%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL736^5 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:43 AM UTC 2026 % Result : Theorem 28.93s 29.26s % Output : Proof 28.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL736^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.34 % Computer : n010.cluster.edu % 0.09/0.34 % Model : x86_64 x86_64 % 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.34 % Memory : 8046.5625MB % 0.09/0.34 % OS : Linux 6.8.0-71-generic % 0.09/0.34 % CPULimit : 300 % 0.09/0.34 % WCLimit : 300 % 0.09/0.34 % DateTime : Fri Sep 4 20:41:38 UTC 2026 % 0.09/0.34 % CPUTime : % 0.16/0.41 %----Proving TH0 % 28.93/29.26 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 28.93/29.26 % SZS status Theorem % 28.93/29.26 % SZS output start Proof % 28.93/29.26 ( % 28.93/29.26 (declare-sort tptp.b 0) % 28.93/29.26 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 28.93/29.26 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 28.93/29.26 (define @t3 () (_ @t2 @t1)) % 28.93/29.26 (define @t4 () (_ @t1 @t3)) % 28.93/29.26 (define @t5 () (@var "Xz" tptp.b)) % 28.93/29.26 (define @t6 () (_ @t1 @t5)) % 28.93/29.26 (define @t7 () (@list @t5)) % 28.93/29.26 (define @t8 () (exists @t7 @t6)) % 28.93/29.26 (define @t9 () (=> @t8 @t4)) % 28.93/29.26 (define @t10 () (@list @t1)) % 28.93/29.26 (define @t11 () (forall @t10 @t9)) % 28.93/29.26 (define @t12 () (@list @t2)) % 28.93/29.26 (define @t13 () (exists @t12 @t11)) % 28.93/29.26 (define @t14 () (@var "Xw_11" tptp.b)) % 28.93/29.26 (define @t15 () (@var "Xx" (-> tptp.b Bool))) % 28.93/29.26 (define @t16 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 28.93/29.26 (define @t17 () (_ @t16 @t15)) % 28.93/29.26 (define @t18 () (@var "Xr_42" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 28.93/29.26 (define @t19 () (_ @t18 @t15)) % 28.93/29.26 (define @t20 () (_ @t19 @t17)) % 28.93/29.26 (define @t21 () (_ @t20 @t14)) % 28.93/29.26 (define @t22 () (@var "Xr_41" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 28.93/29.26 (define @t23 () (_ @t22 @t15)) % 28.93/29.26 (define @t24 () (_ @t23 @t17)) % 28.93/29.26 (define @t25 () (_ @t24 @t14)) % 28.93/29.26 (define @t26 () (or @t25 @t21)) % 28.93/29.26 (define @t27 () (@list @t14)) % 28.93/29.26 (define @t28 () (exists @t27 @t26)) % 28.93/29.26 (define @t29 () (@list @t15)) % 28.93/29.26 (define @t30 () (forall @t29 @t28)) % 28.93/29.26 (define @t31 () (@list @t16)) % 28.93/29.26 (define @t32 () (exists @t31 @t30)) % 28.93/29.26 (define @t33 () (@var "Xy" tptp.b)) % 28.93/29.26 (define @t34 () (_ (_ @t19 @t33) @t14)) % 28.93/29.26 (define @t35 () (_ (_ @t23 @t33) @t14)) % 28.93/29.26 (define @t36 () (or @t35 @t34)) % 28.93/29.26 (define @t37 () (@list @t33 @t14)) % 28.93/29.26 (define @t38 () (exists @t37 @t36)) % 28.93/29.26 (define @t39 () (forall @t29 @t38)) % 28.93/29.26 (define @t40 () (=> @t39 @t32)) % 28.93/29.26 (define @t41 () (@list @t22 @t18)) % 28.93/29.26 (define @t42 () (forall @t41 @t40)) % 28.93/29.26 (define @t43 () (=> @t42 @t13)) % 28.93/29.26 (define @t44 () (not @t43)) % 28.93/29.26 (define @t45 () (_ @t2 @t1)) % 28.93/29.26 (define @t46 () (_ @t1 @t45)) % 28.93/29.26 (define @t47 () (@var "BOUND_VARIABLE_7559" tptp.b)) % 28.93/29.26 (define @t48 () (not (_ @t1 @t47))) % 28.93/29.26 (define @t49 () (or @t48 @t46)) % 28.93/29.26 (define @t50 () (@list @t1 @t47)) % 28.93/29.26 (define @t51 () (forall @t50 @t49)) % 28.93/29.26 (define @t52 () (forall @t12 (not @t51))) % 28.93/29.26 (define @t53 () (@list @t47)) % 28.93/29.26 (define @t54 () (forall @t53 @t49)) % 28.93/29.26 (define @t55 () (forall @t53 @t48)) % 28.93/29.26 (define @t56 () (or @t55 @t46)) % 28.93/29.26 (define @t57 () (_ @t1 @t5)) % 28.93/29.26 (define @t58 () (forall @t7 (not @t57))) % 28.93/29.26 (define @t59 () (or @t58 @t4)) % 28.93/29.26 (define @t60 () (not @t58)) % 28.93/29.26 (define @t61 () (not @t6)) % 28.93/29.26 (define @t62 () (forall @t7 @t61)) % 28.93/29.26 (define @t63 () (not @t62)) % 28.93/29.26 (define @t64 () (@var "BOUND_VARIABLE_7475" tptp.b)) % 28.93/29.26 (define @t65 () (@var "BOUND_VARIABLE_7473" tptp.b)) % 28.93/29.26 (define @t66 () (_ @t18 @t15 @t65 @t64)) % 28.93/29.26 (define @t67 () (@list @t65 @t64)) % 28.93/29.26 (define @t68 () (forall @t67 (not @t66))) % 28.93/29.26 (define @t69 () (@var "BOUND_VARIABLE_7466" tptp.b)) % 28.93/29.26 (define @t70 () (@var "BOUND_VARIABLE_7464" tptp.b)) % 28.93/29.26 (define @t71 () (_ @t22 @t15 @t70 @t69)) % 28.93/29.26 (define @t72 () (@list @t70 @t69)) % 28.93/29.26 (define @t73 () (forall @t72 (not @t71))) % 28.93/29.26 (define @t74 () (forall @t29 (or (not @t73) (not @t68)))) % 28.93/29.26 (define @t75 () (@var "BOUND_VARIABLE_7509" tptp.b)) % 28.93/29.26 (define @t76 () (_ @t16 @t15)) % 28.93/29.26 (define @t77 () (_ @t18 @t15 @t76 @t75)) % 28.93/29.26 (define @t78 () (@list @t75)) % 28.93/29.26 (define @t79 () (forall @t78 (not @t77))) % 28.93/29.26 (define @t80 () (@var "BOUND_VARIABLE_7503" tptp.b)) % 28.93/29.26 (define @t81 () (_ @t22 @t15 @t76 @t80)) % 28.93/29.26 (define @t82 () (@list @t80)) % 28.93/29.26 (define @t83 () (forall @t82 (not @t81))) % 28.93/29.26 (define @t84 () (forall @t29 (or (not @t83) (not @t79)))) % 28.93/29.26 (define @t85 () (not (forall @t31 (not @t84)))) % 28.93/29.26 (define @t86 () (_ @t20 @t75)) % 28.93/29.26 (define @t87 () (not @t86)) % 28.93/29.26 (define @t88 () (forall @t78 @t87)) % 28.93/29.26 (define @t89 () (_ @t24 @t80)) % 28.93/29.26 (define @t90 () (not @t89)) % 28.93/29.26 (define @t91 () (forall @t82 @t90)) % 28.93/29.26 (define @t92 () (not @t21)) % 28.93/29.26 (define @t93 () (forall @t27 @t92)) % 28.93/29.26 (define @t94 () (@list @t14)) % 28.93/29.26 (define @t95 () (not @t25)) % 28.93/29.26 (define @t96 () (forall @t27 @t95)) % 28.93/29.26 (define @t97 () (and @t96 @t93)) % 28.93/29.26 (define @t98 () (forall @t27 (not @t26))) % 28.93/29.26 (define @t99 () (not @t98)) % 28.93/29.26 (define @t100 () (_ (_ @t19 @t65) @t64)) % 28.93/29.26 (define @t101 () (not @t100)) % 28.93/29.26 (define @t102 () (forall @t67 @t101)) % 28.93/29.26 (define @t103 () (_ (_ @t23 @t70) @t69)) % 28.93/29.26 (define @t104 () (not @t103)) % 28.93/29.26 (define @t105 () (forall @t72 @t104)) % 28.93/29.26 (define @t106 () (not @t34)) % 28.93/29.26 (define @t107 () (forall @t37 @t106)) % 28.93/29.26 (define @t108 () (@list @t33 @t14)) % 28.93/29.26 (define @t109 () (not @t35)) % 28.93/29.26 (define @t110 () (forall @t37 @t109)) % 28.93/29.26 (define @t111 () (and @t110 @t107)) % 28.93/29.26 (define @t112 () (forall @t37 (not @t36))) % 28.93/29.26 (define @t113 () (not @t112)) % 28.93/29.26 (define @t114 () (@const 0 (-> (-> tptp.b Bool) tptp.b))) % 28.93/29.26 (define @t115 () (_ @t114 @t1)) % 28.93/29.26 (define @t116 () (@var "BOUND_VARIABLE_517636" (-> tptp.b Bool))) % 28.93/29.26 (define @t117 () (_ @t114 @t116)) % 28.93/29.26 (define @t118 () (@list @t116)) % 28.93/29.26 (define @t119 () (lambda @t118 @t117)) % 28.93/29.26 (define @t120 () (_ @t119 @t1)) % 28.93/29.26 (define @t121 () (_ @t1 @t120)) % 28.93/29.26 (define @t122 () (or @t48 @t121)) % 28.93/29.26 (define @t123 () (forall @t50 @t122)) % 28.93/29.26 (define @t124 () (not @t123)) % 28.93/29.26 (define @t125 () (forall @t50 (or @t48 (_ @t1 @t115)))) % 28.93/29.26 (define @t126 () (@quantifiers_skolemize @t125 1)) % 28.93/29.26 (define @t127 () (@quantifiers_skolemize @t125 0)) % 28.93/29.26 (define @t128 () (_ @t127 @t126)) % 28.93/29.26 (define @t129 () (_ @t127 (_ @t114 @t127))) % 28.93/29.26 (define @t130 () (not @t128)) % 28.93/29.26 (define @t131 () (or @t130 @t129)) % 28.93/29.26 (define @t132 () (@list true)) % 28.93/29.26 (define @t133 () (@list @t131)) % 28.93/29.26 (define @t134 () (@var "x" tptp.b)) % 28.93/29.26 (define @t135 () (@list @t134)) % 28.93/29.26 (define @t136 () (forall @t135 (not (_ @t127 @t134)))) % 28.93/29.26 (define @t137 () (or @t136 @t129)) % 28.93/29.26 (assume @p1 @t44) % 28.93/29.26 (assume @p2 true) % 28.93/29.26 (step @p3 :rule exists-elim :args ((= (exists @t12 @t51) (not @t52)))) % 28.93/29.26 (step @p4 :rule quant-merge-prenex :args ((= (forall @t10 @t54) @t51))) % 28.93/29.26 (step @p5 :rule refl :args (@t46)) % 28.93/29.26 (step @p6 :rule alpha_equiv :args (@t55 (@list @t47) (@list @t5))) % 28.93/29.26 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t56)) % 28.93/29.26 (step @p8 :rule quant-miniscope-or :args ((= @t54 @t56))) % 28.93/29.26 (step @p9 :rule trans :premises (@p8 @p7)) % 28.93/29.26 (step @p10 :rule symm :premises (@p9)) % 28.93/29.26 (step @p11 :rule cong :premises (@p10) :args ((forall @t10 (or @t58 @t46)))) % 28.93/29.26 (step @p12 :rule trans :premises (@p11 @p4)) % 28.93/29.26 (step @p13 :rule refl :args ((_ @t1 @t3))) % 28.93/29.26 (step @p14 :rule refl :args (@t45)) % 28.93/29.26 (step @p15 :rule cong :premises (@p14) :args (@t46)) % 28.93/29.26 (step @p16 :rule trans :premises (@p15 @p13)) % 28.93/29.26 (step @p17 :rule refl :args (@t1)) % 28.93/29.26 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 28.93/29.26 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t45) @t46))) % 28.93/29.26 (step @p20 :rule symm :premises (@p19)) % 28.93/29.26 (step @p21 :rule refl :args (@t4)) % 28.93/29.26 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 28.93/29.26 (step @p23 :rule refl :args (@t3)) % 28.93/29.26 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t3 @t45))) % 28.93/29.26 (step @p25 :rule symm :premises (@p24)) % 28.93/29.26 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 28.93/29.26 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 28.93/29.26 (step @p28 :rule trans :premises (@p27 @p22)) % 28.93/29.26 (step @p29 :rule refl :args (@t58)) % 28.93/29.26 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t59)) % 28.93/29.26 (step @p31 :rule cong :premises (@p30) :args ((forall @t10 @t59))) % 28.93/29.26 (step @p32 :rule trans :premises (@p31 @p12)) % 28.93/29.26 (step @p33 :rule bool-double-not-elim :args (@t58)) % 28.93/29.26 (step @p34 :rule nary_cong :premises (@p33 @p21) :args ((or (not @t60) @t4))) % 28.93/29.26 (step @p35 :rule bool-impl-elim :args (@t60 @t4)) % 28.93/29.26 (step @p36 :rule trans :premises (@p35 @p34)) % 28.93/29.26 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 (=> @t60 @t4)))) % 28.93/29.26 (step @p38 :rule trans :premises (@p37 @p32)) % 28.93/29.26 (step @p39 :rule refl :args (@t4)) % 28.93/29.26 (step @p40 :rule refl :args (@t57)) % 28.93/29.26 (step @p41 :rule refl :args (@t6)) % 28.93/29.26 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t6 @t57))) % 28.93/29.26 (step @p43 :rule symm :premises (@p42)) % 28.93/29.26 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 28.93/29.26 (step @p45 :rule cong :premises (@p44) :args (@t61)) % 28.93/29.26 (step @p46 :rule cong :premises (@p45) :args (@t62)) % 28.93/29.26 (step @p47 :rule cong :premises (@p46) :args (@t63)) % 28.93/29.26 (step @p48 :rule exists-elim :args ((= @t8 @t63))) % 28.93/29.26 (step @p49 :rule trans :premises (@p48 @p47)) % 28.93/29.26 (step @p50 :rule cong :premises (@p49 @p39) :args (@t9)) % 28.93/29.26 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 28.93/29.26 (step @p52 :rule trans :premises (@p51 @p38)) % 28.93/29.26 (step @p53 :rule cong :premises (@p52) :args (@t13)) % 28.93/29.26 (step @p54 :rule trans :premises (@p53 @p3)) % 28.93/29.26 (step @p55 :rule bool-impl-elim :args (@t74 @t85)) % 28.93/29.26 (step @p56 :rule cong :premises (@p55) :args ((forall @t41 (=> @t74 @t85)))) % 28.93/29.26 (step @p57 :rule exists-elim :args ((= (exists @t31 @t84) @t85))) % 28.93/29.26 (step @p58 :rule bool-and-de-morgan :args (@t83 @t79 true)) % 28.93/29.26 (step @p59 :rule cong :premises (@p58) :args ((forall @t29 (not (and @t83 @t79))))) % 28.93/29.26 (step @p60 :rule refl :args ((_ @t18 @t15 @t17 @t75))) % 28.93/29.26 (step @p61 :rule refl :args (@t75)) % 28.93/29.26 (step @p62 :rule refl :args (@t76)) % 28.93/29.26 (step @p63 :rule refl :args (@t15)) % 28.93/29.26 (step @p64 :rule cong :premises (@p63 @p62 @p61) :args (@t77)) % 28.93/29.26 (step @p65 :rule trans :premises (@p64 @p60)) % 28.93/29.26 (step @p66 :rule refl :args (@t19)) % 28.93/29.26 (step @p67 :rule ho_cong :premises (@p66 @p62)) % 28.93/29.26 (step @p68 :rule ho_cong :premises (@p67 @p61)) % 28.93/29.26 (step @p69 :rule cong :premises (@p68 @p65) :args ((= (_ (_ @t19 @t76) @t75) @t77))) % 28.93/29.26 (step @p70 :rule symm :premises (@p69)) % 28.93/29.26 (step @p71 :rule refl :args (@t86)) % 28.93/29.26 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 28.93/29.26 (step @p73 :rule refl :args (@t17)) % 28.93/29.26 (step @p74 :rule cong :premises (@p73 @p62) :args ((= @t17 @t76))) % 28.93/29.26 (step @p75 :rule symm :premises (@p74)) % 28.93/29.26 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 28.93/29.26 (step @p77 :rule ho_cong :premises (@p66 @p76)) % 28.93/29.26 (step @p78 :rule ho_cong :premises (@p77 @p61)) % 28.93/29.26 (step @p79 :rule trans :premises (@p78 @p72)) % 28.93/29.26 (step @p80 :rule cong :premises (@p79) :args (@t87)) % 28.93/29.26 (step @p81 :rule cong :premises (@p80) :args (@t88)) % 28.93/29.26 (step @p82 :rule refl :args ((_ @t22 @t15 @t17 @t80))) % 28.93/29.26 (step @p83 :rule refl :args (@t80)) % 28.93/29.26 (step @p84 :rule cong :premises (@p63 @p62 @p83) :args (@t81)) % 28.93/29.26 (step @p85 :rule trans :premises (@p84 @p82)) % 28.93/29.26 (step @p86 :rule refl :args (@t23)) % 28.93/29.26 (step @p87 :rule ho_cong :premises (@p86 @p62)) % 28.93/29.26 (step @p88 :rule ho_cong :premises (@p87 @p83)) % 28.93/29.26 (step @p89 :rule cong :premises (@p88 @p85) :args ((= (_ (_ @t23 @t76) @t80) @t81))) % 28.93/29.26 (step @p90 :rule symm :premises (@p89)) % 28.93/29.26 (step @p91 :rule refl :args (@t89)) % 28.93/29.26 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 28.93/29.26 (step @p93 :rule ho_cong :premises (@p86 @p76)) % 28.93/29.26 (step @p94 :rule ho_cong :premises (@p93 @p83)) % 28.93/29.26 (step @p95 :rule trans :premises (@p94 @p92)) % 28.93/29.26 (step @p96 :rule cong :premises (@p95) :args (@t90)) % 28.93/29.26 (step @p97 :rule cong :premises (@p96) :args (@t91)) % 28.93/29.26 (step @p98 :rule nary_cong :premises (@p97 @p81) :args ((and @t91 @t88))) % 28.93/29.26 (step @p99 :rule alpha_equiv :args (@t93 @t94 (@list @t75))) % 28.93/29.26 (step @p100 :rule alpha_equiv :args (@t96 @t94 (@list @t80))) % 28.93/29.26 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t97)) % 28.93/29.26 (step @p102 :rule quant-miniscope-and :args ((= (forall @t27 (and @t95 @t92)) @t97))) % 28.93/29.26 (step @p103 :rule trans :premises (@p102 @p101)) % 28.93/29.26 (step @p104 :rule trans :premises (@p103 @p98)) % 28.93/29.26 (step @p105 :rule bool-or-de-morgan :args (@t25 @t21 false)) % 28.93/29.26 (step @p106 :rule cong :premises (@p105) :args (@t98)) % 28.93/29.26 (step @p107 :rule trans :premises (@p106 @p104)) % 28.93/29.26 (step @p108 :rule cong :premises (@p107) :args (@t99)) % 28.93/29.26 (step @p109 :rule exists-elim :args ((= @t28 @t99))) % 28.93/29.26 (step @p110 :rule trans :premises (@p109 @p108)) % 28.93/29.26 (step @p111 :rule cong :premises (@p110) :args (@t30)) % 28.93/29.26 (step @p112 :rule trans :premises (@p111 @p59)) % 28.93/29.26 (step @p113 :rule cong :premises (@p112) :args (@t32)) % 28.93/29.26 (step @p114 :rule trans :premises (@p113 @p57)) % 28.93/29.26 (step @p115 :rule bool-and-de-morgan :args (@t73 @t68 true)) % 28.93/29.26 (step @p116 :rule cong :premises (@p115) :args ((forall @t29 (not (and @t73 @t68))))) % 28.93/29.26 (step @p117 :rule refl :args (@t66)) % 28.93/29.26 (step @p118 :rule refl :args (@t100)) % 28.93/29.26 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t100 @t66))) % 28.93/29.26 (step @p120 :rule symm :premises (@p119)) % 28.93/29.26 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 28.93/29.26 (step @p122 :rule cong :premises (@p121) :args (@t101)) % 28.93/29.26 (step @p123 :rule cong :premises (@p122) :args (@t102)) % 28.93/29.26 (step @p124 :rule refl :args (@t71)) % 28.93/29.26 (step @p125 :rule refl :args (@t103)) % 28.93/29.26 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t103 @t71))) % 28.93/29.26 (step @p127 :rule symm :premises (@p126)) % 28.93/29.26 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 28.93/29.26 (step @p129 :rule cong :premises (@p128) :args (@t104)) % 28.93/29.26 (step @p130 :rule cong :premises (@p129) :args (@t105)) % 28.93/29.26 (step @p131 :rule nary_cong :premises (@p130 @p123) :args ((and @t105 @t102))) % 28.93/29.26 (step @p132 :rule alpha_equiv :args (@t107 @t108 (@list @t65 @t64))) % 28.93/29.26 (step @p133 :rule alpha_equiv :args (@t110 @t108 (@list @t70 @t69))) % 28.93/29.26 (step @p134 :rule nary_cong :premises (@p133 @p132) :args (@t111)) % 28.93/29.27 (step @p135 :rule quant-miniscope-and :args ((= (forall @t37 (and @t109 @t106)) @t111))) % 28.93/29.27 (step @p136 :rule trans :premises (@p135 @p134)) % 28.93/29.27 (step @p137 :rule trans :premises (@p136 @p131)) % 28.93/29.27 (step @p138 :rule bool-or-de-morgan :args (@t35 @t34 false)) % 28.93/29.27 (step @p139 :rule cong :premises (@p138) :args (@t112)) % 28.93/29.27 (step @p140 :rule trans :premises (@p139 @p137)) % 28.93/29.27 (step @p141 :rule cong :premises (@p140) :args (@t113)) % 28.93/29.27 (step @p142 :rule exists-elim :args ((= @t38 @t113))) % 28.93/29.27 (step @p143 :rule trans :premises (@p142 @p141)) % 28.93/29.27 (step @p144 :rule cong :premises (@p143) :args (@t39)) % 28.93/29.27 (step @p145 :rule trans :premises (@p144 @p116)) % 28.93/29.27 (step @p146 :rule cong :premises (@p145 @p114) :args (@t40)) % 28.93/29.27 (step @p147 :rule cong :premises (@p146) :args (@t42)) % 28.93/29.27 (step @p148 :rule trans :premises (@p147 @p56)) % 28.93/29.27 (step @p149 :rule cong :premises (@p148 @p54) :args (@t43)) % 28.93/29.27 (step @p150 :rule cong :premises (@p149) :args (@t44)) % 28.93/29.27 (step @p151 :rule eq_resolve :premises (@p1 @p150)) % 28.93/29.27 (step @p152 :rule not_implies_elim2 :premises (@p151)) % 28.93/29.27 (step @p153 :rule not_not_elim :premises (@p152)) % 28.93/29.27 (step @p154 :rule beta-reduce :args ((= @t120 @t115))) % 28.93/29.27 (step @p155 :rule cong :premises (@p154) :args (@t121)) % 28.93/29.27 (step @p156 :rule refl :args (@t48)) % 28.93/29.27 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t122)) % 28.93/29.27 (step @p158 :rule cong :premises (@p157) :args (@t123)) % 28.93/29.27 (step @p159 :rule cong :premises (@p158) :args (@t124)) % 28.93/29.27 (step @p160 :rule refl :args (@t52)) % 28.93/29.27 (step @p161 :rule cong :premises (@p160 @p159) :args ((=> @t52 @t124))) % 28.93/29.27 (assume-push @p191 @t52) % 28.93/29.27 (step @p163 :rule instantiate :premises (@p153) :args ((@list @t119))) % 28.93/29.27 (step-pop @p192 :rule scope :premises (@p163)) % 28.93/29.27 (step @p164 :rule process_scope :premises (@p192) :args (@t124)) % 28.93/29.27 (step @p166 :rule eq_resolve :premises (@p164 @p161)) % 28.93/29.27 (step @p167 :rule implies_elim :premises (@p166)) % 28.93/29.27 (step @p168 :rule chain_m_resolution :premises (@p167 @p153) :args ((not @t125) (@list false) (@list @t52))) % 28.93/29.27 (step @p169 :rule skolemize :premises (@p168)) % 28.93/29.27 (step @p170 :rule bool-double-not-elim :args (@t128)) % 28.93/29.27 (step @p171 :rule refl :args (@t131)) % 28.93/29.27 (step @p172 :rule nary_cong :premises (@p171 @p170) :args ((or @t131 (not @t130)))) % 28.93/29.27 (step @p173 :rule cnf_or_neg :args (@t131 0)) % 28.93/29.27 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 28.93/29.27 (step @p175 :rule reordering :premises (@p174) :args ((or @t128 @t131))) % 28.93/29.27 (step @p176 :rule chain_m_resolution :premises (@p175 @p169) :args (@t128 @t132 @t133)) % 28.93/29.27 ; WARNING: add trust step for TRUST % 28.93/29.27 ; trust TRUST THEORY_LEMMA % 28.93/29.27 (step @p177 :rule trust :premises () :args ((forall @t118 (or (forall @t135 (not (_ @t116 @t134))) (_ @t116 @t117))))) % 28.93/29.27 (step @p178 :rule instantiate :premises (@p177) :args ((@list @t127))) % 28.93/29.27 (step @p179 :rule cnf_or_neg :args (@t131 1)) % 28.93/29.27 (step @p180 :rule chain_m_resolution :premises (@p179 @p169) :args ((not @t129) @t132 @t133)) % 28.93/29.27 (step @p181 :rule cnf_or_pos :args (@t137)) % 28.93/29.27 (step @p182 :rule reordering :premises (@p181) :args ((or @t129 @t136 (not @t137)))) % 28.93/29.27 (step @p183 :rule chain_m_resolution :premises (@p182 @p180 @p178) :args (@t136 (@list true false) (@list @t129 @t137))) % 28.93/29.27 (assume-push @p193 @t136) % 28.93/29.27 (step @p185 :rule instantiate :premises (@p183) :args ((@list @t126))) % 28.93/29.27 (step-pop @p194 :rule scope :premises (@p185)) % 28.93/29.27 (step @p186 :rule process_scope :premises (@p194) :args (@t130)) % 28.93/29.27 (step @p188 :rule implies_elim :premises (@p186)) % 28.93/29.27 (step @p189 :rule reordering :premises (@p188) :args ((or @t130 (not @t136)))) % 28.93/29.27 (step @p190 false :rule chain_m_resolution :premises (@p189 @p183 @p176) :args (false (@list false false) (@list @t136 @t128))) % 28.93/29.27 ) % 28.93/29.27 % SZS output end Proof % 28.93/29.27 % cvc5 exiting %------------------------------------------------------------------------------