%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU702^2 : 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 : n021.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 08:52:47 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 : SEU702^2 : 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 % 0.15/0.34 % Computer : n021.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 17:48:50 EDT 2026 % 0.15/0.34 % CPUTime : % 0.31/0.49 %----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 $$unsorted 0) % 0.36/0.57 (declare-const tptp.dsetconstrI Bool) % 0.36/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.36/0.57 (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 "Xz" $$unsorted)) % 0.36/0.57 (define @t19 () (@var "Xphi" Bool)) % 0.36/0.57 (define @t20 () (not @t19)) % 0.36/0.57 (define @t21 () (and @t20 (= @t18 @t1))) % 0.36/0.57 (define @t22 () (and @t19 (= @t18 @t9))) % 0.36/0.57 (define @t23 () (or @t22 @t21)) % 0.36/0.57 (define @t24 () (@list @t18)) % 0.36/0.57 (define @t25 () (lambda @t24 @t23)) % 0.36/0.57 (define @t26 () (=> @t19 (_ @t10 (_ @t7 @t25)))) % 0.36/0.57 (define @t27 () (_ (_ tptp.in @t1) @t6)) % 0.36/0.57 (define @t28 () (=> @t27 @t26)) % 0.36/0.57 (define @t29 () (forall @t4 @t28)) % 0.36/0.57 (define @t30 () (=> @t14 @t29)) % 0.36/0.57 (define @t31 () (@list @t6 @t19 @t9)) % 0.36/0.57 (define @t32 () (forall @t31 @t30)) % 0.36/0.57 (define @t33 () (=> tptp.dsetconstrI @t32)) % 0.36/0.57 (define @t34 () (not @t33)) % 0.36/0.57 (define @t35 () (= @t9 @t18)) % 0.36/0.57 (define @t36 () (tptp.in @t9 (tptp.dsetconstr @t6 (lambda @t24 @t35)))) % 0.36/0.57 (define @t37 () (@var "BOUND_VARIABLE_7508" $$unsorted)) % 0.36/0.57 (define @t38 () (not (tptp.in @t37 @t6))) % 0.36/0.57 (define @t39 () (tptp.in @t9 @t6)) % 0.36/0.57 (define @t40 () (not @t39)) % 0.36/0.57 (define @t41 () (or @t40 @t38 @t36)) % 0.36/0.57 (define @t42 () (@list @t6 @t9 @t37)) % 0.36/0.57 (define @t43 () (forall @t42 @t41)) % 0.36/0.57 (define @t44 () (_ @t2 @t1)) % 0.36/0.57 (define @t45 () (lambda @t4 @t44)) % 0.36/0.57 (define @t46 () (tptp.dsetconstr @t6 @t45)) % 0.36/0.57 (define @t47 () (tptp.in @t9 @t46)) % 0.36/0.57 (define @t48 () (_ @t2 @t9)) % 0.36/0.57 (define @t49 () (not @t48)) % 0.36/0.57 (define @t50 () (or @t40 @t49 @t47)) % 0.36/0.57 (define @t51 () (not @t12)) % 0.36/0.57 (define @t52 () (not @t14)) % 0.36/0.57 (define @t53 () (or @t52 @t51 @t11)) % 0.36/0.57 (define @t54 () (=> tptp.dsetconstrI @t43)) % 0.36/0.57 (define @t55 () (= @t18 @t37)) % 0.36/0.57 (define @t56 () (not true)) % 0.36/0.57 (define @t57 () (and @t56 @t55)) % 0.36/0.57 (define @t58 () (and true @t35)) % 0.36/0.57 (define @t59 () (or @t58 @t57)) % 0.36/0.57 (define @t60 () (lambda @t24 @t59)) % 0.36/0.57 (define @t61 () (tptp.dsetconstr @t6 @t60)) % 0.36/0.57 (define @t62 () (tptp.in @t9 @t61)) % 0.36/0.57 (define @t63 () (or @t40 @t56 @t38 @t62)) % 0.36/0.57 (define @t64 () (and @t19 @t35)) % 0.36/0.57 (define @t65 () (tptp.in @t9 (tptp.dsetconstr @t6 (lambda @t24 (or @t64 (and @t20 @t55)))))) % 0.36/0.57 (define @t66 () (@list @t19)) % 0.36/0.57 (define @t67 () (or @t20 @t40 @t20 @t38 @t65)) % 0.36/0.57 (define @t68 () (or @t40 @t20 @t38 @t65)) % 0.36/0.57 (define @t69 () (forall @t66 @t68)) % 0.36/0.57 (define @t70 () (forall @t42 @t69)) % 0.36/0.57 (define @t71 () (forall (@list @t6 @t9 @t37 @t19) @t68)) % 0.36/0.57 (define @t72 () (@list @t6 @t19 @t9 @t37)) % 0.36/0.57 (define @t73 () (and @t20 (= @t37 @t18))) % 0.36/0.57 (define @t74 () (or @t64 @t73)) % 0.36/0.57 (define @t75 () (lambda @t24 @t74)) % 0.36/0.57 (define @t76 () (tptp.dsetconstr @t6 @t75)) % 0.36/0.57 (define @t77 () (tptp.in @t9 @t76)) % 0.36/0.57 (define @t78 () (or @t40 @t20 @t38 @t77)) % 0.36/0.57 (define @t79 () (or @t38 @t77)) % 0.36/0.57 (define @t80 () (or @t40 @t20 @t79)) % 0.36/0.57 (define @t81 () (forall @t72 @t80)) % 0.36/0.57 (define @t82 () (@list @t37)) % 0.36/0.57 (define @t83 () (forall @t82 @t80)) % 0.36/0.57 (define @t84 () (forall @t82 @t79)) % 0.36/0.57 (define @t85 () (or @t40 @t20 @t84)) % 0.36/0.57 (define @t86 () (lambda @t24 (or @t64 (and @t20 (= @t1 @t18))))) % 0.36/0.57 (define @t87 () (tptp.dsetconstr @t6 @t86)) % 0.36/0.57 (define @t88 () (tptp.in @t9 @t87)) % 0.36/0.57 (define @t89 () (tptp.in @t1 @t6)) % 0.36/0.57 (define @t90 () (forall @t4 (or (not @t89) @t88))) % 0.36/0.57 (define @t91 () (or @t52 @t20 @t90)) % 0.36/0.57 (define @t92 () (or @t20 @t90)) % 0.36/0.57 (define @t93 () (_ @t7 @t86)) % 0.36/0.57 (define @t94 () (_ @t10 @t93)) % 0.36/0.57 (define @t95 () (not @t27)) % 0.36/0.57 (define @t96 () (or @t95 @t94)) % 0.36/0.57 (define @t97 () (forall @t4 @t96)) % 0.36/0.57 (define @t98 () (or @t20 @t97)) % 0.36/0.57 (define @t99 () (or @t20 @t96)) % 0.36/0.57 (define @t100 () (or @t95 @t20 @t94)) % 0.36/0.57 (define @t101 () (=> @t19 @t94)) % 0.36/0.57 (define @t102 () (@quantifiers_skolemize @t43 1)) % 0.36/0.57 (define @t103 () (lambda @t24 (= @t18 @t102))) % 0.36/0.57 (define @t104 () (@purify @t103)) % 0.36/0.57 (define @t105 () (@quantifiers_skolemize @t43 0)) % 0.36/0.57 (define @t106 () (tptp.in @t102 (tptp.dsetconstr @t105 @t104))) % 0.36/0.57 (define @t107 () (not (tptp.in (@quantifiers_skolemize @t43 2) @t105))) % 0.36/0.57 (define @t108 () (tptp.in @t102 @t105)) % 0.36/0.57 (define @t109 () (not @t108)) % 0.36/0.57 (define @t110 () (or @t109 @t107 @t106)) % 0.36/0.57 (define @t111 () (not @t110)) % 0.36/0.57 (define @t112 () (not @t43)) % 0.36/0.57 (define @t113 () (tptp.dsetconstr @t105 @t103)) % 0.36/0.57 (define @t114 () (tptp.in @t102 @t113)) % 0.36/0.57 (define @t115 () (or @t109 @t107 @t114)) % 0.36/0.57 (define @t116 () (not @t115)) % 0.36/0.57 (define @t117 () (lambda @t24 (= @t102 @t18))) % 0.36/0.57 (define @t118 () (tptp.dsetconstr @t105 @t117)) % 0.36/0.57 (define @t119 () (tptp.in @t102 @t118)) % 0.36/0.57 (define @t120 () (or @t109 @t107 @t119)) % 0.36/0.57 (define @t121 () (not @t120)) % 0.36/0.57 (define @t122 () (@list true)) % 0.36/0.57 (define @t123 () (@list @t110)) % 0.36/0.57 (define @t124 () (or @t109 @t106)) % 0.36/0.57 (define @t125 () (not @t124)) % 0.36/0.57 (define @t126 () (_ @t104 @t102)) % 0.36/0.57 (define @t127 () (not @t126)) % 0.36/0.57 (define @t128 () (or @t109 @t127 @t106)) % 0.36/0.57 (define @t129 () (forall @t15 (or @t40 @t49 (tptp.in @t9 (tptp.dsetconstr @t6 @t2))))) % 0.36/0.57 (assume @p1 @t17) % 0.36/0.57 (assume @p2 @t34) % 0.36/0.57 (assume @p3 true) % 0.36/0.57 (step @p4 :rule refl :args (@t43)) % 0.36/0.57 (step @p5 :rule lambda-elim :args ((= @t45 @t2))) % 0.36/0.57 (step @p6 :rule refl :args (@t6)) % 0.36/0.57 (step @p7 :rule cong :premises (@p6 @p5) :args (@t46)) % 0.36/0.57 (step @p8 :rule refl :args (@t9)) % 0.36/0.57 (step @p9 :rule cong :premises (@p8 @p7) :args (@t47)) % 0.36/0.57 (step @p10 :rule refl :args (@t49)) % 0.36/0.57 (step @p11 :rule refl :args (@t40)) % 0.36/0.57 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t50)) % 0.36/0.57 (step @p13 :rule cong :premises (@p12) :args ((forall @t15 @t50))) % 0.36/0.57 (step @p14 :rule refl :args ((tptp.in @t9 @t8))) % 0.36/0.57 (step @p15 :rule refl :args ((tptp.dsetconstr @t6 @t5))) % 0.36/0.57 (step @p16 :rule refl :args (@t44)) % 0.36/0.57 (step @p17 :rule cong :premises (@p16) :args (@t45)) % 0.36/0.57 (step @p18 :rule refl :args (@t6)) % 0.36/0.57 (step @p19 :rule cong :premises (@p18 @p17) :args (@t46)) % 0.36/0.57 (step @p20 :rule trans :premises (@p19 @p15)) % 0.36/0.57 (step @p21 :rule refl :args (@t9)) % 0.36/0.57 (step @p22 :rule cong :premises (@p21 @p20) :args (@t47)) % 0.36/0.57 (step @p23 :rule trans :premises (@p22 @p14)) % 0.36/0.57 (step @p24 :rule refl :args (@t10)) % 0.36/0.57 (step @p25 :rule ho_cong :premises (@p24 @p20)) % 0.36/0.57 (step @p26 :rule cong :premises (@p25 @p23) :args ((= (_ @t10 @t46) @t47))) % 0.36/0.57 (step @p27 :rule symm :premises (@p26)) % 0.36/0.57 (step @p28 :rule refl :args (@t11)) % 0.36/0.57 (step @p29 :rule eq_resolve :premises (@p28 @p27)) % 0.36/0.57 (step @p30 :rule refl :args (@t7)) % 0.36/0.57 (step @p31 :rule ho_cong :premises (@p30 @p17)) % 0.36/0.57 (step @p32 :rule cong :premises (@p31 @p20) :args ((= (_ @t7 @t45) @t46))) % 0.36/0.57 (step @p33 :rule symm :premises (@p32)) % 0.36/0.57 (step @p34 :rule refl :args (@t8)) % 0.36/0.57 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.36/0.57 (step @p36 :rule refl :args (@t3)) % 0.36/0.57 (step @p37 :rule cong :premises (@p36 @p16) :args ((= @t3 @t44))) % 0.36/0.57 (step @p38 :rule symm :premises (@p37)) % 0.36/0.57 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.36/0.57 (step @p40 :rule cong :premises (@p39) :args (@t5)) % 0.36/0.57 (step @p41 :rule ho_cong :premises (@p30 @p40)) % 0.36/0.57 (step @p42 :rule trans :premises (@p41 @p35)) % 0.36/0.57 (step @p43 :rule ho_cong :premises (@p24 @p42)) % 0.36/0.57 (step @p44 :rule trans :premises (@p43 @p29)) % 0.36/0.57 (step @p45 :rule refl :args (@t48)) % 0.36/0.57 (step @p46 :rule refl :args (@t12)) % 0.36/0.57 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t12 @t48))) % 0.36/0.57 (step @p48 :rule symm :premises (@p47)) % 0.36/0.57 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.36/0.57 (step @p50 :rule cong :premises (@p49) :args (@t51)) % 0.36/0.57 (step @p51 :rule refl :args (@t39)) % 0.36/0.57 (step @p52 :rule refl :args (@t14)) % 0.36/0.57 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t14 @t39))) % 0.36/0.57 (step @p54 :rule symm :premises (@p53)) % 0.36/0.57 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.36/0.57 (step @p56 :rule cong :premises (@p55) :args (@t52)) % 0.36/0.57 (step @p57 :rule nary_cong :premises (@p56 @p50 @p44) :args (@t53)) % 0.36/0.57 (step @p58 :rule cong :premises (@p57) :args ((forall @t15 @t53))) % 0.36/0.57 (step @p59 :rule trans :premises (@p58 @p13)) % 0.36/0.57 (step @p60 :rule aci_norm :args ((= (or @t52 (or @t51 @t11)) @t53))) % 0.36/0.57 (step @p61 :rule bool-impl-elim :args (@t12 @t11)) % 0.36/0.57 (step @p62 :rule refl :args (@t52)) % 0.36/0.57 (step @p63 :rule nary_cong :premises (@p62 @p61) :args ((or @t52 @t13))) % 0.36/0.57 (step @p64 :rule trans :premises (@p63 @p60)) % 0.36/0.57 (step @p65 :rule bool-impl-elim :args (@t14 @t13)) % 0.36/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.36/0.57 (step @p67 :rule cong :premises (@p66) :args (@t16)) % 0.36/0.57 (step @p68 :rule trans :premises (@p67 @p59)) % 0.36/0.57 (step @p69 :rule refl :args (tptp.dsetconstrI)) % 0.36/0.57 (step @p70 :rule cong :premises (@p69 @p68) :args (@t17)) % 0.36/0.57 (step @p71 :rule eq_resolve :premises (@p1 @p70)) % 0.36/0.57 (step @p72 :rule cong :premises (@p71 @p4) :args (@t54)) % 0.36/0.57 (step @p73 :rule cong :premises (@p72) :args ((not @t54))) % 0.36/0.57 (step @p74 :rule aci_norm :args ((= (or @t40 false @t38 @t36) @t41))) % 0.36/0.57 (step @p75 :rule aci_norm :args ((= (or @t35 false) @t35))) % 0.36/0.57 (step @p76 :rule absorb :args ((= (and false @t55) false))) % 0.36/0.57 (step @p77 :rule refl :args (@t55)) % 0.36/0.57 (step @p78 :rule evaluate :args (@t56)) % 0.36/0.57 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t57)) % 0.36/0.57 (step @p80 :rule trans :premises (@p79 @p76)) % 0.36/0.57 (step @p81 :rule aci_norm :args ((= @t58 @t35))) % 0.36/0.57 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t59)) % 0.36/0.57 (step @p83 :rule trans :premises (@p82 @p75)) % 0.36/0.57 (step @p84 :rule cong :premises (@p83) :args (@t60)) % 0.36/0.57 (step @p85 :rule cong :premises (@p6 @p84) :args (@t61)) % 0.36/0.57 (step @p86 :rule cong :premises (@p8 @p85) :args (@t62)) % 0.36/0.57 (step @p87 :rule refl :args (@t38)) % 0.36/0.57 (step @p88 :rule nary_cong :premises (@p11 @p78 @p87 @p86) :args (@t63)) % 0.36/0.57 (step @p89 :rule trans :premises (@p88 @p74)) % 0.36/0.57 (step @p90 :rule cong :premises (@p89) :args ((forall @t42 @t63))) % 0.36/0.57 (step @p91 :rule quant-var-elim-eq :args ((= (forall @t66 (or (not (= @t19 true)) @t40 @t20 @t38 @t65)) @t63))) % 0.36/0.57 (step @p92 :rule refl :args (@t65)) % 0.36/0.57 (step @p93 :rule refl :args (@t38)) % 0.36/0.57 (step @p94 :rule refl :args (@t20)) % 0.36/0.57 (step @p95 :rule refl :args (@t40)) % 0.36/0.57 (step @p96 :rule bool-eq-true :args (@t19)) % 0.36/0.57 (step @p97 :rule symm :premises (@p96)) % 0.36/0.57 (step @p98 :rule cong :premises (@p97) :args (@t20)) % 0.36/0.57 (step @p99 :rule nary_cong :premises (@p98 @p95 @p94 @p93 @p92) :args (@t67)) % 0.36/0.57 (step @p100 :rule aci_norm :args ((= @t68 @t67))) % 0.36/0.57 (step @p101 :rule trans :premises (@p100 @p99)) % 0.36/0.57 (step @p102 :rule cong :premises (@p101) :args (@t69)) % 0.36/0.57 (step @p103 :rule trans :premises (@p102 @p91)) % 0.36/0.57 (step @p104 :rule cong :premises (@p103) :args (@t70)) % 0.36/0.57 (step @p105 :rule quant-merge-prenex :args ((= @t70 @t71))) % 0.36/0.57 (step @p106 :rule symm :premises (@p105)) % 0.36/0.57 (step @p107 :rule quant_var_reordering :args ((= (forall @t72 @t68) @t71))) % 0.36/0.57 (step @p108 :rule trans :premises (@p107 @p106 @p104)) % 0.36/0.57 (step @p109 :rule trans :premises (@p108 @p90)) % 0.36/0.57 (step @p110 :rule eq-symm :args (@t37 @t18)) % 0.36/0.57 (step @p111 :rule refl :args (@t20)) % 0.36/0.57 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t73)) % 0.36/0.57 (step @p113 :rule refl :args (@t64)) % 0.36/0.57 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t74)) % 0.36/0.57 (step @p115 :rule cong :premises (@p114) :args (@t75)) % 0.36/0.57 (step @p116 :rule cong :premises (@p6 @p115) :args (@t76)) % 0.36/0.57 (step @p117 :rule cong :premises (@p8 @p116) :args (@t77)) % 0.36/0.57 (step @p118 :rule nary_cong :premises (@p11 @p111 @p87 @p117) :args (@t78)) % 0.36/0.57 (step @p119 :rule aci_norm :args ((= @t80 @t78))) % 0.36/0.57 (step @p120 :rule trans :premises (@p119 @p118)) % 0.36/0.57 (step @p121 :rule cong :premises (@p120) :args (@t81)) % 0.36/0.57 (step @p122 :rule trans :premises (@p121 @p109)) % 0.36/0.57 (step @p123 :rule quant-merge-prenex :args ((= (forall @t31 @t83) @t81))) % 0.36/0.57 (step @p124 :rule alpha_equiv :args (@t84 (@list @t37) (@list @t1))) % 0.36/0.57 (step @p125 :rule nary_cong :premises (@p95 @p94 @p124) :args (@t85)) % 0.36/0.57 (step @p126 :rule quant-miniscope-or :args ((= @t83 @t85))) % 0.36/0.57 (step @p127 :rule trans :premises (@p126 @p125)) % 0.36/0.57 (step @p128 :rule symm :premises (@p127)) % 0.36/0.57 (step @p129 :rule cong :premises (@p128) :args ((forall @t31 (or @t40 @t20 @t90)))) % 0.36/0.57 (step @p130 :rule trans :premises (@p129 @p123)) % 0.36/0.57 (step @p131 :rule trans :premises (@p130 @p122)) % 0.36/0.57 (step @p132 :rule refl :args (@t90)) % 0.36/0.57 (step @p133 :rule nary_cong :premises (@p56 @p94 @p132) :args (@t91)) % 0.36/0.57 (step @p134 :rule cong :premises (@p133) :args ((forall @t31 @t91))) % 0.36/0.57 (step @p135 :rule trans :premises (@p134 @p131)) % 0.36/0.57 (step @p136 :rule aci_norm :args ((= (or @t52 @t92) @t91))) % 0.36/0.57 (step @p137 :rule bool-impl-elim :args (@t14 @t92)) % 0.36/0.57 (step @p138 :rule trans :premises (@p137 @p136)) % 0.36/0.57 (step @p139 :rule cong :premises (@p138) :args ((forall @t31 (=> @t14 @t92)))) % 0.36/0.57 (step @p140 :rule trans :premises (@p139 @p135)) % 0.36/0.57 (step @p141 :rule refl :args ((tptp.in @t9 @t93))) % 0.36/0.57 (step @p142 :rule refl :args (@t87)) % 0.36/0.57 (step @p143 :rule cong :premises (@p21 @p142) :args (@t88)) % 0.36/0.57 (step @p144 :rule trans :premises (@p143 @p141)) % 0.36/0.57 (step @p145 :rule ho_cong :premises (@p24 @p142)) % 0.36/0.57 (step @p146 :rule cong :premises (@p145 @p144) :args ((= (_ @t10 @t87) @t88))) % 0.36/0.57 (step @p147 :rule symm :premises (@p146)) % 0.36/0.57 (step @p148 :rule refl :args (@t94)) % 0.36/0.57 (step @p149 :rule eq_resolve :premises (@p148 @p147)) % 0.36/0.57 (step @p150 :rule refl :args (@t93)) % 0.36/0.57 (step @p151 :rule cong :premises (@p150 @p142) :args ((= @t93 @t87))) % 0.36/0.57 (step @p152 :rule symm :premises (@p151)) % 0.36/0.57 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.36/0.57 (step @p154 :rule ho_cong :premises (@p24 @p153)) % 0.36/0.57 (step @p155 :rule trans :premises (@p154 @p149)) % 0.36/0.57 (step @p156 :rule refl :args (@t89)) % 0.36/0.57 (step @p157 :rule refl :args (@t27)) % 0.36/0.57 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t27 @t89))) % 0.36/0.57 (step @p159 :rule symm :premises (@p158)) % 0.36/0.57 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.36/0.57 (step @p161 :rule cong :premises (@p160) :args (@t95)) % 0.36/0.57 (step @p162 :rule nary_cong :premises (@p161 @p155) :args (@t96)) % 0.36/0.57 (step @p163 :rule cong :premises (@p162) :args (@t97)) % 0.36/0.57 (step @p164 :rule nary_cong :premises (@p111 @p163) :args (@t98)) % 0.36/0.57 (step @p165 :rule quant-miniscope-or :args ((= (forall @t4 @t99) @t98))) % 0.36/0.57 (step @p166 :rule aci_norm :args ((= @t100 @t99))) % 0.36/0.57 (step @p167 :rule cong :premises (@p166) :args ((forall @t4 @t100))) % 0.36/0.57 (step @p168 :rule trans :premises (@p167 @p165)) % 0.36/0.57 (step @p169 :rule trans :premises (@p168 @p164)) % 0.36/0.57 (step @p170 :rule aci_norm :args ((= (or @t95 (or @t20 @t94)) @t100))) % 0.36/0.57 (step @p171 :rule bool-impl-elim :args (@t19 @t94)) % 0.36/0.57 (step @p172 :rule refl :args (@t95)) % 0.36/0.57 (step @p173 :rule nary_cong :premises (@p172 @p171) :args ((or @t95 @t101))) % 0.36/0.57 (step @p174 :rule trans :premises (@p173 @p170)) % 0.36/0.57 (step @p175 :rule bool-impl-elim :args (@t27 @t101)) % 0.36/0.57 (step @p176 :rule trans :premises (@p175 @p174)) % 0.36/0.57 (step @p177 :rule cong :premises (@p176) :args ((forall @t4 (=> @t27 @t101)))) % 0.36/0.57 (step @p178 :rule trans :premises (@p177 @p169)) % 0.36/0.57 (step @p179 :rule eq-symm :args (@t18 @t1)) % 0.36/0.57 (step @p180 :rule nary_cong :premises (@p111 @p179) :args (@t21)) % 0.36/0.57 (step @p181 :rule eq-symm :args (@t18 @t9)) % 0.36/0.57 (step @p182 :rule refl :args (@t19)) % 0.36/0.57 (step @p183 :rule nary_cong :premises (@p182 @p181) :args (@t22)) % 0.36/0.57 (step @p184 :rule nary_cong :premises (@p183 @p180) :args (@t23)) % 0.36/0.57 (step @p185 :rule cong :premises (@p184) :args (@t25)) % 0.36/0.57 (step @p186 :rule refl :args (@t7)) % 0.36/0.57 (step @p187 :rule ho_cong :premises (@p186 @p185)) % 0.36/0.57 (step @p188 :rule refl :args (@t10)) % 0.36/0.57 (step @p189 :rule ho_cong :premises (@p188 @p187)) % 0.36/0.57 (step @p190 :rule cong :premises (@p182 @p189) :args (@t26)) % 0.36/0.57 (step @p191 :rule refl :args (@t27)) % 0.36/0.57 (step @p192 :rule cong :premises (@p191 @p190) :args (@t28)) % 0.36/0.57 (step @p193 :rule cong :premises (@p192) :args (@t29)) % 0.36/0.57 (step @p194 :rule trans :premises (@p193 @p178)) % 0.36/0.57 (step @p195 :rule refl :args (@t14)) % 0.36/0.57 (step @p196 :rule cong :premises (@p195 @p194) :args (@t30)) % 0.36/0.57 (step @p197 :rule cong :premises (@p196) :args (@t32)) % 0.36/0.57 (step @p198 :rule trans :premises (@p197 @p140)) % 0.36/0.57 (step @p199 :rule cong :premises (@p69 @p198) :args (@t33)) % 0.36/0.57 (step @p200 :rule cong :premises (@p199) :args (@t34)) % 0.36/0.57 (step @p201 :rule trans :premises (@p200 @p73)) % 0.36/0.57 (step @p202 :rule eq_resolve :premises (@p2 @p201)) % 0.36/0.57 (step @p203 :rule not_implies_elim1 :premises (@p202)) % 0.36/0.57 (step @p204 :rule not_implies_elim2 :premises (@p202)) % 0.36/0.57 (step @p205 :rule refl :args (@t111)) % 0.36/0.57 (step @p206 :rule bool-double-not-elim :args (@t43)) % 0.36/0.57 (step @p207 :rule nary_cong :premises (@p206 @p205) :args ((or (not @t112) @t111))) % 0.36/0.57 (step @p208 :rule eq-refl :args (@t103)) % 0.36/0.57 (step @p209 :rule skolem_intro :args (@t104)) % 0.36/0.57 (step @p210 :rule refl :args (@t103)) % 0.36/0.57 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t103 @t104))) % 0.36/0.57 (step @p212 :rule trans :premises (@p211 @p208)) % 0.36/0.57 (step @p213 :rule true_elim :premises (@p212)) % 0.36/0.57 (step @p214 :rule refl :args (@t105)) % 0.36/0.57 (step @p215 :rule cong :premises (@p214 @p213) :args (@t113)) % 0.36/0.57 (step @p216 :rule refl :args (@t102)) % 0.36/0.57 (step @p217 :rule cong :premises (@p216 @p215) :args (@t114)) % 0.36/0.57 (step @p218 :rule refl :args (@t107)) % 0.36/0.57 (step @p219 :rule refl :args (@t109)) % 0.36/0.57 (step @p220 :rule nary_cong :premises (@p219 @p218 @p217) :args (@t115)) % 0.36/0.57 (step @p221 :rule cong :premises (@p220) :args (@t116)) % 0.36/0.57 (step @p222 :rule refl :args (@t112)) % 0.36/0.57 (step @p223 :rule cong :premises (@p222 @p221) :args ((=> @t112 @t116))) % 0.36/0.57 (step @p224 :rule eq-symm :args (@t102 @t18)) % 0.36/0.57 (step @p225 :rule cong :premises (@p224) :args (@t117)) % 0.36/0.57 (step @p226 :rule cong :premises (@p214 @p225) :args (@t118)) % 0.36/0.57 (step @p227 :rule cong :premises (@p216 @p226) :args (@t119)) % 0.36/0.57 (step @p228 :rule nary_cong :premises (@p219 @p218 @p227) :args (@t120)) % 0.36/0.57 (step @p229 :rule cong :premises (@p228) :args (@t121)) % 0.36/0.57 (step @p230 :rule cong :premises (@p222 @p229) :args ((=> @t112 @t121))) % 0.36/0.57 (step @p231 :rule trans :premises (@p230 @p223)) % 0.36/0.57 (assume-push @p274 @t112) % 0.36/0.57 (step @p233 :rule skolemize :premises (@p204)) % 0.36/0.57 (step-pop @p275 :rule scope :premises (@p233)) % 0.36/0.57 (step @p234 :rule process_scope :premises (@p275) :args (@t121)) % 0.36/0.57 (step @p236 :rule eq_resolve :premises (@p234 @p231)) % 0.36/0.57 (step @p237 :rule implies_elim :premises (@p236)) % 0.36/0.57 (step @p238 :rule eq_resolve :premises (@p237 @p207)) % 0.36/0.57 (step @p239 :rule chain_m_resolution :premises (@p238 @p204) :args (@t111 @t122 (@list @t43))) % 0.36/0.57 (step @p240 :rule cnf_or_neg :args (@t110 2)) % 0.36/0.57 (step @p241 :rule chain_m_resolution :premises (@p240 @p239) :args ((not @t106) @t122 @t123)) % 0.36/0.57 (step @p242 :rule bool-double-not-elim :args (@t108)) % 0.36/0.57 (step @p243 :rule refl :args (@t110)) % 0.36/0.57 (step @p244 :rule nary_cong :premises (@p243 @p242) :args ((or @t110 (not @t109)))) % 0.36/0.57 (step @p245 :rule cnf_or_neg :args (@t110 0)) % 0.36/0.57 (step @p246 :rule eq_resolve :premises (@p245 @p244)) % 0.36/0.57 (step @p247 :rule reordering :premises (@p246) :args ((or @t108 @t110))) % 0.36/0.57 (step @p248 :rule chain_m_resolution :premises (@p247 @p239) :args (@t108 @t122 @t123)) % 0.36/0.57 (step @p249 :rule cnf_or_pos :args (@t124)) % 0.36/0.57 (step @p250 :rule reordering :premises (@p249) :args ((or @t109 @t106 @t125))) % 0.36/0.57 (step @p251 :rule chain_m_resolution :premises (@p250 @p248 @p241) :args (@t125 (@list false true) (@list @t108 @t106))) % 0.36/0.57 (step @p252 :rule aci_norm :args ((= (or @t109 false @t106) @t124))) % 0.36/0.57 (step @p253 :rule refl :args (@t106)) % 0.36/0.57 (step @p254 :rule eq-refl :args (@t102)) % 0.36/0.57 (step @p255 :rule beta-reduce :args ((= (_ @t103 @t102) (= @t102 @t102)))) % 0.36/0.57 (step @p256 :rule trans :premises (@p255 @p254)) % 0.36/0.57 (step @p257 :rule ho_cong :premises (@p209 @p216)) % 0.36/0.57 (step @p258 :rule bool-eq-true :args (@t126)) % 0.36/0.57 (step @p259 :rule trans :premises (@p258 @p257 @p256)) % 0.36/0.57 (step @p260 :rule true_elim :premises (@p259)) % 0.36/0.57 (step @p261 :rule cong :premises (@p260) :args (@t127)) % 0.36/0.57 (step @p262 :rule trans :premises (@p261 @p78)) % 0.36/0.57 (step @p263 :rule nary_cong :premises (@p219 @p262 @p253) :args (@t128)) % 0.36/0.57 (step @p264 :rule trans :premises (@p263 @p252)) % 0.36/0.57 (step @p265 :rule refl :args (@t129)) % 0.36/0.57 (step @p266 :rule cong :premises (@p265 @p264) :args ((=> @t129 @t128))) % 0.36/0.57 (assume-push @p276 @t129) % 0.36/0.57 (step @p268 :rule instantiate :premises (@p203) :args ((@list @t105 @t104 @t102))) % 0.36/0.57 (step-pop @p277 :rule scope :premises (@p268)) % 0.36/0.57 (step @p269 :rule process_scope :premises (@p277) :args (@t128)) % 0.36/0.57 (step @p271 :rule eq_resolve :premises (@p269 @p266)) % 0.36/0.57 (step @p272 :rule implies_elim :premises (@p271)) % 0.36/0.57 (step @p273 false :rule chain_m_resolution :premises (@p272 @p251 @p203) :args (false (@list true false) (@list @t124 @t129))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------