%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV220^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.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 08:55:37 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 : SEV220^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 18:19:50 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.48 %----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 tptp.b 0) % 0.36/0.57 (declare-sort tptp.a 0) % 0.36/0.57 (declare-const tptp.w (-> (-> tptp.b Bool) Bool)) % 0.36/0.57 (declare-const tptp.f (-> tptp.b tptp.a)) % 0.36/0.57 (define @t1 () (@var "Xx" tptp.a)) % 0.36/0.57 (define @t2 () (@var "S" (-> tptp.a Bool))) % 0.36/0.57 (define @t3 () (_ @t2 @t1)) % 0.36/0.57 (define @t4 () (@var "Xt0" tptp.b)) % 0.36/0.57 (define @t5 () (_ tptp.f @t4)) % 0.36/0.57 (define @t6 () (@var "Xz" tptp.a)) % 0.36/0.57 (define @t7 () (= @t6 @t5)) % 0.36/0.57 (define @t8 () (@var "Xt" (-> tptp.b Bool))) % 0.36/0.57 (define @t9 () (_ @t8 @t4)) % 0.36/0.57 (define @t10 () (and @t9 @t7)) % 0.36/0.57 (define @t11 () (@list @t4)) % 0.36/0.57 (define @t12 () (exists @t11 @t10)) % 0.36/0.57 (define @t13 () (@list @t6)) % 0.36/0.57 (define @t14 () (lambda @t13 @t12)) % 0.36/0.57 (define @t15 () (= @t2 @t14)) % 0.36/0.57 (define @t16 () (_ tptp.w @t8)) % 0.36/0.57 (define @t17 () (and @t16 @t15)) % 0.36/0.57 (define @t18 () (@list @t8)) % 0.36/0.57 (define @t19 () (exists @t18 @t17)) % 0.36/0.57 (define @t20 () (=> @t19 @t3)) % 0.36/0.57 (define @t21 () (@list @t2)) % 0.36/0.57 (define @t22 () (forall @t21 @t20)) % 0.36/0.57 (define @t23 () (@var "Xt" tptp.b)) % 0.36/0.57 (define @t24 () (_ tptp.f @t23)) % 0.36/0.57 (define @t25 () (= @t1 @t24)) % 0.36/0.57 (define @t26 () (@var "S" (-> tptp.b Bool))) % 0.36/0.57 (define @t27 () (_ @t26 @t23)) % 0.36/0.57 (define @t28 () (_ tptp.w @t26)) % 0.36/0.57 (define @t29 () (@list @t26)) % 0.36/0.57 (define @t30 () (forall @t29 (=> @t28 @t27))) % 0.36/0.57 (define @t31 () (and @t30 @t25)) % 0.36/0.57 (define @t32 () (@list @t23)) % 0.36/0.57 (define @t33 () (exists @t32 @t31)) % 0.36/0.57 (define @t34 () (=> @t33 @t22)) % 0.36/0.57 (define @t35 () (@list @t1)) % 0.36/0.57 (define @t36 () (forall @t35 @t34)) % 0.36/0.57 (define @t37 () (not @t36)) % 0.36/0.57 (define @t38 () (@var "BOUND_VARIABLE_7559" (-> tptp.b Bool))) % 0.36/0.57 (define @t39 () (not (tptp.w @t38))) % 0.36/0.57 (define @t40 () (@var "BOUND_VARIABLE_7549" tptp.b)) % 0.36/0.57 (define @t41 () (tptp.f @t40)) % 0.36/0.57 (define @t42 () (tptp.f @t4)) % 0.36/0.57 (define @t43 () (not (_ @t38 @t4))) % 0.36/0.57 (define @t44 () (not (forall @t11 (or @t43 (not (= @t42 @t41)))))) % 0.36/0.57 (define @t45 () (tptp.w @t26)) % 0.36/0.57 (define @t46 () (not @t45)) % 0.36/0.57 (define @t47 () (not (forall @t29 (or @t46 (_ @t26 @t40))))) % 0.36/0.57 (define @t48 () (or @t47 @t44 @t39)) % 0.36/0.57 (define @t49 () (not (= @t41 @t42))) % 0.36/0.57 (define @t50 () (or @t43 @t49)) % 0.36/0.57 (define @t51 () (forall @t11 @t50)) % 0.36/0.57 (define @t52 () (not @t51)) % 0.36/0.57 (define @t53 () (not (= @t41 @t41))) % 0.36/0.57 (define @t54 () (or @t47 @t53 @t52 @t39)) % 0.36/0.57 (define @t55 () (@list @t40 @t38)) % 0.36/0.57 (define @t56 () (not (= @t1 @t42))) % 0.36/0.57 (define @t57 () (not (forall @t11 (or @t43 @t56)))) % 0.36/0.57 (define @t58 () (not (= @t1 @t41))) % 0.36/0.57 (define @t59 () (or @t58 @t47 @t58 @t57 @t39)) % 0.36/0.57 (define @t60 () (or @t47 @t58 @t57 @t39)) % 0.36/0.57 (define @t61 () (forall @t35 @t60)) % 0.36/0.57 (define @t62 () (forall @t55 @t61)) % 0.36/0.57 (define @t63 () (forall (@list @t40 @t38 @t1) @t60)) % 0.36/0.57 (define @t64 () (@list @t1 @t40 @t38)) % 0.36/0.57 (define @t65 () (or @t57 @t39)) % 0.36/0.57 (define @t66 () (or @t47 @t58)) % 0.36/0.57 (define @t67 () (or @t66 @t65)) % 0.36/0.57 (define @t68 () (forall @t64 @t67)) % 0.36/0.57 (define @t69 () (forall @t55 @t67)) % 0.36/0.57 (define @t70 () (forall (@list @t38) @t65)) % 0.36/0.57 (define @t71 () (@var "BOUND_VARIABLE_7513" (-> tptp.b Bool))) % 0.36/0.57 (define @t72 () (@list @t71)) % 0.36/0.57 (define @t73 () (forall (@list @t40) @t66)) % 0.36/0.57 (define @t74 () (or @t73 @t70)) % 0.36/0.57 (define @t75 () (not (tptp.w @t71))) % 0.36/0.57 (define @t76 () (not (_ @t71 @t4))) % 0.36/0.57 (define @t77 () (not (forall @t11 (or @t76 @t56)))) % 0.36/0.57 (define @t78 () (or @t77 @t75)) % 0.36/0.57 (define @t79 () (@list @t71)) % 0.36/0.57 (define @t80 () (forall @t79 @t78)) % 0.36/0.57 (define @t81 () (tptp.f @t23)) % 0.36/0.57 (define @t82 () (_ @t26 @t23)) % 0.36/0.57 (define @t83 () (forall @t29 (or @t46 @t82))) % 0.36/0.57 (define @t84 () (not @t83)) % 0.36/0.57 (define @t85 () (forall @t32 (or @t84 (not (= @t1 @t81))))) % 0.36/0.57 (define @t86 () (not @t85)) % 0.36/0.57 (define @t87 () (not (= @t6 @t42))) % 0.36/0.57 (define @t88 () (lambda @t13 (not (forall @t11 (or @t76 @t87))))) % 0.36/0.57 (define @t89 () (not (= @t88 @t88))) % 0.36/0.57 (define @t90 () (_ @t88 @t1)) % 0.36/0.57 (define @t91 () (or @t90 @t75 @t89)) % 0.36/0.57 (define @t92 () (not (= @t2 @t88))) % 0.36/0.57 (define @t93 () (_ @t2 @t1)) % 0.36/0.57 (define @t94 () (or @t92 @t93 @t75 @t92)) % 0.36/0.57 (define @t95 () (or @t93 @t75 @t92)) % 0.36/0.57 (define @t96 () (forall @t21 @t95)) % 0.36/0.57 (define @t97 () (forall @t79 @t96)) % 0.36/0.57 (define @t98 () (forall (@list @t71 @t2) @t95)) % 0.36/0.57 (define @t99 () (@list @t2 @t71)) % 0.36/0.57 (define @t100 () (or @t75 @t92)) % 0.36/0.57 (define @t101 () (or @t100 @t93)) % 0.36/0.57 (define @t102 () (forall @t99 @t101)) % 0.36/0.57 (define @t103 () (forall @t79 @t101)) % 0.36/0.57 (define @t104 () (forall @t79 @t100)) % 0.36/0.57 (define @t105 () (or @t104 @t93)) % 0.36/0.57 (define @t106 () (_ @t8 @t4)) % 0.36/0.57 (define @t107 () (= @t2 (lambda @t13 (not (forall @t11 (or (not @t106) @t87)))))) % 0.36/0.57 (define @t108 () (not @t107)) % 0.36/0.57 (define @t109 () (tptp.w @t8)) % 0.36/0.57 (define @t110 () (forall @t18 (or (not @t109) @t108))) % 0.36/0.57 (define @t111 () (or @t110 @t3)) % 0.36/0.57 (define @t112 () (not @t110)) % 0.36/0.57 (define @t113 () (not @t16)) % 0.36/0.57 (define @t114 () (or @t113 @t108)) % 0.36/0.57 (define @t115 () (and @t16 @t107)) % 0.36/0.57 (define @t116 () (forall @t18 (not @t115))) % 0.36/0.57 (define @t117 () (not @t116)) % 0.36/0.57 (define @t118 () (not @t7)) % 0.36/0.57 (define @t119 () (not @t9)) % 0.36/0.57 (define @t120 () (or @t119 @t118)) % 0.36/0.57 (define @t121 () (forall @t11 (not @t10))) % 0.36/0.57 (define @t122 () (not @t121)) % 0.36/0.57 (define @t123 () (not @t25)) % 0.36/0.57 (define @t124 () (or @t84 @t123)) % 0.36/0.57 (define @t125 () (and @t83 @t25)) % 0.36/0.57 (define @t126 () (forall @t32 (not @t125))) % 0.36/0.57 (define @t127 () (not @t126)) % 0.36/0.57 (define @t128 () (not @t28)) % 0.36/0.57 (define @t129 () (or @t128 @t27)) % 0.36/0.57 (define @t130 () (forall @t55 @t48)) % 0.36/0.57 (define @t131 () (@quantifiers_skolemize @t130 0)) % 0.36/0.57 (define @t132 () (tptp.f @t131)) % 0.36/0.57 (define @t133 () (@quantifiers_skolemize @t130 1)) % 0.36/0.57 (define @t134 () (forall @t11 (or (not (_ @t133 @t4)) (not (= @t42 @t132))))) % 0.36/0.57 (define @t135 () (tptp.w @t133)) % 0.36/0.57 (define @t136 () (not @t135)) % 0.36/0.57 (define @t137 () (not @t134)) % 0.36/0.57 (define @t138 () (forall @t29 (or @t46 (_ @t26 @t131)))) % 0.36/0.57 (define @t139 () (not @t138)) % 0.36/0.57 (define @t140 () (or @t139 @t137 @t136)) % 0.36/0.57 (define @t141 () (@list true)) % 0.36/0.57 (define @t142 () (@list @t140)) % 0.36/0.57 (define @t143 () (_ @t133 @t131)) % 0.36/0.57 (define @t144 () (or @t136 @t143)) % 0.36/0.57 (define @t145 () (@list false false)) % 0.36/0.57 (define @t146 () (not @t143)) % 0.36/0.57 (define @t147 () (not (= @t132 @t132))) % 0.36/0.57 (define @t148 () (or @t146 @t147)) % 0.36/0.57 (assume @p1 @t37) % 0.36/0.57 (assume @p2 true) % 0.36/0.57 (step @p3 :rule aci_norm :args ((= (or @t47 false @t44 @t39) @t48))) % 0.36/0.57 (step @p4 :rule refl :args (@t39)) % 0.36/0.57 (step @p5 :rule eq-symm :args (@t41 @t42)) % 0.36/0.57 (step @p6 :rule cong :premises (@p5) :args (@t49)) % 0.36/0.57 (step @p7 :rule refl :args (@t43)) % 0.36/0.57 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t50)) % 0.36/0.57 (step @p9 :rule cong :premises (@p8) :args (@t51)) % 0.36/0.57 (step @p10 :rule cong :premises (@p9) :args (@t52)) % 0.36/0.57 (step @p11 :rule evaluate :args ((not true))) % 0.36/0.57 (step @p12 :rule eq-refl :args (@t41)) % 0.36/0.57 (step @p13 :rule cong :premises (@p12) :args (@t53)) % 0.36/0.57 (step @p14 :rule trans :premises (@p13 @p11)) % 0.36/0.57 (step @p15 :rule refl :args (@t47)) % 0.36/0.57 (step @p16 :rule nary_cong :premises (@p15 @p14 @p10 @p4) :args (@t54)) % 0.36/0.57 (step @p17 :rule trans :premises (@p16 @p3)) % 0.36/0.57 (step @p18 :rule cong :premises (@p17) :args ((forall @t55 @t54))) % 0.36/0.57 (step @p19 :rule quant-var-elim-eq :args ((= (forall @t35 @t59) @t54))) % 0.36/0.57 (step @p20 :rule aci_norm :args ((= @t60 @t59))) % 0.36/0.57 (step @p21 :rule cong :premises (@p20) :args (@t61)) % 0.36/0.57 (step @p22 :rule trans :premises (@p21 @p19)) % 0.36/0.57 (step @p23 :rule cong :premises (@p22) :args (@t62)) % 0.36/0.57 (step @p24 :rule quant-merge-prenex :args ((= @t62 @t63))) % 0.36/0.57 (step @p25 :rule symm :premises (@p24)) % 0.36/0.57 (step @p26 :rule quant_var_reordering :args ((= (forall @t64 @t60) @t63))) % 0.36/0.57 (step @p27 :rule trans :premises (@p26 @p25 @p23)) % 0.36/0.57 (step @p28 :rule trans :premises (@p27 @p18)) % 0.36/0.57 (step @p29 :rule aci_norm :args ((= @t67 @t60))) % 0.36/0.57 (step @p30 :rule cong :premises (@p29) :args (@t68)) % 0.36/0.57 (step @p31 :rule trans :premises (@p30 @p28)) % 0.36/0.57 (step @p32 :rule quant-merge-prenex :args ((= (forall @t35 @t69) @t68))) % 0.36/0.57 (step @p33 :rule alpha_equiv :args (@t70 (@list @t38) @t72)) % 0.36/0.57 (step @p34 :rule alpha_equiv :args (@t73 (@list @t40) (@list @t23))) % 0.36/0.57 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t74)) % 0.36/0.57 (step @p36 :rule quant-miniscope-or :args ((= @t69 @t74))) % 0.36/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.36/0.57 (step @p38 :rule symm :premises (@p37)) % 0.36/0.57 (step @p39 :rule cong :premises (@p38) :args ((forall @t35 (or @t85 @t80)))) % 0.36/0.57 (step @p40 :rule trans :premises (@p39 @p32)) % 0.36/0.57 (step @p41 :rule trans :premises (@p40 @p31)) % 0.36/0.57 (step @p42 :rule refl :args (@t80)) % 0.36/0.57 (step @p43 :rule bool-double-not-elim :args (@t85)) % 0.36/0.57 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or (not @t86) @t80))) % 0.36/0.57 (step @p45 :rule bool-impl-elim :args (@t86 @t80)) % 0.36/0.57 (step @p46 :rule trans :premises (@p45 @p44)) % 0.36/0.57 (step @p47 :rule cong :premises (@p46) :args ((forall @t35 (=> @t86 @t80)))) % 0.36/0.57 (step @p48 :rule trans :premises (@p47 @p41)) % 0.36/0.57 (step @p49 :rule aci_norm :args ((= (or @t77 @t75 false) @t78))) % 0.36/0.57 (step @p50 :rule eq-refl :args (@t88)) % 0.36/0.57 (step @p51 :rule cong :premises (@p50) :args (@t89)) % 0.36/0.57 (step @p52 :rule trans :premises (@p51 @p11)) % 0.36/0.57 (step @p53 :rule refl :args (@t75)) % 0.36/0.57 (step @p54 :rule beta-reduce :args ((= @t90 @t77))) % 0.36/0.57 (step @p55 :rule nary_cong :premises (@p54 @p53 @p52) :args (@t91)) % 0.36/0.57 (step @p56 :rule trans :premises (@p55 @p49)) % 0.36/0.57 (step @p57 :rule cong :premises (@p56) :args ((forall @t79 @t91))) % 0.36/0.57 (step @p58 :rule quant-var-elim-eq :args ((= (forall @t21 @t94) @t91))) % 0.36/0.57 (step @p59 :rule aci_norm :args ((= @t95 @t94))) % 0.36/0.57 (step @p60 :rule cong :premises (@p59) :args (@t96)) % 0.36/0.57 (step @p61 :rule trans :premises (@p60 @p58)) % 0.36/0.57 (step @p62 :rule cong :premises (@p61) :args (@t97)) % 0.36/0.57 (step @p63 :rule quant-merge-prenex :args ((= @t97 @t98))) % 0.36/0.57 (step @p64 :rule symm :premises (@p63)) % 0.36/0.57 (step @p65 :rule quant_var_reordering :args ((= (forall @t99 @t95) @t98))) % 0.36/0.57 (step @p66 :rule trans :premises (@p65 @p64 @p62)) % 0.36/0.57 (step @p67 :rule trans :premises (@p66 @p57)) % 0.36/0.57 (step @p68 :rule aci_norm :args ((= @t101 @t95))) % 0.36/0.57 (step @p69 :rule cong :premises (@p68) :args (@t102)) % 0.36/0.57 (step @p70 :rule trans :premises (@p69 @p67)) % 0.36/0.57 (step @p71 :rule quant-merge-prenex :args ((= (forall @t21 @t103) @t102))) % 0.36/0.57 (step @p72 :rule refl :args (@t93)) % 0.36/0.57 (step @p73 :rule alpha_equiv :args (@t104 @t72 (@list @t8))) % 0.36/0.57 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t105)) % 0.36/0.57 (step @p75 :rule quant-miniscope-or :args ((= @t103 @t105))) % 0.36/0.57 (step @p76 :rule trans :premises (@p75 @p74)) % 0.36/0.57 (step @p77 :rule symm :premises (@p76)) % 0.36/0.57 (step @p78 :rule cong :premises (@p77) :args ((forall @t21 (or @t110 @t93)))) % 0.36/0.57 (step @p79 :rule trans :premises (@p78 @p71)) % 0.36/0.57 (step @p80 :rule trans :premises (@p79 @p70)) % 0.36/0.57 (step @p81 :rule refl :args (@t93)) % 0.36/0.57 (step @p82 :rule refl :args (@t3)) % 0.36/0.57 (step @p83 :rule cong :premises (@p82 @p81) :args ((= @t3 @t93))) % 0.36/0.57 (step @p84 :rule symm :premises (@p83)) % 0.36/0.57 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.36/0.57 (step @p86 :rule refl :args (@t110)) % 0.36/0.57 (step @p87 :rule nary_cong :premises (@p86 @p85) :args (@t111)) % 0.36/0.57 (step @p88 :rule cong :premises (@p87) :args ((forall @t21 @t111))) % 0.36/0.57 (step @p89 :rule trans :premises (@p88 @p80)) % 0.36/0.57 (step @p90 :rule bool-double-not-elim :args (@t110)) % 0.36/0.57 (step @p91 :rule nary_cong :premises (@p90 @p82) :args ((or (not @t112) @t3))) % 0.36/0.57 (step @p92 :rule bool-impl-elim :args (@t112 @t3)) % 0.36/0.57 (step @p93 :rule trans :premises (@p92 @p91)) % 0.36/0.57 (step @p94 :rule cong :premises (@p93) :args ((forall @t21 (=> @t112 @t3)))) % 0.36/0.57 (step @p95 :rule trans :premises (@p94 @p89)) % 0.36/0.57 (step @p96 :rule refl :args (@t3)) % 0.36/0.57 (step @p97 :rule refl :args (@t108)) % 0.36/0.57 (step @p98 :rule refl :args (@t109)) % 0.36/0.57 (step @p99 :rule refl :args (@t16)) % 0.36/0.57 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t16 @t109))) % 0.36/0.57 (step @p101 :rule symm :premises (@p100)) % 0.36/0.57 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.36/0.57 (step @p103 :rule cong :premises (@p102) :args (@t113)) % 0.36/0.57 (step @p104 :rule nary_cong :premises (@p103 @p97) :args (@t114)) % 0.36/0.57 (step @p105 :rule cong :premises (@p104) :args ((forall @t18 @t114))) % 0.36/0.57 (step @p106 :rule bool-and-de-morgan :args (@t16 @t107 true)) % 0.36/0.57 (step @p107 :rule cong :premises (@p106) :args (@t116)) % 0.36/0.57 (step @p108 :rule trans :premises (@p107 @p105)) % 0.36/0.57 (step @p109 :rule cong :premises (@p108) :args (@t117)) % 0.36/0.57 (step @p110 :rule exists-elim :args ((= (exists @t18 @t115) @t117))) % 0.36/0.57 (step @p111 :rule trans :premises (@p110 @p109)) % 0.36/0.57 (step @p112 :rule refl :args (@t42)) % 0.36/0.57 (step @p113 :rule refl :args (@t5)) % 0.36/0.57 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t5 @t42))) % 0.36/0.57 (step @p115 :rule symm :premises (@p114)) % 0.36/0.57 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 0.36/0.57 (step @p117 :rule refl :args (@t6)) % 0.36/0.57 (step @p118 :rule cong :premises (@p117 @p116) :args (@t7)) % 0.36/0.57 (step @p119 :rule cong :premises (@p118) :args (@t118)) % 0.36/0.57 (step @p120 :rule refl :args (@t106)) % 0.36/0.57 (step @p121 :rule refl :args (@t9)) % 0.36/0.57 (step @p122 :rule cong :premises (@p121 @p120) :args ((= @t9 @t106))) % 0.36/0.57 (step @p123 :rule symm :premises (@p122)) % 0.36/0.57 (step @p124 :rule eq_resolve :premises (@p121 @p123)) % 0.36/0.57 (step @p125 :rule cong :premises (@p124) :args (@t119)) % 0.36/0.57 (step @p126 :rule nary_cong :premises (@p125 @p119) :args (@t120)) % 0.36/0.57 (step @p127 :rule cong :premises (@p126) :args ((forall @t11 @t120))) % 0.36/0.57 (step @p128 :rule bool-and-de-morgan :args (@t9 @t7 true)) % 0.36/0.57 (step @p129 :rule cong :premises (@p128) :args (@t121)) % 0.36/0.57 (step @p130 :rule trans :premises (@p129 @p127)) % 0.36/0.57 (step @p131 :rule cong :premises (@p130) :args (@t122)) % 0.36/0.57 (step @p132 :rule exists-elim :args ((= @t12 @t122))) % 0.36/0.57 (step @p133 :rule trans :premises (@p132 @p131)) % 0.36/0.57 (step @p134 :rule cong :premises (@p133) :args (@t14)) % 0.36/0.57 (step @p135 :rule refl :args (@t2)) % 0.36/0.57 (step @p136 :rule cong :premises (@p135 @p134) :args (@t15)) % 0.36/0.57 (step @p137 :rule refl :args (@t16)) % 0.36/0.57 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t17)) % 0.36/0.57 (step @p139 :rule cong :premises (@p138) :args (@t19)) % 0.36/0.57 (step @p140 :rule trans :premises (@p139 @p111)) % 0.36/0.57 (step @p141 :rule cong :premises (@p140 @p96) :args (@t20)) % 0.36/0.57 (step @p142 :rule cong :premises (@p141) :args (@t22)) % 0.36/0.57 (step @p143 :rule trans :premises (@p142 @p95)) % 0.36/0.57 (step @p144 :rule refl :args (@t81)) % 0.36/0.57 (step @p145 :rule refl :args (@t24)) % 0.36/0.57 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t24 @t81))) % 0.36/0.57 (step @p147 :rule symm :premises (@p146)) % 0.36/0.57 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.36/0.57 (step @p149 :rule refl :args (@t1)) % 0.36/0.57 (step @p150 :rule cong :premises (@p149 @p148) :args (@t25)) % 0.36/0.57 (step @p151 :rule cong :premises (@p150) :args (@t123)) % 0.36/0.57 (step @p152 :rule refl :args (@t84)) % 0.36/0.57 (step @p153 :rule nary_cong :premises (@p152 @p151) :args (@t124)) % 0.36/0.57 (step @p154 :rule cong :premises (@p153) :args ((forall @t32 @t124))) % 0.36/0.57 (step @p155 :rule bool-and-de-morgan :args (@t83 @t25 true)) % 0.36/0.57 (step @p156 :rule cong :premises (@p155) :args (@t126)) % 0.36/0.57 (step @p157 :rule trans :premises (@p156 @p154)) % 0.36/0.57 (step @p158 :rule cong :premises (@p157) :args (@t127)) % 0.36/0.57 (step @p159 :rule exists-elim :args ((= (exists @t32 @t125) @t127))) % 0.36/0.57 (step @p160 :rule trans :premises (@p159 @p158)) % 0.36/0.57 (step @p161 :rule refl :args (@t25)) % 0.36/0.57 (step @p162 :rule refl :args (@t82)) % 0.36/0.57 (step @p163 :rule refl :args (@t27)) % 0.36/0.57 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t27 @t82))) % 0.36/0.57 (step @p165 :rule symm :premises (@p164)) % 0.36/0.57 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.36/0.57 (step @p167 :rule refl :args (@t45)) % 0.36/0.57 (step @p168 :rule refl :args (@t28)) % 0.36/0.57 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t28 @t45))) % 0.36/0.57 (step @p170 :rule symm :premises (@p169)) % 0.36/0.57 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.36/0.57 (step @p172 :rule cong :premises (@p171) :args (@t128)) % 0.36/0.57 (step @p173 :rule nary_cong :premises (@p172 @p166) :args (@t129)) % 0.36/0.57 (step @p174 :rule cong :premises (@p173) :args ((forall @t29 @t129))) % 0.36/0.57 (step @p175 :rule bool-impl-elim :args (@t28 @t27)) % 0.36/0.57 (step @p176 :rule cong :premises (@p175) :args (@t30)) % 0.36/0.57 (step @p177 :rule trans :premises (@p176 @p174)) % 0.36/0.57 (step @p178 :rule nary_cong :premises (@p177 @p161) :args (@t31)) % 0.36/0.57 (step @p179 :rule cong :premises (@p178) :args (@t33)) % 0.36/0.57 (step @p180 :rule trans :premises (@p179 @p160)) % 0.36/0.57 (step @p181 :rule cong :premises (@p180 @p143) :args (@t34)) % 0.36/0.57 (step @p182 :rule cong :premises (@p181) :args (@t36)) % 0.36/0.57 (step @p183 :rule trans :premises (@p182 @p48)) % 0.36/0.57 (step @p184 :rule cong :premises (@p183) :args (@t37)) % 0.36/0.57 (step @p185 :rule eq_resolve :premises (@p1 @p184)) % 0.36/0.57 (step @p186 :rule skolemize :premises (@p185)) % 0.36/0.57 (step @p187 :rule bool-double-not-elim :args (@t134)) % 0.36/0.57 (step @p188 :rule refl :args (@t140)) % 0.36/0.57 (step @p189 :rule nary_cong :premises (@p188 @p187) :args ((or @t140 (not @t137)))) % 0.36/0.57 (step @p190 :rule cnf_or_neg :args (@t140 1)) % 0.36/0.57 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.36/0.57 (step @p192 :rule reordering :premises (@p191) :args ((or @t134 @t140))) % 0.36/0.57 (step @p193 :rule chain_m_resolution :premises (@p192 @p186) :args (@t134 @t141 @t142)) % 0.36/0.57 (step @p194 :rule bool-double-not-elim :args (@t138)) % 0.36/0.57 (step @p195 :rule nary_cong :premises (@p188 @p194) :args ((or @t140 (not @t139)))) % 0.36/0.57 (step @p196 :rule cnf_or_neg :args (@t140 0)) % 0.36/0.57 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 0.36/0.57 (step @p198 :rule reordering :premises (@p197) :args ((or @t138 @t140))) % 0.36/0.57 (step @p199 :rule chain_m_resolution :premises (@p198 @p186) :args (@t138 @t141 @t142)) % 0.36/0.57 (step @p200 :rule instantiate :premises (@p199) :args ((@list @t133))) % 0.36/0.57 (step @p201 :rule bool-double-not-elim :args (@t135)) % 0.36/0.57 (step @p202 :rule nary_cong :premises (@p188 @p201) :args ((or @t140 (not @t136)))) % 0.36/0.57 (step @p203 :rule cnf_or_neg :args (@t140 2)) % 0.36/0.57 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.36/0.57 (step @p205 :rule reordering :premises (@p204) :args ((or @t135 @t140))) % 0.36/0.57 (step @p206 :rule chain_m_resolution :premises (@p205 @p186) :args (@t135 @t141 @t142)) % 0.36/0.57 (step @p207 :rule cnf_or_pos :args (@t144)) % 0.36/0.57 (step @p208 :rule reordering :premises (@p207) :args ((or @t136 @t143 (not @t144)))) % 0.36/0.57 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p200) :args (@t143 @t145 (@list @t135 @t144))) % 0.36/0.57 (step @p210 :rule aci_norm :args ((= (or @t146 false) @t146))) % 0.36/0.57 (step @p211 :rule eq-refl :args (@t132)) % 0.36/0.57 (step @p212 :rule cong :premises (@p211) :args (@t147)) % 0.36/0.57 (step @p213 :rule trans :premises (@p212 @p11)) % 0.36/0.57 (step @p214 :rule refl :args (@t146)) % 0.36/0.57 (step @p215 :rule nary_cong :premises (@p214 @p213) :args (@t148)) % 0.36/0.57 (step @p216 :rule trans :premises (@p215 @p210)) % 0.36/0.57 (step @p217 :rule refl :args (@t134)) % 0.36/0.57 (step @p218 :rule cong :premises (@p217 @p216) :args ((=> @t134 @t148))) % 0.36/0.57 (assume-push @p226 @t134) % 0.36/0.57 (step @p220 :rule instantiate :premises (@p193) :args ((@list @t131))) % 0.36/0.57 (step-pop @p227 :rule scope :premises (@p220)) % 0.36/0.57 (step @p221 :rule process_scope :premises (@p227) :args (@t148)) % 0.36/0.57 (step @p223 :rule eq_resolve :premises (@p221 @p218)) % 0.36/0.57 (step @p224 :rule implies_elim :premises (@p223)) % 0.36/0.57 (step @p225 false :rule chain_m_resolution :premises (@p224 @p209 @p193) :args (false @t145 (@list @t143 @t134))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------