%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU805^2 : 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 : n002.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 08:53:16 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SEU805^2 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n002.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:52:48 EDT 2026 % 0.18/0.35 % CPUTime : % 0.34/0.50 %----Proving TH0 % 0.39/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-const tptp.emptyset $$unsorted) % 0.39/0.62 (declare-const tptp.disjointsetsI1 Bool) % 0.39/0.62 (declare-const tptp.nonemptyE1 Bool) % 0.39/0.62 (declare-const tptp.foundationAx Bool) % 0.39/0.62 (declare-const tptp.binintersect (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.62 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.62 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.39/0.62 (define @t1 () (@var "A" $$unsorted)) % 0.39/0.62 (define @t2 () (@var "Xx" $$unsorted)) % 0.39/0.62 (define @t3 () (_ tptp.in @t2)) % 0.39/0.62 (define @t4 () (_ @t3 @t1)) % 0.39/0.62 (define @t5 () (@var "B" $$unsorted)) % 0.39/0.62 (define @t6 () (_ @t3 @t5)) % 0.39/0.62 (define @t7 () (and @t6 @t4)) % 0.39/0.62 (define @t8 () (@list @t2)) % 0.39/0.62 (define @t9 () (exists @t8 @t7)) % 0.39/0.62 (define @t10 () (not @t9)) % 0.39/0.62 (define @t11 () (_ (_ tptp.in @t5) @t1)) % 0.39/0.62 (define @t12 () (and @t11 @t10)) % 0.39/0.62 (define @t13 () (@list @t5)) % 0.39/0.62 (define @t14 () (exists @t13 @t12)) % 0.39/0.62 (define @t15 () (exists @t8 @t4)) % 0.39/0.62 (define @t16 () (=> @t15 @t14)) % 0.39/0.62 (define @t17 () (@list @t1)) % 0.39/0.62 (define @t18 () (forall @t17 @t16)) % 0.39/0.62 (define @t19 () (= tptp.foundationAx @t18)) % 0.39/0.62 (define @t20 () (_ tptp.nonempty @t1)) % 0.39/0.62 (define @t21 () (=> @t20 @t15)) % 0.39/0.62 (define @t22 () (forall @t17 @t21)) % 0.39/0.62 (define @t23 () (= tptp.nonemptyE1 @t22)) % 0.39/0.62 (define @t24 () (_ (_ tptp.binintersect @t1) @t5)) % 0.39/0.62 (define @t25 () (and @t4 @t6)) % 0.39/0.62 (define @t26 () (exists @t8 @t25)) % 0.39/0.62 (define @t27 () (not @t26)) % 0.39/0.62 (define @t28 () (=> @t27 (= @t24 tptp.emptyset))) % 0.39/0.62 (define @t29 () (@list @t1 @t5)) % 0.39/0.62 (define @t30 () (forall @t29 @t28)) % 0.39/0.62 (define @t31 () (= tptp.disjointsetsI1 @t30)) % 0.39/0.62 (define @t32 () (@var "X" $$unsorted)) % 0.39/0.62 (define @t33 () (_ (_ tptp.binintersect @t32) @t1)) % 0.39/0.62 (define @t34 () (_ (_ tptp.in @t32) @t1)) % 0.39/0.62 (define @t35 () (and @t34 (= @t33 tptp.emptyset))) % 0.39/0.62 (define @t36 () (@list @t32)) % 0.39/0.62 (define @t37 () (exists @t36 @t35)) % 0.39/0.62 (define @t38 () (=> @t20 @t37)) % 0.39/0.62 (define @t39 () (forall @t17 @t38)) % 0.39/0.62 (define @t40 () (=> tptp.disjointsetsI1 @t39)) % 0.39/0.62 (define @t41 () (=> tptp.nonemptyE1 @t40)) % 0.39/0.62 (define @t42 () (=> tptp.foundationAx @t41)) % 0.39/0.62 (define @t43 () (not @t42)) % 0.39/0.62 (define @t44 () (not (= @t2 tptp.emptyset))) % 0.39/0.62 (define @t45 () (lambda @t8 @t44)) % 0.39/0.62 (define @t46 () (tptp.binintersect @t32 @t1)) % 0.39/0.62 (define @t47 () (tptp.in @t32 @t1)) % 0.39/0.62 (define @t48 () (not (forall @t36 (or (not @t47) (not (= tptp.emptyset @t46)))))) % 0.39/0.62 (define @t49 () (= tptp.emptyset @t1)) % 0.39/0.62 (define @t50 () (forall @t17 (or @t49 @t48))) % 0.39/0.62 (define @t51 () (tptp.binintersect @t1 @t5)) % 0.39/0.62 (define @t52 () (= tptp.emptyset @t24)) % 0.39/0.62 (define @t53 () (tptp.in @t2 @t5)) % 0.39/0.62 (define @t54 () (not @t53)) % 0.39/0.62 (define @t55 () (tptp.in @t2 @t1)) % 0.39/0.62 (define @t56 () (not @t55)) % 0.39/0.62 (define @t57 () (forall @t8 (or @t56 @t54))) % 0.39/0.62 (define @t58 () (not @t57)) % 0.39/0.62 (define @t59 () (or @t58 @t52)) % 0.39/0.62 (define @t60 () (not @t6)) % 0.39/0.62 (define @t61 () (not @t4)) % 0.39/0.62 (define @t62 () (or @t61 @t60)) % 0.39/0.62 (define @t63 () (forall @t8 (not @t25))) % 0.39/0.62 (define @t64 () (not @t63)) % 0.39/0.62 (define @t65 () (=> tptp.disjointsetsI1 @t50)) % 0.39/0.62 (define @t66 () (forall @t8 @t56)) % 0.39/0.62 (define @t67 () (not @t66)) % 0.39/0.62 (define @t68 () (not @t49)) % 0.39/0.62 (define @t69 () (not @t68)) % 0.39/0.62 (define @t70 () (forall @t8 @t61)) % 0.39/0.62 (define @t71 () (not @t70)) % 0.39/0.62 (define @t72 () (_ (lambda @t8 (not (= tptp.emptyset @t2))) @t1)) % 0.39/0.62 (define @t73 () (=> @t72 @t15)) % 0.39/0.62 (define @t74 () (forall @t17 @t73)) % 0.39/0.62 (define @t75 () (=> tptp.nonemptyE1 @t65)) % 0.39/0.62 (define @t76 () (forall @t8 (or @t54 @t56))) % 0.39/0.62 (define @t77 () (not @t76)) % 0.39/0.62 (define @t78 () (tptp.in @t5 @t1)) % 0.39/0.62 (define @t79 () (not (forall @t13 (or (not @t78) @t77)))) % 0.39/0.62 (define @t80 () (@var "BOUND_VARIABLE_7516" $$unsorted)) % 0.39/0.62 (define @t81 () (not (tptp.in @t80 @t1))) % 0.39/0.62 (define @t82 () (or @t81 @t79)) % 0.39/0.62 (define @t83 () (@list @t80)) % 0.39/0.62 (define @t84 () (forall @t83 @t82)) % 0.39/0.62 (define @t85 () (forall @t83 @t81)) % 0.39/0.62 (define @t86 () (or @t85 @t79)) % 0.39/0.62 (define @t87 () (not @t11)) % 0.39/0.62 (define @t88 () (or @t87 @t77)) % 0.39/0.62 (define @t89 () (and @t11 @t76)) % 0.39/0.62 (define @t90 () (forall @t13 (not @t89))) % 0.39/0.62 (define @t91 () (not @t90)) % 0.39/0.62 (define @t92 () (or @t60 @t61)) % 0.39/0.62 (define @t93 () (forall @t8 (not @t7))) % 0.39/0.62 (define @t94 () (not @t93)) % 0.39/0.62 (define @t95 () (=> tptp.foundationAx @t75)) % 0.39/0.62 (define @t96 () (= tptp.emptyset @t33)) % 0.39/0.62 (define @t97 () (not @t96)) % 0.39/0.62 (define @t98 () (not @t34)) % 0.39/0.62 (define @t99 () (or @t98 @t97)) % 0.39/0.62 (define @t100 () (and @t34 @t96)) % 0.39/0.62 (define @t101 () (forall @t36 (not @t100))) % 0.39/0.62 (define @t102 () (not @t101)) % 0.39/0.62 (define @t103 () (=> @t72 @t37)) % 0.39/0.62 (define @t104 () (forall @t17 @t103)) % 0.39/0.62 (define @t105 () (=> tptp.disjointsetsI1 @t104)) % 0.39/0.62 (define @t106 () (=> tptp.nonemptyE1 @t105)) % 0.39/0.62 (define @t107 () (=> tptp.foundationAx @t106)) % 0.39/0.62 (define @t108 () (@quantifiers_skolemize @t50 0)) % 0.39/0.62 (define @t109 () (forall @t36 (or (not (tptp.in @t32 @t108)) (not (= tptp.emptyset (tptp.binintersect @t32 @t108)))))) % 0.39/0.62 (define @t110 () (not @t109)) % 0.39/0.62 (define @t111 () (= tptp.emptyset @t108)) % 0.39/0.62 (define @t112 () (or @t111 @t110)) % 0.39/0.62 (define @t113 () (@list true)) % 0.39/0.62 (define @t114 () (@list @t112)) % 0.39/0.62 (define @t115 () (not (tptp.in @t2 @t108))) % 0.39/0.62 (define @t116 () (forall @t13 (or (not (tptp.in @t5 @t108)) (not (forall @t8 (or @t54 @t115)))))) % 0.39/0.62 (define @t117 () (@quantifiers_skolemize @t116 0)) % 0.39/0.62 (define @t118 () (forall @t8 @t115)) % 0.39/0.62 (define @t119 () (@quantifiers_skolemize @t118 0)) % 0.39/0.62 (define @t120 () (not @t118)) % 0.39/0.62 (define @t121 () (or @t111 @t120)) % 0.39/0.62 (define @t122 () (@list true false)) % 0.39/0.62 (define @t123 () (tptp.in @t119 @t108)) % 0.39/0.62 (define @t124 () (not @t123)) % 0.39/0.62 (define @t125 () (not @t124)) % 0.39/0.62 (define @t126 () (not @t116)) % 0.39/0.62 (define @t127 () (or @t124 @t126)) % 0.39/0.62 (define @t128 () (@list false false)) % 0.39/0.62 (define @t129 () (tptp.in @t117 @t108)) % 0.39/0.62 (define @t130 () (forall @t8 (or (not (tptp.in @t2 @t117)) @t115))) % 0.39/0.62 (define @t131 () (not @t130)) % 0.39/0.62 (define @t132 () (not @t129)) % 0.39/0.62 (define @t133 () (or @t132 @t131)) % 0.39/0.62 (define @t134 () (@list @t133)) % 0.39/0.62 (define @t135 () (= tptp.emptyset (tptp.binintersect @t117 @t108))) % 0.39/0.62 (define @t136 () (not @t135)) % 0.39/0.62 (define @t137 () (or @t132 @t136)) % 0.39/0.62 (define @t138 () (or @t131 @t135)) % 0.39/0.62 (define @t139 () (not @t138)) % 0.39/0.62 (define @t140 () (forall @t29 (or @t58 (= tptp.emptyset @t51)))) % 0.39/0.62 (assume @p1 @t19) % 0.39/0.62 (assume @p2 @t23) % 0.39/0.62 (assume @p3 @t31) % 0.39/0.62 (assume @p4 @t43) % 0.39/0.62 (assume @p5 true) % 0.39/0.62 (step @p6 (= tptp.nonempty @t45) :rule refl :args (@t45)) % 0.39/0.62 (step @p7 :rule refl :args (@t50)) % 0.39/0.62 (step @p8 :rule refl :args (@t51)) % 0.39/0.62 (step @p9 :rule refl :args (@t24)) % 0.39/0.62 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t24 @t51))) % 0.39/0.62 (step @p11 :rule symm :premises (@p10)) % 0.39/0.62 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.39/0.62 (step @p13 :rule refl :args (tptp.emptyset)) % 0.39/0.62 (step @p14 :rule cong :premises (@p13 @p12) :args (@t52)) % 0.39/0.62 (step @p15 :rule refl :args (@t58)) % 0.39/0.62 (step @p16 :rule nary_cong :premises (@p15 @p14) :args (@t59)) % 0.39/0.62 (step @p17 :rule cong :premises (@p16) :args ((forall @t29 @t59))) % 0.39/0.62 (step @p18 :rule bool-impl-elim :args (@t57 @t52)) % 0.39/0.62 (step @p19 :rule cong :premises (@p18) :args ((forall @t29 (=> @t57 @t52)))) % 0.39/0.62 (step @p20 :rule trans :premises (@p19 @p17)) % 0.39/0.62 (step @p21 :rule eq-symm :args (@t24 tptp.emptyset)) % 0.39/0.62 (step @p22 :rule bool-double-not-elim :args (@t57)) % 0.39/0.62 (step @p23 :rule refl :args (@t53)) % 0.39/0.62 (step @p24 :rule refl :args (@t6)) % 0.39/0.62 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t6 @t53))) % 0.39/0.62 (step @p26 :rule symm :premises (@p25)) % 0.39/0.62 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.39/0.62 (step @p28 :rule cong :premises (@p27) :args (@t60)) % 0.39/0.62 (step @p29 :rule refl :args (@t55)) % 0.39/0.62 (step @p30 :rule refl :args (@t4)) % 0.39/0.62 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t4 @t55))) % 0.39/0.62 (step @p32 :rule symm :premises (@p31)) % 0.39/0.62 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.39/0.62 (step @p34 :rule cong :premises (@p33) :args (@t61)) % 0.39/0.62 (step @p35 :rule nary_cong :premises (@p34 @p28) :args (@t62)) % 0.39/0.62 (step @p36 :rule cong :premises (@p35) :args ((forall @t8 @t62))) % 0.39/0.62 (step @p37 :rule bool-and-de-morgan :args (@t4 @t6 true)) % 0.39/0.62 (step @p38 :rule cong :premises (@p37) :args (@t63)) % 0.39/0.62 (step @p39 :rule trans :premises (@p38 @p36)) % 0.39/0.62 (step @p40 :rule cong :premises (@p39) :args (@t64)) % 0.39/0.62 (step @p41 :rule exists-elim :args ((= @t26 @t64))) % 0.39/0.62 (step @p42 :rule trans :premises (@p41 @p40)) % 0.39/0.62 (step @p43 :rule cong :premises (@p42) :args (@t27)) % 0.39/0.62 (step @p44 :rule trans :premises (@p43 @p22)) % 0.39/0.62 (step @p45 :rule cong :premises (@p44 @p21) :args (@t28)) % 0.39/0.62 (step @p46 :rule cong :premises (@p45) :args (@t30)) % 0.39/0.62 (step @p47 :rule trans :premises (@p46 @p20)) % 0.39/0.62 (step @p48 :rule refl :args (tptp.disjointsetsI1)) % 0.39/0.62 (step @p49 :rule cong :premises (@p48 @p47) :args (@t31)) % 0.39/0.62 (step @p50 :rule eq_resolve :premises (@p3 @p49)) % 0.39/0.62 (step @p51 :rule cong :premises (@p50 @p7) :args (@t65)) % 0.39/0.62 (step @p52 :rule refl :args (@t67)) % 0.39/0.62 (step @p53 :rule bool-double-not-elim :args (@t49)) % 0.39/0.62 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((or @t69 @t67))) % 0.39/0.62 (step @p55 :rule bool-impl-elim :args (@t68 @t67)) % 0.39/0.62 (step @p56 :rule trans :premises (@p55 @p54)) % 0.39/0.62 (step @p57 :rule cong :premises (@p56) :args ((forall @t17 (=> @t68 @t67)))) % 0.39/0.62 (step @p58 :rule cong :premises (@p34) :args (@t70)) % 0.39/0.62 (step @p59 :rule cong :premises (@p58) :args (@t71)) % 0.39/0.62 (step @p60 :rule exists-elim :args ((= @t15 @t71))) % 0.39/0.62 (step @p61 :rule trans :premises (@p60 @p59)) % 0.39/0.62 (step @p62 :rule beta-reduce :args ((= @t72 @t68))) % 0.39/0.62 (step @p63 :rule cong :premises (@p62 @p61) :args (@t73)) % 0.39/0.62 (step @p64 :rule cong :premises (@p63) :args (@t74)) % 0.39/0.62 (step @p65 :rule trans :premises (@p64 @p57)) % 0.39/0.62 (step @p66 :rule refl :args (tptp.nonemptyE1)) % 0.39/0.62 (step @p67 :rule cong :premises (@p66 @p65) :args ((= tptp.nonemptyE1 @t74))) % 0.39/0.62 (step @p68 :rule refl :args (@t15)) % 0.39/0.62 (step @p69 :rule refl :args (@t1)) % 0.39/0.62 (step @p70 :rule eq-symm :args (@t2 tptp.emptyset)) % 0.39/0.62 (step @p71 :rule cong :premises (@p70) :args (@t44)) % 0.39/0.62 (step @p72 :rule cong :premises (@p71) :args (@t45)) % 0.39/0.62 (step @p73 :rule trans :premises (@p6 @p72)) % 0.39/0.62 (step @p74 :rule ho_cong :premises (@p73 @p69)) % 0.39/0.62 (step @p75 :rule cong :premises (@p74 @p68) :args (@t21)) % 0.39/0.62 (step @p76 :rule cong :premises (@p75) :args (@t22)) % 0.39/0.62 (step @p77 :rule cong :premises (@p66 @p76) :args (@t23)) % 0.39/0.62 (step @p78 :rule trans :premises (@p77 @p67)) % 0.39/0.62 (step @p79 :rule eq_resolve :premises (@p2 @p78)) % 0.39/0.62 (step @p80 :rule cong :premises (@p79 @p51) :args (@t75)) % 0.39/0.62 (step @p81 :rule quant-merge-prenex :args ((= (forall @t17 @t84) (forall (@list @t1 @t80) @t82)))) % 0.39/0.62 (step @p82 :rule refl :args (@t79)) % 0.39/0.62 (step @p83 :rule alpha_equiv :args (@t85 (@list @t80) (@list @t2))) % 0.39/0.62 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t86)) % 0.39/0.62 (step @p85 :rule quant-miniscope-or :args ((= @t84 @t86))) % 0.39/0.62 (step @p86 :rule trans :premises (@p85 @p84)) % 0.39/0.62 (step @p87 :rule symm :premises (@p86)) % 0.39/0.62 (step @p88 :rule cong :premises (@p87) :args ((forall @t17 (or @t66 @t79)))) % 0.39/0.62 (step @p89 :rule trans :premises (@p88 @p81)) % 0.39/0.62 (step @p90 :rule bool-double-not-elim :args (@t66)) % 0.39/0.62 (step @p91 :rule nary_cong :premises (@p90 @p82) :args ((or (not @t67) @t79))) % 0.39/0.62 (step @p92 :rule bool-impl-elim :args (@t67 @t79)) % 0.39/0.62 (step @p93 :rule trans :premises (@p92 @p91)) % 0.39/0.62 (step @p94 :rule cong :premises (@p93) :args ((forall @t17 (=> @t67 @t79)))) % 0.39/0.62 (step @p95 :rule trans :premises (@p94 @p89)) % 0.39/0.62 (step @p96 :rule refl :args (@t77)) % 0.39/0.62 (step @p97 :rule refl :args (@t78)) % 0.39/0.62 (step @p98 :rule refl :args (@t11)) % 0.39/0.62 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t11 @t78))) % 0.39/0.62 (step @p100 :rule symm :premises (@p99)) % 0.39/0.62 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.39/0.62 (step @p102 :rule cong :premises (@p101) :args (@t87)) % 0.39/0.62 (step @p103 :rule nary_cong :premises (@p102 @p96) :args (@t88)) % 0.39/0.62 (step @p104 :rule cong :premises (@p103) :args ((forall @t13 @t88))) % 0.39/0.62 (step @p105 :rule bool-and-de-morgan :args (@t11 @t76 true)) % 0.39/0.62 (step @p106 :rule cong :premises (@p105) :args (@t90)) % 0.39/0.62 (step @p107 :rule trans :premises (@p106 @p104)) % 0.39/0.62 (step @p108 :rule cong :premises (@p107) :args (@t91)) % 0.39/0.62 (step @p109 :rule exists-elim :args ((= (exists @t13 @t89) @t91))) % 0.39/0.62 (step @p110 :rule trans :premises (@p109 @p108)) % 0.39/0.62 (step @p111 :rule bool-double-not-elim :args (@t76)) % 0.39/0.62 (step @p112 :rule nary_cong :premises (@p28 @p34) :args (@t92)) % 0.39/0.62 (step @p113 :rule cong :premises (@p112) :args ((forall @t8 @t92))) % 0.39/0.62 (step @p114 :rule bool-and-de-morgan :args (@t6 @t4 true)) % 0.39/0.62 (step @p115 :rule cong :premises (@p114) :args (@t93)) % 0.39/0.62 (step @p116 :rule trans :premises (@p115 @p113)) % 0.39/0.62 (step @p117 :rule cong :premises (@p116) :args (@t94)) % 0.39/0.62 (step @p118 :rule exists-elim :args ((= @t9 @t94))) % 0.39/0.62 (step @p119 :rule trans :premises (@p118 @p117)) % 0.39/0.62 (step @p120 :rule cong :premises (@p119) :args (@t10)) % 0.39/0.62 (step @p121 :rule trans :premises (@p120 @p111)) % 0.39/0.62 (step @p122 :rule refl :args (@t11)) % 0.39/0.62 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t12)) % 0.39/0.62 (step @p124 :rule cong :premises (@p123) :args (@t14)) % 0.39/0.62 (step @p125 :rule trans :premises (@p124 @p110)) % 0.39/0.62 (step @p126 :rule cong :premises (@p61 @p125) :args (@t16)) % 0.39/0.62 (step @p127 :rule cong :premises (@p126) :args (@t18)) % 0.39/0.62 (step @p128 :rule trans :premises (@p127 @p95)) % 0.39/0.62 (step @p129 :rule refl :args (tptp.foundationAx)) % 0.39/0.62 (step @p130 :rule cong :premises (@p129 @p128) :args (@t19)) % 0.39/0.62 (step @p131 :rule eq_resolve :premises (@p1 @p130)) % 0.39/0.62 (step @p132 :rule cong :premises (@p131 @p80) :args (@t95)) % 0.39/0.62 (step @p133 :rule cong :premises (@p132) :args ((not @t95))) % 0.39/0.62 (step @p134 :rule refl :args (@t48)) % 0.39/0.62 (step @p135 :rule nary_cong :premises (@p53 @p134) :args ((or @t69 @t48))) % 0.39/0.62 (step @p136 :rule bool-impl-elim :args (@t68 @t48)) % 0.39/0.62 (step @p137 :rule trans :premises (@p136 @p135)) % 0.39/0.62 (step @p138 :rule cong :premises (@p137) :args ((forall @t17 (=> @t68 @t48)))) % 0.39/0.62 (step @p139 :rule refl :args (@t46)) % 0.39/0.62 (step @p140 :rule refl :args (@t33)) % 0.39/0.62 (step @p141 :rule cong :premises (@p140 @p139) :args ((= @t33 @t46))) % 0.39/0.62 (step @p142 :rule symm :premises (@p141)) % 0.39/0.62 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 0.39/0.62 (step @p144 :rule cong :premises (@p13 @p143) :args (@t96)) % 0.39/0.62 (step @p145 :rule cong :premises (@p144) :args (@t97)) % 0.39/0.62 (step @p146 :rule refl :args (@t47)) % 0.39/0.62 (step @p147 :rule refl :args (@t34)) % 0.39/0.62 (step @p148 :rule cong :premises (@p147 @p146) :args ((= @t34 @t47))) % 0.39/0.62 (step @p149 :rule symm :premises (@p148)) % 0.39/0.62 (step @p150 :rule eq_resolve :premises (@p147 @p149)) % 0.39/0.62 (step @p151 :rule cong :premises (@p150) :args (@t98)) % 0.39/0.62 (step @p152 :rule nary_cong :premises (@p151 @p145) :args (@t99)) % 0.39/0.62 (step @p153 :rule cong :premises (@p152) :args ((forall @t36 @t99))) % 0.39/0.62 (step @p154 :rule bool-and-de-morgan :args (@t34 @t96 true)) % 0.39/0.62 (step @p155 :rule cong :premises (@p154) :args (@t101)) % 0.39/0.62 (step @p156 :rule trans :premises (@p155 @p153)) % 0.39/0.62 (step @p157 :rule cong :premises (@p156) :args (@t102)) % 0.39/0.62 (step @p158 :rule exists-elim :args ((= (exists @t36 @t100) @t102))) % 0.39/0.62 (step @p159 :rule trans :premises (@p158 @p157)) % 0.39/0.62 (step @p160 :rule eq-symm :args (@t33 tptp.emptyset)) % 0.39/0.62 (step @p161 :rule refl :args (@t34)) % 0.39/0.62 (step @p162 :rule nary_cong :premises (@p161 @p160) :args (@t35)) % 0.39/0.62 (step @p163 :rule cong :premises (@p162) :args (@t37)) % 0.39/0.62 (step @p164 :rule trans :premises (@p163 @p159)) % 0.39/0.62 (step @p165 :rule cong :premises (@p62 @p164) :args (@t103)) % 0.39/0.62 (step @p166 :rule cong :premises (@p165) :args (@t104)) % 0.39/0.62 (step @p167 :rule trans :premises (@p166 @p138)) % 0.39/0.62 (step @p168 :rule cong :premises (@p48 @p167) :args (@t105)) % 0.39/0.62 (step @p169 :rule cong :premises (@p66 @p168) :args (@t106)) % 0.39/0.62 (step @p170 :rule cong :premises (@p129 @p169) :args (@t107)) % 0.39/0.62 (step @p171 :rule cong :premises (@p170) :args ((not @t107))) % 0.39/0.62 (step @p172 :rule refl :args (@t37)) % 0.39/0.62 (step @p173 :rule cong :premises (@p74 @p172) :args (@t38)) % 0.39/0.62 (step @p174 :rule cong :premises (@p173) :args (@t39)) % 0.39/0.62 (step @p175 :rule cong :premises (@p48 @p174) :args (@t40)) % 0.39/0.62 (step @p176 :rule cong :premises (@p66 @p175) :args (@t41)) % 0.39/0.62 (step @p177 :rule cong :premises (@p129 @p176) :args (@t42)) % 0.39/0.62 (step @p178 :rule cong :premises (@p177) :args (@t43)) % 0.39/0.62 (step @p179 :rule trans :premises (@p178 @p171)) % 0.39/0.62 (step @p180 :rule trans :premises (@p179 @p133)) % 0.39/0.62 (step @p181 :rule eq_resolve :premises (@p4 @p180)) % 0.39/0.62 (step @p182 :rule not_implies_elim2 :premises (@p181)) % 0.39/0.62 (step @p183 :rule not_implies_elim2 :premises (@p182)) % 0.39/0.62 (step @p184 :rule not_implies_elim1 :premises (@p183)) % 0.39/0.62 (step @p185 :rule not_implies_elim2 :premises (@p183)) % 0.39/0.62 (step @p186 :rule skolemize :premises (@p185)) % 0.39/0.62 (step @p187 :rule bool-double-not-elim :args (@t109)) % 0.39/0.62 (step @p188 :rule refl :args (@t112)) % 0.39/0.62 (step @p189 :rule nary_cong :premises (@p188 @p187) :args ((or @t112 (not @t110)))) % 0.39/0.62 (step @p190 :rule cnf_or_neg :args (@t112 1)) % 0.39/0.62 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.39/0.62 (step @p192 :rule reordering :premises (@p191) :args ((or @t109 @t112))) % 0.39/0.62 (step @p193 :rule chain_m_resolution :premises (@p192 @p186) :args (@t109 @t113 @t114)) % 0.39/0.62 (step @p194 :rule instantiate :premises (@p193) :args ((@list @t117))) % 0.39/0.62 (step @p195 :rule not_implies_elim1 :premises (@p181)) % 0.39/0.62 (step @p196 :rule instantiate :premises (@p195) :args ((@list @t108 @t119))) % 0.36/0.62 (step @p197 :rule not_implies_elim1 :premises (@p182)) % 0.36/0.62 (step @p198 :rule instantiate :premises (@p197) :args ((@list @t108))) % 0.36/0.62 (step @p199 :rule cnf_or_neg :args (@t112 0)) % 0.36/0.62 (step @p200 :rule chain_m_resolution :premises (@p199 @p186) :args ((not @t111) @t113 @t114)) % 0.36/0.62 (step @p201 :rule cnf_or_pos :args (@t121)) % 0.36/0.62 (step @p202 :rule reordering :premises (@p201) :args ((or @t111 @t120 (not @t121)))) % 0.36/0.62 (step @p203 :rule chain_m_resolution :premises (@p202 @p200 @p198) :args (@t120 @t122 (@list @t111 @t121))) % 0.36/0.62 (step @p204 :rule refl :args (@t123)) % 0.36/0.62 (step @p205 :rule bool-double-not-elim :args (@t118)) % 0.36/0.62 (step @p206 :rule nary_cong :premises (@p205 @p204) :args ((or (not @t120) @t123))) % 0.36/0.62 (step @p207 :rule bool-double-not-elim :args (@t123)) % 0.36/0.62 (step @p208 :rule refl :args (@t120)) % 0.36/0.62 (step @p209 :rule cong :premises (@p208 @p207) :args ((=> @t120 @t125))) % 0.36/0.62 (assume-push @p247 @t120) % 0.36/0.62 (step @p211 :rule skolemize :premises (@p203)) % 0.36/0.62 (step-pop @p248 :rule scope :premises (@p211)) % 0.36/0.62 (step @p212 :rule process_scope :premises (@p248) :args (@t125)) % 0.36/0.62 (step @p214 :rule eq_resolve :premises (@p212 @p209)) % 0.36/0.62 (step @p215 :rule implies_elim :premises (@p214)) % 0.36/0.62 (step @p216 :rule eq_resolve :premises (@p215 @p206)) % 0.36/0.62 (step @p217 :rule chain_m_resolution :premises (@p216 @p203) :args (@t123 @t113 (@list @t118))) % 0.36/0.62 (step @p218 :rule cnf_or_pos :args (@t127)) % 0.36/0.62 (step @p219 :rule reordering :premises (@p218) :args ((or @t124 @t126 (not @t127)))) % 0.36/0.62 (step @p220 :rule chain_m_resolution :premises (@p219 @p217 @p196) :args (@t126 @t128 (@list @t123 @t127))) % 0.36/0.62 (step @p221 :rule skolemize :premises (@p220)) % 0.36/0.62 (step @p222 :rule bool-double-not-elim :args (@t129)) % 0.36/0.62 (step @p223 :rule refl :args (@t133)) % 0.36/0.62 (step @p224 :rule nary_cong :premises (@p223 @p222) :args ((or @t133 (not @t132)))) % 0.36/0.62 (step @p225 :rule cnf_or_neg :args (@t133 0)) % 0.36/0.62 (step @p226 :rule eq_resolve :premises (@p225 @p224)) % 0.36/0.62 (step @p227 :rule reordering :premises (@p226) :args ((or @t129 @t133))) % 0.36/0.62 (step @p228 :rule chain_m_resolution :premises (@p227 @p221) :args (@t129 @t113 @t134)) % 0.36/0.62 (step @p229 :rule cnf_or_pos :args (@t137)) % 0.36/0.62 (step @p230 :rule reordering :premises (@p229) :args ((or @t132 @t136 (not @t137)))) % 0.36/0.62 (step @p231 :rule chain_m_resolution :premises (@p230 @p228 @p194) :args (@t136 @t128 (@list @t129 @t137))) % 0.36/0.62 (step @p232 :rule bool-double-not-elim :args (@t130)) % 0.36/0.62 (step @p233 :rule nary_cong :premises (@p223 @p232) :args ((or @t133 (not @t131)))) % 0.36/0.62 (step @p234 :rule cnf_or_neg :args (@t133 1)) % 0.36/0.62 (step @p235 :rule eq_resolve :premises (@p234 @p233)) % 0.36/0.62 (step @p236 :rule reordering :premises (@p235) :args ((or @t130 @t133))) % 0.36/0.62 (step @p237 :rule chain_m_resolution :premises (@p236 @p221) :args (@t130 @t113 @t134)) % 0.36/0.62 (step @p238 :rule cnf_or_pos :args (@t138)) % 0.36/0.62 (step @p239 :rule reordering :premises (@p238) :args ((or @t131 @t135 @t139))) % 0.36/0.62 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p231) :args (@t139 (@list false true) (@list @t130 @t135))) % 0.36/0.62 (assume-push @p249 @t140) % 0.36/0.62 (step @p242 :rule instantiate :premises (@p184) :args ((@list @t117 @t108))) % 0.36/0.62 (step-pop @p250 :rule scope :premises (@p242)) % 0.36/0.62 (step @p243 :rule process_scope :premises (@p250) :args (@t138)) % 0.36/0.62 (step @p245 :rule implies_elim :premises (@p243)) % 0.36/0.62 (step @p246 false :rule chain_m_resolution :premises (@p245 @p240 @p184) :args (false @t122 (@list @t138 @t140))) % 0.36/0.62 ) % 0.36/0.62 % SZS output end Proof % 0.36/0.62 % cvc5 exiting %------------------------------------------------------------------------------