%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV223^5 : 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 : n029.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 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV223^5 : 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 : n029.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 18:21:02 EDT 2026 % 0.17/0.34 % CPUTime : % 0.26/0.48 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort tptp.b 0) % 0.38/0.57 (declare-sort tptp.a 0) % 0.38/0.57 (declare-const tptp.w (-> (-> tptp.b Bool) Bool)) % 0.38/0.57 (declare-const tptp.f (-> tptp.b tptp.a)) % 0.38/0.57 (define @t1 () (@var "Xx" tptp.a)) % 0.38/0.57 (define @t2 () (@var "S" (-> tptp.a Bool))) % 0.38/0.57 (define @t3 () (_ @t2 @t1)) % 0.38/0.57 (define @t4 () (@var "Xt0" tptp.b)) % 0.38/0.57 (define @t5 () (_ tptp.f @t4)) % 0.38/0.57 (define @t6 () (@var "Xz" tptp.a)) % 0.38/0.57 (define @t7 () (= @t6 @t5)) % 0.38/0.57 (define @t8 () (@var "Xt" (-> tptp.b Bool))) % 0.38/0.57 (define @t9 () (_ @t8 @t4)) % 0.38/0.57 (define @t10 () (and @t9 @t7)) % 0.38/0.57 (define @t11 () (@list @t4)) % 0.38/0.57 (define @t12 () (exists @t11 @t10)) % 0.38/0.57 (define @t13 () (@list @t6)) % 0.38/0.57 (define @t14 () (lambda @t13 @t12)) % 0.38/0.57 (define @t15 () (= @t2 @t14)) % 0.38/0.57 (define @t16 () (_ tptp.w @t8)) % 0.38/0.57 (define @t17 () (and @t16 @t15)) % 0.38/0.57 (define @t18 () (@list @t8)) % 0.38/0.57 (define @t19 () (exists @t18 @t17)) % 0.38/0.57 (define @t20 () (and @t19 @t3)) % 0.38/0.57 (define @t21 () (@list @t2)) % 0.38/0.57 (define @t22 () (exists @t21 @t20)) % 0.38/0.57 (define @t23 () (@list @t1)) % 0.38/0.57 (define @t24 () (lambda @t23 @t22)) % 0.38/0.57 (define @t25 () (@var "Xt" tptp.b)) % 0.38/0.57 (define @t26 () (_ tptp.f @t25)) % 0.38/0.57 (define @t27 () (= @t6 @t26)) % 0.38/0.57 (define @t28 () (@var "S" (-> tptp.b Bool))) % 0.38/0.57 (define @t29 () (_ @t28 @t25)) % 0.38/0.57 (define @t30 () (_ tptp.w @t28)) % 0.38/0.57 (define @t31 () (and @t30 @t29)) % 0.38/0.57 (define @t32 () (@list @t28)) % 0.38/0.57 (define @t33 () (exists @t32 @t31)) % 0.38/0.57 (define @t34 () (and @t33 @t27)) % 0.38/0.57 (define @t35 () (@list @t25)) % 0.38/0.57 (define @t36 () (exists @t35 @t34)) % 0.38/0.57 (define @t37 () (lambda @t13 @t36)) % 0.38/0.57 (define @t38 () (= @t37 @t24)) % 0.38/0.57 (define @t39 () (not @t38)) % 0.38/0.57 (define @t40 () (@var "BOUND_VARIABLE_7480" (-> tptp.b Bool))) % 0.38/0.57 (define @t41 () (not (_ @t40 @t25))) % 0.38/0.57 (define @t42 () (not (tptp.w @t40))) % 0.38/0.57 (define @t43 () (tptp.f @t25)) % 0.38/0.57 (define @t44 () (not (= @t6 @t43))) % 0.38/0.57 (define @t45 () (or @t44 @t42 @t41)) % 0.38/0.57 (define @t46 () (@list @t25 @t40)) % 0.38/0.57 (define @t47 () (lambda @t13 (not (forall @t46 @t45)))) % 0.38/0.57 (define @t48 () (@purify @t47)) % 0.38/0.57 (define @t49 () (@var "BOUND_VARIABLE_7571" tptp.b)) % 0.38/0.57 (define @t50 () (tptp.f @t49)) % 0.38/0.57 (define @t51 () (not (= @t1 @t50))) % 0.38/0.57 (define @t52 () (@var "BOUND_VARIABLE_7537" (-> tptp.b Bool))) % 0.38/0.57 (define @t53 () (not (_ @t52 @t49))) % 0.38/0.57 (define @t54 () (not (tptp.w @t52))) % 0.38/0.57 (define @t55 () (or @t54 @t53 @t51)) % 0.38/0.57 (define @t56 () (@list @t52 @t49)) % 0.38/0.57 (define @t57 () (lambda @t23 (not (forall @t56 @t55)))) % 0.38/0.57 (define @t58 () (@purify @t57)) % 0.38/0.57 (define @t59 () (= @t47 @t57)) % 0.38/0.57 (define @t60 () (or @t53 @t51)) % 0.38/0.57 (define @t61 () (or @t60 @t54)) % 0.38/0.57 (define @t62 () (forall @t56 @t61)) % 0.38/0.57 (define @t63 () (@list @t49)) % 0.38/0.57 (define @t64 () (forall @t63 @t61)) % 0.38/0.57 (define @t65 () (@list @t52)) % 0.38/0.57 (define @t66 () (forall @t63 @t60)) % 0.38/0.57 (define @t67 () (or @t66 @t54)) % 0.38/0.57 (define @t68 () (tptp.f @t4)) % 0.38/0.57 (define @t69 () (not (_ @t52 @t4))) % 0.38/0.57 (define @t70 () (forall @t11 (or @t69 (not (= @t1 @t68))))) % 0.38/0.57 (define @t71 () (or @t70 @t54)) % 0.38/0.57 (define @t72 () (not (= @t6 @t68))) % 0.38/0.57 (define @t73 () (lambda @t13 (not (forall @t11 (or @t69 @t72))))) % 0.38/0.57 (define @t74 () (not (= @t73 @t73))) % 0.38/0.57 (define @t75 () (_ @t73 @t1)) % 0.38/0.57 (define @t76 () (not @t75)) % 0.38/0.57 (define @t77 () (or @t76 @t54 @t74)) % 0.38/0.57 (define @t78 () (not (= @t2 @t73))) % 0.38/0.57 (define @t79 () (_ @t2 @t1)) % 0.38/0.57 (define @t80 () (not @t79)) % 0.38/0.57 (define @t81 () (or @t78 @t80 @t54 @t78)) % 0.38/0.57 (define @t82 () (or @t80 @t54 @t78)) % 0.38/0.57 (define @t83 () (forall @t21 @t82)) % 0.38/0.57 (define @t84 () (forall @t65 @t83)) % 0.38/0.57 (define @t85 () (forall (@list @t52 @t2) @t82)) % 0.38/0.57 (define @t86 () (@list @t2 @t52)) % 0.38/0.57 (define @t87 () (or @t54 @t78)) % 0.38/0.57 (define @t88 () (or @t87 @t80)) % 0.38/0.57 (define @t89 () (forall @t86 @t88)) % 0.38/0.57 (define @t90 () (forall @t65 @t88)) % 0.38/0.57 (define @t91 () (forall @t65 @t87)) % 0.38/0.57 (define @t92 () (or @t91 @t80)) % 0.38/0.57 (define @t93 () (_ @t8 @t4)) % 0.38/0.57 (define @t94 () (= @t2 (lambda @t13 (not (forall @t11 (or (not @t93) @t72)))))) % 0.38/0.57 (define @t95 () (not @t94)) % 0.38/0.57 (define @t96 () (tptp.w @t8)) % 0.38/0.57 (define @t97 () (forall @t18 (or (not @t96) @t95))) % 0.38/0.57 (define @t98 () (not @t3)) % 0.38/0.57 (define @t99 () (or @t97 @t98)) % 0.38/0.57 (define @t100 () (not @t97)) % 0.38/0.57 (define @t101 () (and @t100 @t3)) % 0.38/0.57 (define @t102 () (forall @t21 (not @t101))) % 0.38/0.57 (define @t103 () (not @t102)) % 0.38/0.57 (define @t104 () (not @t16)) % 0.38/0.57 (define @t105 () (or @t104 @t95)) % 0.38/0.57 (define @t106 () (and @t16 @t94)) % 0.38/0.57 (define @t107 () (forall @t18 (not @t106))) % 0.38/0.57 (define @t108 () (not @t107)) % 0.38/0.57 (define @t109 () (not @t7)) % 0.38/0.57 (define @t110 () (not @t9)) % 0.38/0.57 (define @t111 () (or @t110 @t109)) % 0.38/0.57 (define @t112 () (forall @t11 (not @t10))) % 0.38/0.57 (define @t113 () (not @t112)) % 0.38/0.57 (define @t114 () (or @t42 @t41)) % 0.38/0.57 (define @t115 () (or @t114 @t44)) % 0.38/0.57 (define @t116 () (forall @t46 @t115)) % 0.38/0.57 (define @t117 () (@list @t40)) % 0.38/0.57 (define @t118 () (forall @t117 @t115)) % 0.38/0.57 (define @t119 () (forall @t117 @t114)) % 0.38/0.57 (define @t120 () (or @t119 @t44)) % 0.38/0.57 (define @t121 () (_ @t28 @t25)) % 0.38/0.57 (define @t122 () (tptp.w @t28)) % 0.38/0.57 (define @t123 () (forall @t32 (or (not @t122) (not @t121)))) % 0.38/0.57 (define @t124 () (not @t27)) % 0.38/0.57 (define @t125 () (or @t123 @t124)) % 0.38/0.57 (define @t126 () (not @t123)) % 0.38/0.57 (define @t127 () (and @t126 @t27)) % 0.38/0.57 (define @t128 () (forall @t35 (not @t127))) % 0.38/0.57 (define @t129 () (not @t128)) % 0.38/0.57 (define @t130 () (not @t29)) % 0.38/0.57 (define @t131 () (not @t30)) % 0.38/0.57 (define @t132 () (or @t131 @t130)) % 0.38/0.57 (define @t133 () (forall @t32 (not @t31))) % 0.38/0.57 (define @t134 () (not @t133)) % 0.38/0.57 (define @t135 () (@const 0 tptp.a)) % 0.38/0.57 (define @t136 () (not (= @t50 @t135))) % 0.38/0.57 (define @t137 () (or @t54 @t53 @t136)) % 0.38/0.57 (define @t138 () (forall @t56 @t137)) % 0.38/0.57 (define @t139 () (not @t138)) % 0.38/0.57 (define @t140 () (forall @t46 (or (not (= @t43 @t135)) @t42 @t41))) % 0.38/0.57 (define @t141 () (not @t140)) % 0.38/0.57 (define @t142 () (not (= @t135 @t43))) % 0.38/0.57 (define @t143 () (or @t142 @t42 @t41)) % 0.38/0.57 (define @t144 () (forall @t46 @t143)) % 0.38/0.57 (define @t145 () (not @t144)) % 0.38/0.57 (define @t146 () (_ @t47 @t135)) % 0.38/0.57 (define @t147 () (_ @t48 @t135)) % 0.38/0.57 (define @t148 () (not (= @t135 @t50))) % 0.38/0.57 (define @t149 () (or @t54 @t53 @t148)) % 0.38/0.57 (define @t150 () (forall @t56 @t149)) % 0.38/0.57 (define @t151 () (not @t150)) % 0.38/0.57 (define @t152 () (_ @t57 @t135)) % 0.38/0.57 (define @t153 () (_ @t58 @t135)) % 0.38/0.57 (define @t154 () (= @t153 @t147)) % 0.38/0.57 (define @t155 () (not @t154)) % 0.38/0.57 (define @t156 () (= @t58 @t48)) % 0.38/0.57 (define @t157 () (or @t156 @t155)) % 0.38/0.57 (define @t158 () (= @t141 @t139)) % 0.38/0.57 (define @t159 () (@list true)) % 0.38/0.57 (define @t160 () (or @t136 @t54 @t53)) % 0.38/0.57 (define @t161 () (forall @t56 @t160)) % 0.38/0.57 (assume @p1 @t39) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 :rule eq-symm :args (@t48 @t58)) % 0.38/0.57 (step @p4 :rule eq-refl :args (@t57)) % 0.38/0.57 (step @p5 :rule skolem_intro :args (@t58)) % 0.38/0.57 (step @p6 :rule refl :args (@t57)) % 0.38/0.57 (step @p7 :rule cong :premises (@p6 @p5) :args ((= @t57 @t58))) % 0.38/0.57 (step @p8 :rule trans :premises (@p7 @p4)) % 0.38/0.57 (step @p9 :rule true_elim :premises (@p8)) % 0.38/0.57 (step @p10 :rule eq-refl :args (@t47)) % 0.38/0.57 (step @p11 :rule skolem_intro :args (@t48)) % 0.38/0.57 (step @p12 :rule refl :args (@t47)) % 0.38/0.57 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t47 @t48))) % 0.38/0.57 (step @p14 :rule trans :premises (@p13 @p10)) % 0.38/0.57 (step @p15 :rule true_elim :premises (@p14)) % 0.38/0.57 (step @p16 :rule cong :premises (@p15 @p9) :args (@t59)) % 0.38/0.57 (step @p17 :rule trans :premises (@p16 @p3)) % 0.38/0.57 (step @p18 :rule cong :premises (@p17) :args ((not @t59))) % 0.38/0.57 (step @p19 :rule aci_norm :args ((= @t61 @t55))) % 0.38/0.57 (step @p20 :rule cong :premises (@p19) :args (@t62)) % 0.38/0.57 (step @p21 :rule quant-merge-prenex :args ((= (forall @t65 @t64) @t62))) % 0.38/0.57 (step @p22 :rule refl :args (@t54)) % 0.38/0.57 (step @p23 :rule alpha_equiv :args (@t66 (@list @t49) (@list @t4))) % 0.38/0.57 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t67)) % 0.38/0.57 (step @p25 :rule quant-miniscope-or :args ((= @t64 @t67))) % 0.38/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.38/0.57 (step @p27 :rule symm :premises (@p26)) % 0.38/0.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t65 @t71))) % 0.38/0.57 (step @p29 :rule trans :premises (@p28 @p21)) % 0.38/0.57 (step @p30 :rule trans :premises (@p29 @p20)) % 0.38/0.57 (step @p31 :rule aci_norm :args ((= (or @t70 @t54 false) @t71))) % 0.38/0.57 (step @p32 :rule evaluate :args ((not true))) % 0.38/0.57 (step @p33 :rule eq-refl :args (@t73)) % 0.38/0.57 (step @p34 :rule cong :premises (@p33) :args (@t74)) % 0.38/0.57 (step @p35 :rule trans :premises (@p34 @p32)) % 0.38/0.57 (step @p36 :rule refl :args (@t54)) % 0.38/0.57 (step @p37 :rule bool-double-not-elim :args (@t70)) % 0.38/0.57 (step @p38 :rule beta-reduce :args ((= @t75 (not @t70)))) % 0.38/0.57 (step @p39 :rule cong :premises (@p38) :args (@t76)) % 0.38/0.57 (step @p40 :rule trans :premises (@p39 @p37)) % 0.38/0.57 (step @p41 :rule nary_cong :premises (@p40 @p36 @p35) :args (@t77)) % 0.38/0.57 (step @p42 :rule trans :premises (@p41 @p31)) % 0.38/0.57 (step @p43 :rule cong :premises (@p42) :args ((forall @t65 @t77))) % 0.38/0.57 (step @p44 :rule trans :premises (@p43 @p30)) % 0.38/0.57 (step @p45 :rule quant-var-elim-eq :args ((= (forall @t21 @t81) @t77))) % 0.38/0.57 (step @p46 :rule aci_norm :args ((= @t82 @t81))) % 0.38/0.57 (step @p47 :rule cong :premises (@p46) :args (@t83)) % 0.38/0.57 (step @p48 :rule trans :premises (@p47 @p45)) % 0.38/0.57 (step @p49 :rule cong :premises (@p48) :args (@t84)) % 0.38/0.57 (step @p50 :rule quant-merge-prenex :args ((= @t84 @t85))) % 0.38/0.57 (step @p51 :rule symm :premises (@p50)) % 0.38/0.57 (step @p52 :rule quant_var_reordering :args ((= (forall @t86 @t82) @t85))) % 0.38/0.57 (step @p53 :rule trans :premises (@p52 @p51 @p49)) % 0.38/0.57 (step @p54 :rule trans :premises (@p53 @p44)) % 0.38/0.57 (step @p55 :rule aci_norm :args ((= @t88 @t82))) % 0.38/0.57 (step @p56 :rule cong :premises (@p55) :args (@t89)) % 0.38/0.57 (step @p57 :rule trans :premises (@p56 @p54)) % 0.38/0.57 (step @p58 :rule quant-merge-prenex :args ((= (forall @t21 @t90) @t89))) % 0.38/0.57 (step @p59 :rule refl :args (@t80)) % 0.38/0.57 (step @p60 :rule alpha_equiv :args (@t91 (@list @t52) (@list @t8))) % 0.38/0.57 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t92)) % 0.38/0.57 (step @p62 :rule quant-miniscope-or :args ((= @t90 @t92))) % 0.38/0.57 (step @p63 :rule trans :premises (@p62 @p61)) % 0.38/0.57 (step @p64 :rule symm :premises (@p63)) % 0.38/0.57 (step @p65 :rule cong :premises (@p64) :args ((forall @t21 (or @t97 @t80)))) % 0.38/0.57 (step @p66 :rule trans :premises (@p65 @p58)) % 0.38/0.57 (step @p67 :rule trans :premises (@p66 @p57)) % 0.38/0.57 (step @p68 :rule refl :args (@t79)) % 0.38/0.57 (step @p69 :rule refl :args (@t3)) % 0.38/0.57 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t3 @t79))) % 0.38/0.57 (step @p71 :rule symm :premises (@p70)) % 0.38/0.57 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.38/0.57 (step @p73 :rule cong :premises (@p72) :args (@t98)) % 0.38/0.57 (step @p74 :rule refl :args (@t97)) % 0.38/0.57 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t99)) % 0.38/0.57 (step @p76 :rule cong :premises (@p75) :args ((forall @t21 @t99))) % 0.38/0.57 (step @p77 :rule trans :premises (@p76 @p67)) % 0.38/0.57 (step @p78 :rule refl :args (@t98)) % 0.38/0.57 (step @p79 :rule bool-double-not-elim :args (@t97)) % 0.38/0.57 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t100) @t98))) % 0.38/0.57 (step @p81 :rule bool-and-de-morgan :args (@t100 @t3 true)) % 0.38/0.57 (step @p82 :rule trans :premises (@p81 @p80)) % 0.38/0.57 (step @p83 :rule cong :premises (@p82) :args (@t102)) % 0.38/0.57 (step @p84 :rule trans :premises (@p83 @p77)) % 0.38/0.57 (step @p85 :rule cong :premises (@p84) :args (@t103)) % 0.38/0.57 (step @p86 :rule exists-elim :args ((= (exists @t21 @t101) @t103))) % 0.38/0.57 (step @p87 :rule trans :premises (@p86 @p85)) % 0.38/0.57 (step @p88 :rule refl :args (@t3)) % 0.38/0.57 (step @p89 :rule refl :args (@t95)) % 0.38/0.57 (step @p90 :rule refl :args (@t96)) % 0.38/0.57 (step @p91 :rule refl :args (@t16)) % 0.38/0.57 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t16 @t96))) % 0.38/0.57 (step @p93 :rule symm :premises (@p92)) % 0.38/0.57 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.38/0.57 (step @p95 :rule cong :premises (@p94) :args (@t104)) % 0.38/0.57 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t105)) % 0.38/0.57 (step @p97 :rule cong :premises (@p96) :args ((forall @t18 @t105))) % 0.38/0.57 (step @p98 :rule bool-and-de-morgan :args (@t16 @t94 true)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98) :args (@t107)) % 0.38/0.57 (step @p100 :rule trans :premises (@p99 @p97)) % 0.38/0.57 (step @p101 :rule cong :premises (@p100) :args (@t108)) % 0.38/0.57 (step @p102 :rule exists-elim :args ((= (exists @t18 @t106) @t108))) % 0.38/0.57 (step @p103 :rule trans :premises (@p102 @p101)) % 0.38/0.57 (step @p104 :rule refl :args (@t68)) % 0.38/0.57 (step @p105 :rule refl :args (@t5)) % 0.38/0.57 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t5 @t68))) % 0.38/0.57 (step @p107 :rule symm :premises (@p106)) % 0.38/0.57 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.38/0.57 (step @p109 :rule refl :args (@t6)) % 0.38/0.57 (step @p110 :rule cong :premises (@p109 @p108) :args (@t7)) % 0.38/0.57 (step @p111 :rule cong :premises (@p110) :args (@t109)) % 0.38/0.57 (step @p112 :rule refl :args (@t93)) % 0.38/0.57 (step @p113 :rule refl :args (@t9)) % 0.38/0.57 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t9 @t93))) % 0.38/0.57 (step @p115 :rule symm :premises (@p114)) % 0.38/0.57 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 0.38/0.57 (step @p117 :rule cong :premises (@p116) :args (@t110)) % 0.38/0.57 (step @p118 :rule nary_cong :premises (@p117 @p111) :args (@t111)) % 0.38/0.57 (step @p119 :rule cong :premises (@p118) :args ((forall @t11 @t111))) % 0.38/0.57 (step @p120 :rule bool-and-de-morgan :args (@t9 @t7 true)) % 0.38/0.57 (step @p121 :rule cong :premises (@p120) :args (@t112)) % 0.38/0.57 (step @p122 :rule trans :premises (@p121 @p119)) % 0.38/0.57 (step @p123 :rule cong :premises (@p122) :args (@t113)) % 0.38/0.57 (step @p124 :rule exists-elim :args ((= @t12 @t113))) % 0.38/0.57 (step @p125 :rule trans :premises (@p124 @p123)) % 0.38/0.57 (step @p126 :rule cong :premises (@p125) :args (@t14)) % 0.38/0.57 (step @p127 :rule refl :args (@t2)) % 0.38/0.57 (step @p128 :rule cong :premises (@p127 @p126) :args (@t15)) % 0.38/0.57 (step @p129 :rule refl :args (@t16)) % 0.38/0.57 (step @p130 :rule nary_cong :premises (@p129 @p128) :args (@t17)) % 0.38/0.57 (step @p131 :rule cong :premises (@p130) :args (@t19)) % 0.38/0.57 (step @p132 :rule trans :premises (@p131 @p103)) % 0.38/0.57 (step @p133 :rule nary_cong :premises (@p132 @p88) :args (@t20)) % 0.38/0.57 (step @p134 :rule cong :premises (@p133) :args (@t22)) % 0.38/0.57 (step @p135 :rule trans :premises (@p134 @p87)) % 0.38/0.57 (step @p136 :rule cong :premises (@p135) :args (@t24)) % 0.38/0.57 (step @p137 :rule aci_norm :args ((= @t115 @t45))) % 0.38/0.57 (step @p138 :rule cong :premises (@p137) :args (@t116)) % 0.38/0.57 (step @p139 :rule quant-merge-prenex :args ((= (forall @t35 @t118) @t116))) % 0.38/0.57 (step @p140 :rule refl :args (@t44)) % 0.38/0.57 (step @p141 :rule alpha_equiv :args (@t119 (@list @t40) (@list @t28))) % 0.38/0.57 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t120)) % 0.38/0.57 (step @p143 :rule quant-miniscope-or :args ((= @t118 @t120))) % 0.38/0.57 (step @p144 :rule trans :premises (@p143 @p142)) % 0.38/0.57 (step @p145 :rule symm :premises (@p144)) % 0.38/0.57 (step @p146 :rule cong :premises (@p145) :args ((forall @t35 (or @t123 @t44)))) % 0.38/0.57 (step @p147 :rule trans :premises (@p146 @p139)) % 0.38/0.57 (step @p148 :rule trans :premises (@p147 @p138)) % 0.38/0.57 (step @p149 :rule refl :args (@t43)) % 0.38/0.57 (step @p150 :rule refl :args (@t26)) % 0.38/0.57 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t26 @t43))) % 0.38/0.57 (step @p152 :rule symm :premises (@p151)) % 0.38/0.57 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.38/0.57 (step @p154 :rule cong :premises (@p109 @p153) :args (@t27)) % 0.38/0.57 (step @p155 :rule cong :premises (@p154) :args (@t124)) % 0.38/0.57 (step @p156 :rule refl :args (@t123)) % 0.38/0.57 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t125)) % 0.38/0.57 (step @p158 :rule cong :premises (@p157) :args ((forall @t35 @t125))) % 0.38/0.57 (step @p159 :rule trans :premises (@p158 @p148)) % 0.38/0.57 (step @p160 :rule refl :args (@t124)) % 0.38/0.57 (step @p161 :rule bool-double-not-elim :args (@t123)) % 0.38/0.57 (step @p162 :rule nary_cong :premises (@p161 @p160) :args ((or (not @t126) @t124))) % 0.38/0.57 (step @p163 :rule bool-and-de-morgan :args (@t126 @t27 true)) % 0.38/0.57 (step @p164 :rule trans :premises (@p163 @p162)) % 0.38/0.57 (step @p165 :rule cong :premises (@p164) :args (@t128)) % 0.38/0.57 (step @p166 :rule trans :premises (@p165 @p159)) % 0.38/0.57 (step @p167 :rule cong :premises (@p166) :args (@t129)) % 0.38/0.57 (step @p168 :rule exists-elim :args ((= (exists @t35 @t127) @t129))) % 0.38/0.57 (step @p169 :rule trans :premises (@p168 @p167)) % 0.38/0.57 (step @p170 :rule refl :args (@t27)) % 0.38/0.57 (step @p171 :rule refl :args (@t121)) % 0.38/0.57 (step @p172 :rule refl :args (@t29)) % 0.38/0.57 (step @p173 :rule cong :premises (@p172 @p171) :args ((= @t29 @t121))) % 0.38/0.57 (step @p174 :rule symm :premises (@p173)) % 0.38/0.57 (step @p175 :rule eq_resolve :premises (@p172 @p174)) % 0.38/0.57 (step @p176 :rule cong :premises (@p175) :args (@t130)) % 0.38/0.57 (step @p177 :rule refl :args (@t122)) % 0.38/0.57 (step @p178 :rule refl :args (@t30)) % 0.38/0.57 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t30 @t122))) % 0.38/0.57 (step @p180 :rule symm :premises (@p179)) % 0.38/0.57 (step @p181 :rule eq_resolve :premises (@p178 @p180)) % 0.38/0.57 (step @p182 :rule cong :premises (@p181) :args (@t131)) % 0.38/0.57 (step @p183 :rule nary_cong :premises (@p182 @p176) :args (@t132)) % 0.38/0.57 (step @p184 :rule cong :premises (@p183) :args ((forall @t32 @t132))) % 0.38/0.57 (step @p185 :rule bool-and-de-morgan :args (@t30 @t29 true)) % 0.38/0.57 (step @p186 :rule cong :premises (@p185) :args (@t133)) % 0.38/0.57 (step @p187 :rule trans :premises (@p186 @p184)) % 0.38/0.57 (step @p188 :rule cong :premises (@p187) :args (@t134)) % 0.38/0.57 (step @p189 :rule exists-elim :args ((= @t33 @t134))) % 0.38/0.57 (step @p190 :rule trans :premises (@p189 @p188)) % 0.38/0.57 (step @p191 :rule nary_cong :premises (@p190 @p170) :args (@t34)) % 0.38/0.57 (step @p192 :rule cong :premises (@p191) :args (@t36)) % 0.38/0.57 (step @p193 :rule trans :premises (@p192 @p169)) % 0.38/0.57 (step @p194 :rule cong :premises (@p193) :args (@t37)) % 0.38/0.57 (step @p195 :rule cong :premises (@p194 @p136) :args (@t38)) % 0.38/0.57 (step @p196 :rule cong :premises (@p195) :args (@t39)) % 0.38/0.57 (step @p197 :rule trans :premises (@p196 @p18)) % 0.38/0.57 (step @p198 :rule eq_resolve :premises (@p1 @p197)) % 0.38/0.57 (step @p199 :rule eq-symm :args (@t139 @t141)) % 0.38/0.57 (step @p200 :rule eq-refl :args (@t141)) % 0.38/0.57 (step @p201 :rule refl :args (@t141)) % 0.38/0.57 (step @p202 :rule refl :args (@t41)) % 0.38/0.57 (step @p203 :rule refl :args (@t42)) % 0.38/0.57 (step @p204 :rule eq-symm :args (@t135 @t43)) % 0.38/0.57 (step @p205 :rule cong :premises (@p204) :args (@t142)) % 0.38/0.57 (step @p206 :rule nary_cong :premises (@p205 @p203 @p202) :args (@t143)) % 0.38/0.57 (step @p207 :rule cong :premises (@p206) :args (@t144)) % 0.38/0.57 (step @p208 :rule cong :premises (@p207) :args (@t145)) % 0.38/0.57 (step @p209 :rule beta-reduce :args ((= @t146 @t145))) % 0.38/0.57 (step @p210 :rule trans :premises (@p209 @p208)) % 0.38/0.57 (step @p211 :rule cong :premises (@p210 @p201) :args ((= @t146 @t141))) % 0.38/0.57 (step @p212 :rule trans :premises (@p211 @p200)) % 0.38/0.57 (step @p213 :rule refl :args (@t135)) % 0.38/0.57 (step @p214 :rule ho_cong :premises (@p11 @p213)) % 0.38/0.57 (step @p215 :rule cong :premises (@p214 @p201) :args ((= @t147 @t141))) % 0.38/0.57 (step @p216 :rule trans :premises (@p215 @p212)) % 0.38/0.57 (step @p217 :rule true_elim :premises (@p216)) % 0.38/0.57 (step @p218 :rule eq-refl :args (@t139)) % 0.38/0.57 (step @p219 :rule refl :args (@t139)) % 0.38/0.57 (step @p220 :rule eq-symm :args (@t135 @t50)) % 0.38/0.57 (step @p221 :rule cong :premises (@p220) :args (@t148)) % 0.38/0.57 (step @p222 :rule refl :args (@t53)) % 0.38/0.57 (step @p223 :rule nary_cong :premises (@p36 @p222 @p221) :args (@t149)) % 0.38/0.57 (step @p224 :rule cong :premises (@p223) :args (@t150)) % 0.38/0.57 (step @p225 :rule cong :premises (@p224) :args (@t151)) % 0.38/0.57 (step @p226 :rule beta-reduce :args ((= @t152 @t151))) % 0.38/0.57 (step @p227 :rule trans :premises (@p226 @p225)) % 0.38/0.57 (step @p228 :rule cong :premises (@p227 @p219) :args ((= @t152 @t139))) % 0.38/0.57 (step @p229 :rule trans :premises (@p228 @p218)) % 0.38/0.57 (step @p230 :rule ho_cong :premises (@p5 @p213)) % 0.38/0.57 (step @p231 :rule cong :premises (@p230 @p219) :args ((= @t153 @t139))) % 0.38/0.57 (step @p232 :rule trans :premises (@p231 @p229)) % 0.38/0.57 (step @p233 :rule true_elim :premises (@p232)) % 0.38/0.57 (step @p234 :rule cong :premises (@p233 @p217) :args (@t154)) % 0.38/0.57 (step @p235 :rule trans :premises (@p234 @p199)) % 0.38/0.57 (step @p236 :rule cong :premises (@p235) :args (@t155)) % 0.38/0.57 (step @p237 :rule refl :args (@t156)) % 0.38/0.57 (step @p238 :rule nary_cong :premises (@p237 @p236) :args (@t157)) % 0.38/0.57 ; WARNING: add trust step for TRUST % 0.38/0.57 ; trust TRUST THEORY_LEMMA % 0.38/0.57 (step @p239 :rule trust :premises () :args (@t157)) % 0.38/0.57 (step @p240 :rule eq_resolve :premises (@p239 @p238)) % 0.38/0.57 (step @p241 :rule chain_m_resolution :premises (@p240 @p198) :args ((not @t158) @t159 (@list @t156))) % 0.38/0.57 (step @p242 :rule aci_norm :args ((= @t137 @t160))) % 0.38/0.57 (step @p243 :rule cong :premises (@p242) :args (@t138)) % 0.38/0.57 (step @p244 :rule symm :premises (@p243)) % 0.38/0.57 (step @p245 :rule true_intro :premises (@p244)) % 0.38/0.57 (step @p246 :rule eq-symm :args (@t138 @t161)) % 0.38/0.57 (step @p247 :rule trans :premises (@p246 @p245)) % 0.38/0.57 (step @p248 :rule cong :premises (@p244 @p243) :args ((= @t161 @t138))) % 0.38/0.57 (step @p249 :rule trans :premises (@p248 @p247)) % 0.38/0.57 (step @p250 :rule true_elim :premises (@p249)) % 0.38/0.57 (step @p251 :rule quant_var_reordering :args ((= (forall (@list @t49 @t52) @t160) @t161))) % 0.38/0.57 (step @p252 :rule alpha_equiv :args (@t140 (@list @t40 @t25) (@list @t52 @t49))) % 0.38/0.57 (step @p253 :rule trans :premises (@p252 @p251 @p250)) % 0.38/0.57 (step @p254 :rule equiv_elim1 :premises (@p253)) % 0.38/0.57 (step @p255 :rule cnf_equiv_neg1 :args (@t158)) % 0.38/0.57 (step @p256 :rule reordering :premises (@p255) :args ((or @t141 @t139 @t158))) % 0.38/0.57 (step @p257 :rule chain_m_resolution :premises (@p256 @p241 @p254) :args (@t141 (@list true false) (@list @t158 @t138))) % 0.38/0.57 (step @p258 :rule equiv_elim2 :premises (@p253)) % 0.38/0.57 (step @p259 :rule chain_m_resolution :premises (@p258 @p257) :args (@t139 @t159 (@list @t140))) % 0.38/0.57 (step @p260 :rule bool-double-not-elim :args (@t138)) % 0.38/0.57 (step @p261 :rule bool-double-not-elim :args (@t140)) % 0.38/0.57 (step @p262 :rule refl :args (@t158)) % 0.38/0.57 (step @p263 :rule nary_cong :premises (@p262 @p261 @p260) :args ((or @t158 (not @t141) (not @t139)))) % 0.38/0.57 (step @p264 :rule cnf_equiv_neg2 :args (@t158)) % 0.38/0.57 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.38/0.57 (step @p266 :rule reordering :premises (@p265) :args ((or @t140 @t138 @t158))) % 0.38/0.57 (step @p267 false :rule chain_m_resolution :premises (@p266 @p259 @p257 @p241) :args (false (@list true true true) (@list @t138 @t140 @t158))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------