step @p208 :rule nary_cong :premises (@p207 @p206) :args (@t133)) % 0.40/0.58 (step @p209 :rule cong :premises (@p208) :args (@t134)) % 0.40/0.58 (step @p210 :rule trans :premises (@p209 @p204)) % 0.40/0.58 (step @p211 :rule cong :premises (@p210) :args (@t135)) % 0.40/0.58 (step @p212 :rule beta-reduce :args ((= (_ (lambda @t33 (not (forall @t20 (or @t43 (not (= @t1 @t69)))))) @t35) @t135))) % 0.40/0.58 (step @p213 :rule trans :premises (@p212 @p211)) % 0.40/0.58 (step @p214 :rule refl :args (@t35)) % 0.40/0.58 (step @p215 :rule refl :args (@t69)) % 0.40/0.58 (step @p216 :rule refl :args (@t29)) % 0.40/0.58 (step @p217 :rule cong :premises (@p216 @p215) :args ((= @t29 @t69))) % 0.40/0.58 (step @p218 :rule symm :premises (@p217)) % 0.40/0.58 (step @p219 :rule eq_resolve :premises (@p216 @p218)) % 0.40/0.58 (step @p220 :rule cong :premises (@p26 @p219) :args (@t30)) % 0.40/0.58 (step @p221 :rule cong :premises (@p220) :args (@t136)) % 0.40/0.58 (step @p222 :rule nary_cong :premises (@p108 @p221) :args (@t137)) % 0.40/0.58 (step @p223 :rule cong :premises (@p222) :args ((forall @t20 @t137))) % 0.40/0.58 (step @p224 :rule bool-and-de-morgan :args (@t4 @t30 true)) % 0.40/0.58 (step @p225 :rule cong :premises (@p224) :args (@t138)) % 0.40/0.58 (step @p226 :rule trans :premises (@p225 @p223)) % 0.40/0.58 (step @p227 :rule cong :premises (@p226) :args (@t139)) % 0.40/0.58 (step @p228 :rule exists-elim :args ((= @t32 @t139))) % 0.40/0.58 (step @p229 :rule trans :premises (@p228 @p227)) % 0.40/0.58 (step @p230 :rule cong :premises (@p229) :args (@t34)) % 0.40/0.58 (step @p231 :rule trans :premises (@p5 @p230)) % 0.40/0.58 (step @p232 :rule ho_cong :premises (@p231 @p214)) % 0.40/0.58 (step @p233 :rule trans :premises (@p232 @p213)) % 0.40/0.58 (step @p234 :rule cong :premises (@p233) :args (@t36)) % 0.40/0.58 (step @p235 :rule trans :premises (@p6 @p234)) % 0.40/0.58 (step @p236 :rule ho_cong :premises (@p235 @p10)) % 0.40/0.58 (step @p237 :rule ho_cong :premises (@p236 @p153)) % 0.40/0.58 (step @p238 :rule cong :premises (@p237 @p163) :args (@t23)) % 0.40/0.58 (step @p239 :rule cong :premises (@p238) :args (@t25)) % 0.40/0.58 (step @p240 :rule cong :premises (@p60 @p239) :args (@t26)) % 0.40/0.58 (step @p241 :rule cong :premises (@p78 @p240) :args (@t27)) % 0.40/0.58 (step @p242 :rule cong :premises (@p241) :args (@t28)) % 0.40/0.58 (step @p243 :rule trans :premises (@p242 @p162)) % 0.40/0.58 (step @p244 :rule trans :premises (@p243 @p82)) % 0.40/0.58 (step @p245 :rule eq_resolve :premises (@p3 @p244)) % 0.40/0.58 (step @p246 :rule not_implies_elim2 :premises (@p245)) % 0.40/0.58 (step @p247 :rule not_implies_elim2 :premises (@p246)) % 0.40/0.58 (step @p248 :rule skolemize :premises (@p247)) % 0.40/0.58 (step @p249 :rule bool-double-not-elim :args (@t142)) % 0.40/0.58 (step @p250 :rule refl :args (@t148)) % 0.40/0.58 (step @p251 :rule nary_cong :premises (@p250 @p249) :args ((or @t148 (not @t147)))) % 0.40/0.58 (step @p252 :rule cnf_or_neg :args (@t148 0)) % 0.40/0.58 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.40/0.58 (step @p254 :rule reordering :premises (@p253) :args ((or @t142 @t148))) % 0.40/0.59 (step @p255 :rule chain_m_resolution :premises (@p254 @p248) :args (@t142 @t149 @t150)) % 0.40/0.59 (step @p256 :rule not_implies_elim1 :premises (@p246)) % 0.40/0.59 (step @p257 :rule instantiate :premises (@p256) :args (@t151)) % 0.40/0.59 (step @p258 :rule bool-double-not-elim :args (@t145)) % 0.40/0.59 (step @p259 :rule nary_cong :premises (@p250 @p258) :args ((or @t148 (not @t146)))) % 0.40/0.59 (step @p260 :rule cnf_or_neg :args (@t148 1)) % 0.40/0.59 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.40/0.59 (step @p262 :rule reordering :premises (@p261) :args ((or @t145 @t148))) % 0.40/0.59 (step @p263 :rule chain_m_resolution :premises (@p262 @p248) :args (@t145 @t149 @t150)) % 0.40/0.59 (step @p264 :rule cnf_or_pos :args (@t153)) % 0.40/0.59 (step @p265 :rule reordering :premises (@p264) :args ((or @t146 @t152 (not @t153)))) % 0.40/0.59 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p257) :args (@t152 @t154 (@list @t145 @t153))) % 0.40/0.59 (step @p267 :rule not_implies_elim1 :premises (@p245)) % 0.40/0.59 (step @p268 :rule instantiate :premises (@p267) :args (@t151)) % 0.40/0.59 (step @p269 :rule cnf_or_pos :args (@t156)) % 0.40/0.59 (step @p270 :rule reordering :premises (@p269) :args ((or @t146 @t155 (not @t156)))) % 0.40/0.59 (step @p271 :rule chain_m_resolution :premises (@p270 @p263 @p268) :args (@t155 @t154 (@list @t145 @t156))) % 0.40/0.59 (step @p272 :rule cnf_or_pos :args (@t159)) % 0.40/0.59 (step @p273 :rule reordering :premises (@p272) :args ((or @t158 @t157 @t160))) % 0.40/0.59 (step @p274 :rule chain_m_resolution :premises (@p273 @p271 @p266) :args (@t160 @t154 (@list @t155 @t152))) % 0.40/0.59 (assume-push @p281 @t142) % 0.40/0.59 (step @p276 :rule instantiate :premises (@p255) :args ((@list @t143))) % 0.40/0.59 (step-pop @p282 :rule scope :premises (@p276)) % 0.40/0.59 (step @p277 :rule process_scope :premises (@p282) :args (@t159)) % 0.40/0.59 (step @p279 :rule implies_elim :premises (@p277)) % 0.40/0.59 (step @p280 false :rule chain_m_resolution :premises (@p279 @p274 @p255) :args (false (@list true false) (@list @t159 @t142))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------