%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO560^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 09:13:07 AM UTC 2026 % Result : Theorem 0.94s 1.15s % Output : Proof 0.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO560^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 : Wed Jun 3 00:21:02 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.94/1.15 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.94/1.15 % SZS status Theorem % 0.94/1.15 % SZS output start Proof % 0.94/1.15 ( % 0.94/1.15 (declare-const tptp.q (-> (-> Bool Bool) Bool)) % 0.94/1.15 (declare-const tptp.epsoo (-> (-> (-> Bool Bool) Bool) Bool Bool)) % 0.94/1.15 (declare-const tptp.epso (-> (-> Bool Bool) Bool)) % 0.94/1.15 (define @t1 () (@var "P" (-> Bool Bool))) % 0.94/1.15 (define @t2 () (_ tptp.epso @t1)) % 0.94/1.15 (define @t3 () (_ @t1 @t2)) % 0.94/1.15 (define @t4 () (@var "X" Bool)) % 0.94/1.15 (define @t5 () (_ @t1 @t4)) % 0.94/1.15 (define @t6 () (@list @t4)) % 0.94/1.15 (define @t7 () (exists @t6 @t5)) % 0.94/1.15 (define @t8 () (=> @t7 @t3)) % 0.94/1.15 (define @t9 () (@list @t1)) % 0.94/1.15 (define @t10 () (forall @t9 @t8)) % 0.94/1.15 (define @t11 () (@var "P" (-> (-> Bool Bool) Bool))) % 0.94/1.15 (define @t12 () (_ tptp.epsoo @t11)) % 0.94/1.15 (define @t13 () (_ @t11 @t12)) % 0.94/1.15 (define @t14 () (@var "X" (-> Bool Bool))) % 0.94/1.15 (define @t15 () (_ @t11 @t14)) % 0.94/1.15 (define @t16 () (@list @t14)) % 0.94/1.15 (define @t17 () (exists @t16 @t15)) % 0.94/1.15 (define @t18 () (=> @t17 @t13)) % 0.94/1.15 (define @t19 () (@list @t11)) % 0.94/1.15 (define @t20 () (forall @t19 @t18)) % 0.94/1.15 (define @t21 () (lambda @t6 true)) % 0.94/1.15 (define @t22 () (lambda @t6 false)) % 0.94/1.15 (define @t23 () (lambda @t6 @t4)) % 0.94/1.15 (define @t24 () (_ tptp.epsoo tptp.epso)) % 0.94/1.15 (define @t25 () (_ tptp.q @t24)) % 0.94/1.15 (define @t26 () (not @t25)) % 0.94/1.15 (define @t27 () (@var "BOUND_VARIABLE_7504" Bool)) % 0.94/1.15 (define @t28 () (lambda (@list @t27) true)) % 0.94/1.15 (define @t29 () (@purify @t28)) % 0.94/1.15 (define @t30 () (tptp.q @t29)) % 0.94/1.15 (define @t31 () (_ tptp.q @t29)) % 0.94/1.15 (define @t32 () (@list @t4)) % 0.94/1.15 (define @t33 () (tptp.q @t24)) % 0.94/1.15 (define @t34 () (= @t24 @t29)) % 0.94/1.15 (define @t35 () (not @t34)) % 0.94/1.15 (define @t36 () (not @t30)) % 0.94/1.15 (define @t37 () (not @t33)) % 0.94/1.15 (define @t38 () (not @t37)) % 0.94/1.15 (define @t39 () (and @t30 @t34 @t37)) % 0.94/1.15 (define @t40 () (@list true false)) % 0.94/1.15 (define @t41 () (@const 0 Bool)) % 0.94/1.15 (define @t42 () (@purify @t41)) % 0.94/1.15 (define @t43 () (tptp.epsoo tptp.epso @t42)) % 0.94/1.15 (define @t44 () (_ @t29 @t41)) % 0.94/1.15 (define @t45 () (tptp.epsoo tptp.epso @t41)) % 0.94/1.15 (define @t46 () (= @t45 @t44)) % 0.94/1.15 (define @t47 () (not @t46)) % 0.94/1.15 (define @t48 () (or @t34 @t47)) % 0.94/1.15 (define @t49 () (not @t43)) % 0.94/1.15 (define @t50 () (@list true)) % 0.94/1.15 (define @t51 () (_ @t11 @t12)) % 0.94/1.15 (define @t52 () (@var "BOUND_VARIABLE_7479" (-> Bool Bool))) % 0.94/1.15 (define @t53 () (not (_ @t11 @t52))) % 0.94/1.15 (define @t54 () (or @t53 @t51)) % 0.94/1.15 (define @t55 () (@list @t52)) % 0.94/1.15 (define @t56 () (forall @t55 @t54)) % 0.94/1.15 (define @t57 () (forall @t55 @t53)) % 0.94/1.15 (define @t58 () (or @t57 @t51)) % 0.94/1.15 (define @t59 () (_ @t11 @t14)) % 0.94/1.15 (define @t60 () (forall @t16 (not @t59))) % 0.94/1.15 (define @t61 () (or @t60 @t13)) % 0.94/1.15 (define @t62 () (not @t60)) % 0.94/1.15 (define @t63 () (not @t15)) % 0.94/1.15 (define @t64 () (forall @t16 @t63)) % 0.94/1.15 (define @t65 () (not @t64)) % 0.94/1.15 (define @t66 () (@var "BOUND_VARIABLE_7532" Bool)) % 0.94/1.15 (define @t67 () (= @t66 false)) % 0.94/1.15 (define @t68 () (ite @t67 false true)) % 0.94/1.15 (define @t69 () (@list @t66)) % 0.94/1.15 (define @t70 () (lambda @t69 @t68)) % 0.94/1.15 (define @t71 () (@purify @t70)) % 0.94/1.15 (define @t72 () (tptp.epso @t1)) % 0.94/1.15 (define @t73 () (_ @t1 @t72)) % 0.94/1.15 (define @t74 () (@var "BOUND_VARIABLE_7457" Bool)) % 0.94/1.15 (define @t75 () (not (_ @t1 @t74))) % 0.94/1.15 (define @t76 () (or @t75 @t73)) % 0.94/1.15 (define @t77 () (forall (@list @t1 @t74) @t76)) % 0.94/1.15 (define @t78 () (@list @t74)) % 0.94/1.15 (define @t79 () (forall @t78 @t76)) % 0.94/1.15 (define @t80 () (forall @t78 @t75)) % 0.94/1.15 (define @t81 () (or @t80 @t73)) % 0.94/1.15 (define @t82 () (_ @t1 @t4)) % 0.94/1.15 (define @t83 () (forall @t6 (not @t82))) % 0.94/1.15 (define @t84 () (or @t83 @t3)) % 0.94/1.15 (define @t85 () (not @t83)) % 0.94/1.15 (define @t86 () (not @t5)) % 0.94/1.15 (define @t87 () (forall @t6 @t86)) % 0.94/1.15 (define @t88 () (not @t87)) % 0.94/1.15 (define @t89 () (= false @t66)) % 0.94/1.15 (define @t90 () (not true)) % 0.94/1.15 (define @t91 () (not @t67)) % 0.94/1.15 (define @t92 () (tptp.epso @t70)) % 0.94/1.15 (define @t93 () (@var "BOUND_VARIABLE_18137" Bool)) % 0.94/1.15 (define @t94 () (lambda (@list @t93) @t93)) % 0.94/1.15 (define @t95 () (@list @t66)) % 0.94/1.15 (define @t96 () (tptp.epso @t94)) % 0.94/1.15 (define @t97 () (_ @t94 @t96)) % 0.94/1.15 (define @t98 () (_ @t94 true)) % 0.94/1.15 (define @t99 () (not @t98)) % 0.94/1.15 (define @t100 () (or @t99 @t97)) % 0.94/1.15 (define @t101 () (tptp.epso @t71)) % 0.94/1.15 (define @t102 () (@list false)) % 0.94/1.15 (define @t103 () (@list @t77)) % 0.94/1.15 (define @t104 () (tptp.epso @t24)) % 0.94/1.15 (define @t105 () (not @t101)) % 0.94/1.15 (define @t106 () (or @t105 @t104)) % 0.94/1.15 (define @t107 () (@list false false)) % 0.94/1.15 (define @t108 () (@purify @t104)) % 0.94/1.15 (define @t109 () (tptp.epsoo tptp.epso @t108)) % 0.94/1.15 (define @t110 () (_ @t24 @t108)) % 0.94/1.15 (define @t111 () (@const 1 Bool)) % 0.94/1.15 (define @t112 () (@purify @t111)) % 0.94/1.15 (define @t113 () (tptp.epsoo tptp.epso @t112)) % 0.94/1.15 (define @t114 () (_ @t24 @t112)) % 0.94/1.15 (define @t115 () (not @t114)) % 0.94/1.15 (define @t116 () (_ @t24 @t104)) % 0.94/1.15 (define @t117 () (or @t115 @t116)) % 0.94/1.15 (define @t118 () (_ tptp.epso @t24)) % 0.94/1.15 (define @t119 () (_ @t24 @t104)) % 0.94/1.15 (define @t120 () (_ @t24 @t112)) % 0.94/1.15 (define @t121 () (not @t120)) % 0.94/1.15 (define @t122 () (or @t121 @t119)) % 0.94/1.15 (define @t123 () (not @t113)) % 0.94/1.15 (define @t124 () (or @t123 @t109)) % 0.94/1.15 (define @t125 () (@var "BOUND_VARIABLE_7518" Bool)) % 0.94/1.15 (define @t126 () (lambda (@list @t125) false)) % 0.94/1.15 (define @t127 () (@purify @t126)) % 0.94/1.15 (define @t128 () (tptp.q @t127)) % 0.94/1.15 (define @t129 () (_ tptp.q @t127)) % 0.94/1.15 (define @t130 () (= @t24 @t127)) % 0.94/1.15 (define @t131 () (not @t130)) % 0.94/1.15 (define @t132 () (not @t128)) % 0.94/1.15 (define @t133 () (= true false)) % 0.94/1.15 (define @t134 () (and @t37 @t130 @t128)) % 0.94/1.15 (define @t135 () (_ @t126 @t111)) % 0.94/1.15 (define @t136 () (_ @t127 @t112)) % 0.94/1.15 (define @t137 () (_ @t127 @t111)) % 0.94/1.15 (define @t138 () (tptp.epsoo tptp.epso @t111)) % 0.94/1.15 (define @t139 () (= @t138 @t137)) % 0.94/1.15 (define @t140 () (not @t139)) % 0.94/1.15 (define @t141 () (or @t130 @t140)) % 0.94/1.15 (define @t142 () (not @t109)) % 0.94/1.15 (define @t143 () (not @t108)) % 0.94/1.15 (define @t144 () (not @t42)) % 0.94/1.15 (define @t145 () (not @t49)) % 0.94/1.15 (define @t146 () (and @t49 @t42 @t108 @t109)) % 0.94/1.15 (define @t147 () (tptp.q @t71)) % 0.94/1.15 (define @t148 () (_ tptp.q @t71)) % 0.94/1.15 (define @t149 () (= @t24 @t71)) % 0.94/1.15 (define @t150 () (not @t149)) % 0.94/1.15 (define @t151 () (not @t147)) % 0.94/1.15 (define @t152 () (and @t37 @t149 @t147)) % 0.94/1.15 (define @t153 () (@const 2 Bool)) % 0.94/1.15 (define @t154 () (@purify @t153)) % 0.94/1.15 (define @t155 () (tptp.epsoo tptp.epso @t154)) % 0.94/1.15 (define @t156 () (= @t153 false)) % 0.94/1.15 (define @t157 () (not @t156)) % 0.94/1.15 (define @t158 () (_ @t70 @t153)) % 0.94/1.15 (define @t159 () (_ @t71 @t154)) % 0.94/1.15 (define @t160 () (_ @t71 @t153)) % 0.94/1.15 (define @t161 () (tptp.epsoo tptp.epso @t153)) % 0.94/1.15 (define @t162 () (= @t161 @t160)) % 0.94/1.15 (define @t163 () (not @t162)) % 0.94/1.15 (define @t164 () (or @t149 @t163)) % 0.94/1.15 (define @t165 () (= @t154 @t155)) % 0.94/1.15 (define @t166 () (not @t155)) % 0.94/1.15 (define @t167 () (not @t154)) % 0.94/1.15 (define @t168 () (@purify true)) % 0.94/1.15 (define @t169 () (and @t154 @t108 @t109 @t168)) % 0.94/1.15 (define @t170 () (and @t49 @t144 @t167)) % 0.94/1.15 (assume @p1 @t10) % 0.94/1.15 (assume @p2 @t20) % 0.94/1.15 (assume @p3 (_ tptp.q @t21)) % 0.94/1.15 (assume @p4 (_ tptp.q @t22)) % 0.94/1.15 (assume @p5 (_ tptp.q @t23)) % 0.94/1.15 (assume @p6 @t26) % 0.94/1.15 (assume @p7 true) % 0.94/1.15 (step @p8 :rule refl :args (@t30)) % 0.94/1.15 (step @p9 :rule refl :args (@t31)) % 0.94/1.15 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t31 @t30))) % 0.94/1.15 (step @p11 :rule symm :premises (@p10)) % 0.94/1.15 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.94/1.15 (step @p13 :rule eq-refl :args (@t28)) % 0.94/1.15 (step @p14 :rule refl :args (@t28)) % 0.94/1.15 (step @p15 :rule symm :premises (@p14)) % 0.94/1.15 (step @p16 :rule refl :args (@t28)) % 0.94/1.15 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t28 @t28))) % 0.94/1.15 (step @p18 :rule trans :premises (@p17 @p13)) % 0.94/1.15 (step @p19 :rule skolem_intro :args (@t29)) % 0.94/1.15 (step @p20 :rule cong :premises (@p16 @p19) :args ((= @t28 @t29))) % 0.94/1.15 (step @p21 :rule trans :premises (@p20 @p18)) % 0.94/1.15 (step @p22 :rule true_elim :premises (@p21)) % 0.94/1.15 (step @p23 :rule refl :args (tptp.q)) % 0.94/1.15 (step @p24 :rule ho_cong :premises (@p23 @p22)) % 0.94/1.15 (step @p25 :rule trans :premises (@p24 @p12)) % 0.94/1.15 (step @p26 :rule symm :premises (@p14)) % 0.94/1.15 (step @p27 :rule alpha_equiv :args (@t21 @t32 (@list @t27))) % 0.94/1.15 (step @p28 :rule trans :premises (@p27 @p26)) % 0.94/1.15 (step @p29 :rule ho_cong :premises (@p23 @p28)) % 0.94/1.15 (step @p30 :rule trans :premises (@p29 @p25)) % 0.94/1.15 (step @p31 :rule eq_resolve :premises (@p3 @p30)) % 0.94/1.15 (step @p32 :rule refl :args (@t33)) % 0.94/1.15 (step @p33 :rule refl :args (@t25)) % 0.94/1.15 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t25 @t33))) % 0.94/1.15 (step @p35 :rule symm :premises (@p34)) % 0.94/1.15 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.94/1.15 (step @p37 :rule cong :premises (@p36) :args (@t26)) % 0.94/1.15 (step @p38 :rule eq_resolve :premises (@p6 @p37)) % 0.94/1.15 (step @p39 :rule refl :args (@t35)) % 0.94/1.15 (step @p40 :rule bool-double-not-elim :args (@t33)) % 0.94/1.15 (step @p41 :rule refl :args (@t36)) % 0.94/1.15 (step @p42 :rule nary_cong :premises (@p41 @p40 @p39) :args ((or @t36 @t38 @t35))) % 0.94/1.15 (assume-push @p576 @t30) % 0.94/1.15 (assume-push @p577 @t34) % 0.94/1.15 (assume-push @p578 @t37) % 0.94/1.15 (step @p46 :rule evaluate :args ((= false true))) % 0.94/1.15 (step @p47 :rule true_intro :premises (@p31)) % 0.94/1.15 (step @p48 :rule cong :premises (@p577) :args (@t33)) % 0.94/1.15 (step @p49 :rule false_intro :premises (@p38)) % 0.94/1.15 (step @p50 :rule symm :premises (@p49)) % 0.94/1.15 (step @p51 :rule trans :premises (@p50 @p48 @p47)) % 0.94/1.15 (step @p52 false :rule eq_resolve :premises (@p51 @p46)) % 0.94/1.15 (step-pop @p579 :rule scope :premises (@p52)) % 0.94/1.15 (step-pop @p580 :rule scope :premises (@p579)) % 0.94/1.15 (step-pop @p581 :rule scope :premises (@p580)) % 0.94/1.15 (step @p53 :rule process_scope :premises (@p581) :args (false)) % 0.94/1.15 (assume-push @p582 @t30) % 0.94/1.15 (assume-push @p583 @t37) % 0.94/1.15 (assume-push @p584 @t34) % 0.94/1.15 (step @p60 :rule and_intro :premises (@p31 @p584 @p38)) % 0.94/1.15 (step-pop @p585 :rule scope :premises (@p60)) % 0.94/1.15 (step-pop @p586 :rule scope :premises (@p585)) % 0.94/1.15 (step-pop @p587 :rule scope :premises (@p586)) % 0.94/1.15 (step @p61 :rule process_scope :premises (@p587) :args (@t39)) % 0.94/1.15 (step @p65 :rule implies_elim :premises (@p61)) % 0.94/1.15 (step @p66 :rule resolution :premises (@p65 @p53) :args (true @t39)) % 0.94/1.15 (step @p67 :rule not_and :premises (@p66)) % 0.94/1.15 (step @p68 :rule eq_resolve :premises (@p67 @p42)) % 0.94/1.15 (step @p69 :rule reordering :premises (@p68) :args ((or @t33 @t36 @t35))) % 0.94/1.15 (step @p70 :rule chain_m_resolution :premises (@p69 @p38 @p31) :args (@t35 @t40 (@list @t33 @t30))) % 0.94/1.15 (step @p71 :rule bool-eq-true :args (@t43)) % 0.94/1.15 (step @p72 :rule beta-reduce :args ((= (_ @t28 @t41) true))) % 0.94/1.15 (step @p73 :rule skolem_intro :args (@t42)) % 0.94/1.15 (step @p74 :rule ho_cong :premises (@p19 @p73)) % 0.94/1.15 (step @p75 :rule bool-eq-true :args ((_ @t29 @t42))) % 0.94/1.15 (step @p76 :rule trans :premises (@p75 @p74 @p72)) % 0.94/1.15 (step @p77 :rule true_elim :premises (@p76)) % 0.94/1.15 (step @p78 :rule eq-refl :args (@t41)) % 0.94/1.15 (step @p79 :rule refl :args (@t41)) % 0.94/1.15 (step @p80 :rule cong :premises (@p79 @p73) :args ((= @t41 @t42))) % 0.94/1.15 (step @p81 :rule trans :premises (@p80 @p78)) % 0.94/1.15 (step @p82 :rule true_elim :premises (@p81)) % 0.94/1.15 (step @p83 :rule cong :premises (@p82) :args (@t44)) % 0.94/1.15 (step @p84 :rule trans :premises (@p83 @p77)) % 0.94/1.15 (step @p85 :rule refl :args (tptp.epso)) % 0.94/1.15 (step @p86 :rule cong :premises (@p85 @p82) :args (@t45)) % 0.94/1.15 (step @p87 :rule cong :premises (@p86 @p84) :args (@t46)) % 0.94/1.15 (step @p88 :rule trans :premises (@p87 @p71)) % 0.94/1.15 (step @p89 :rule cong :premises (@p88) :args (@t47)) % 0.94/1.15 (step @p90 :rule refl :args (@t34)) % 0.94/1.15 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t48)) % 0.94/1.15 ; WARNING: add trust step for TRUST % 0.94/1.15 ; trust TRUST THEORY_LEMMA % 0.94/1.15 (step @p92 :rule trust :premises () :args (@t48)) % 0.94/1.15 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.94/1.15 (step @p94 :rule chain_m_resolution :premises (@p93 @p70) :args (@t49 @t50 (@list @t34))) % 0.94/1.15 (step @p95 :rule quant-merge-prenex :args ((= (forall @t19 @t56) (forall (@list @t11 @t52) @t54)))) % 0.94/1.15 (step @p96 :rule refl :args (@t51)) % 0.94/1.15 (step @p97 :rule alpha_equiv :args (@t57 (@list @t52) (@list @t14))) % 0.94/1.15 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t58)) % 0.94/1.15 (step @p99 :rule quant-miniscope-or :args ((= @t56 @t58))) % 0.94/1.15 (step @p100 :rule trans :premises (@p99 @p98)) % 0.94/1.15 (step @p101 :rule symm :premises (@p100)) % 0.94/1.15 (step @p102 :rule cong :premises (@p101) :args ((forall @t19 (or @t60 @t51)))) % 0.94/1.15 (step @p103 :rule trans :premises (@p102 @p95)) % 0.94/1.15 (step @p104 :rule refl :args (@t51)) % 0.94/1.15 (step @p105 :rule refl :args (@t13)) % 0.94/1.15 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t13 @t51))) % 0.94/1.15 (step @p107 :rule symm :premises (@p106)) % 0.94/1.15 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.94/1.15 (step @p109 :rule refl :args (@t60)) % 0.94/1.15 (step @p110 :rule nary_cong :premises (@p109 @p108) :args (@t61)) % 0.94/1.15 (step @p111 :rule cong :premises (@p110) :args ((forall @t19 @t61))) % 0.94/1.15 (step @p112 :rule trans :premises (@p111 @p103)) % 0.94/1.15 (step @p113 :rule bool-double-not-elim :args (@t60)) % 0.94/1.15 (step @p114 :rule nary_cong :premises (@p113 @p105) :args ((or (not @t62) @t13))) % 0.94/1.15 (step @p115 :rule bool-impl-elim :args (@t62 @t13)) % 0.94/1.15 (step @p116 :rule trans :premises 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0.94/1.16 (step-pop @p596 :rule scope :premises (@p595)) % 0.94/1.16 (step-pop @p597 :rule scope :premises (@p596)) % 0.94/1.16 (step @p331 :rule process_scope :premises (@p597) :args (false)) % 0.94/1.16 (assume-push @p598 @t128) % 0.94/1.16 (assume-push @p599 @t37) % 0.94/1.16 (assume-push @p600 @t130) % 0.94/1.16 (step @p338 :rule and_intro :premises (@p38 @p600 @p317)) % 0.94/1.16 (step-pop @p601 :rule scope :premises (@p338)) % 0.94/1.16 (step-pop @p602 :rule scope :premises (@p601)) % 0.94/1.16 (step-pop @p603 :rule scope :premises (@p602)) % 0.94/1.16 (step @p339 :rule process_scope :premises (@p603) :args (@t134)) % 0.94/1.16 (step @p343 :rule implies_elim :premises (@p339)) % 0.94/1.16 (step @p344 :rule resolution :premises (@p343 @p331) :args (true @t134)) % 0.94/1.16 (step @p345 :rule not_and :premises (@p344)) % 0.94/1.16 (step @p346 :rule eq_resolve :premises (@p345 @p320)) % 0.94/1.16 (step @p347 :rule reordering :premises (@p346) :args ((or @t33 @t132 @t131))) % 0.94/1.16 (step @p348 :rule chain_m_resolution :premises (@p347 @p38 @p317) :args (@t131 @t40 (@list @t33 @t128))) % 0.94/1.16 (step @p349 :rule bool-double-not-elim :args (@t113)) % 0.94/1.16 (step @p350 :rule bool-eq-false :args (@t113)) % 0.94/1.16 (step @p351 :rule evaluate :args ((not false))) % 0.94/1.16 (step @p352 :rule beta-reduce :args ((= @t135 false))) % 0.94/1.16 (step @p353 :rule cong :premises (@p352) :args ((not @t135))) % 0.94/1.16 (step @p354 :rule trans :premises (@p353 @p351)) % 0.94/1.16 (step @p355 :rule skolem_intro :args (@t112)) % 0.94/1.16 (step @p356 :rule ho_cong :premises (@p306 @p355)) % 0.94/1.16 (step @p357 :rule cong :premises (@p356) :args ((not @t136))) % 0.94/1.16 (step @p358 :rule bool-eq-false :args (@t136)) % 0.94/1.16 (step @p359 :rule trans :premises (@p358 @p357 @p354)) % 0.94/1.16 (step @p360 :rule true_elim :premises (@p359)) % 0.94/1.16 (step @p361 :rule eq-refl :args (@t111)) % 0.94/1.16 (step @p362 :rule refl :args (@t111)) % 0.94/1.16 (step @p363 :rule cong :premises (@p362 @p355) :args ((= @t111 @t112))) % 0.94/1.16 (step @p364 :rule trans :premises (@p363 @p361)) % 0.94/1.16 (step @p365 :rule true_elim :premises (@p364)) % 0.94/1.16 (step @p366 :rule cong :premises (@p365) :args (@t137)) % 0.94/1.16 (step @p367 :rule trans :premises (@p366 @p360)) % 0.94/1.16 (step @p368 :rule cong :premises (@p85 @p365) :args (@t138)) % 0.94/1.16 (step @p369 :rule cong :premises (@p368 @p367) :args (@t139)) % 0.94/1.16 (step @p370 :rule trans :premises (@p369 @p350)) % 0.94/1.16 (step @p371 :rule cong :premises (@p370) :args (@t140)) % 0.94/1.16 (step @p372 :rule trans :premises (@p371 @p349)) % 0.94/1.16 (step @p373 :rule refl :args (@t130)) % 0.94/1.16 (step @p374 :rule nary_cong :premises (@p373 @p372) :args (@t141)) % 0.94/1.16 ; trust TRUST THEORY_LEMMA % 0.94/1.16 (step @p375 :rule trust :premises () :args (@t141)) % 0.94/1.16 (step @p376 :rule eq_resolve :premises (@p375 @p374)) % 0.94/1.16 (step @p377 :rule chain_m_resolution :premises (@p376 @p348) :args (@t113 @t50 (@list @t130))) % 0.94/1.16 (step @p378 :rule cnf_or_pos :args (@t124)) % 0.94/1.16 (step @p379 :rule reordering :premises (@p378) :args ((or @t123 @t109 (not @t124)))) % 0.94/1.16 (step @p380 :rule chain_m_resolution :premises (@p379 @p377 @p294) :args (@t109 @t107 (@list @t113 @t124))) % 0.94/1.16 (step @p381 :rule refl :args (@t142)) % 0.94/1.16 (step @p382 :rule refl :args (@t143)) % 0.94/1.16 (step @p383 :rule bool-double-not-elim :args (@t43)) % 0.94/1.16 (step @p384 :rule refl :args (@t144)) % 0.94/1.16 (step @p385 :rule nary_cong :premises (@p384 @p383 @p382 @p381) :args ((or @t144 @t145 @t143 @t142))) % 0.94/1.16 (assume-push @p604 @t49) % 0.94/1.16 (assume-push @p605 @t42) % 0.94/1.16 (assume-push @p606 @t108) % 0.94/1.16 (assume-push @p607 @t109) % 0.94/1.16 (step @p324 :rule evaluate :args (@t133)) % 0.94/1.16 (step @p390 :rule false_intro :premises (@p604)) % 0.94/1.16 (step @p391 :rule true_intro :premises (@p605)) % 0.94/1.16 (step @p392 :rule symm :premises (@p391)) % 0.94/1.16 (step @p393 :rule true_intro :premises (@p256)) % 0.94/1.16 (step @p394 :rule trans :premises (@p393 @p392)) % 0.94/1.16 (step @p395 :rule cong :premises (@p85 @p394) :args (@t109)) % 0.94/1.16 (step @p396 :rule true_intro :premises (@p607)) % 0.94/1.16 (step @p397 :rule symm :premises (@p396)) % 0.94/1.16 (step @p398 :rule trans :premises (@p397 @p395 @p390)) % 0.94/1.16 (step @p399 false :rule eq_resolve :premises (@p398 @p324)) % 0.94/1.16 (step-pop @p608 :rule scope :premises (@p399)) % 0.94/1.16 (step-pop @p609 :rule scope :premises (@p608)) % 0.94/1.16 (step-pop @p610 :rule scope :premises (@p609)) % 0.94/1.16 (step-pop @p611 :rule scope :premises (@p610)) % 0.94/1.16 (step @p400 :rule process_scope :premises (@p611) :args (false)) % 0.94/1.16 (assume-push @p612 @t42) % 0.94/1.16 (assume-push @p613 @t49) % 0.94/1.16 (assume-push @p614 @t108) % 0.94/1.16 (assume-push @p615 @t109) % 0.94/1.16 (step @p409 :rule and_intro :premises (@p613 @p612 @p256 @p615)) % 0.94/1.16 (step-pop @p616 :rule scope :premises (@p409)) % 0.94/1.16 (step-pop @p617 :rule scope :premises (@p616)) % 0.94/1.16 (step-pop @p618 :rule scope :premises (@p617)) % 0.94/1.16 (step-pop @p619 :rule scope :premises (@p618)) % 0.94/1.16 (step @p410 :rule process_scope :premises (@p619) :args (@t146)) % 0.94/1.16 (step @p415 :rule implies_elim :premises (@p410)) % 0.94/1.16 (step @p416 :rule resolution :premises (@p415 @p400) :args (true @t146)) % 0.94/1.16 (step @p417 :rule not_and :premises (@p416)) % 0.94/1.16 (step @p418 :rule eq_resolve :premises (@p417 @p385)) % 0.94/1.16 (step @p419 :rule reordering :premises (@p418) :args ((or @t43 @t144 @t142 @t143))) % 0.94/1.16 (step @p420 :rule chain_m_resolution :premises (@p419 @p94 @p380 @p256) :args (@t144 (@list true false false) (@list @t43 @t109 @t108))) % 0.94/1.16 (step @p421 :rule refl :args (@t147)) % 0.94/1.16 (step @p422 :rule refl :args (@t148)) % 0.94/1.16 (step @p423 :rule cong :premises (@p422 @p421) :args ((= @t148 @t147))) % 0.94/1.16 (step @p424 :rule symm :premises (@p423)) % 0.94/1.16 (step @p425 :rule eq_resolve :premises (@p422 @p424)) % 0.94/1.16 (step @p426 :rule ho_cong :premises (@p23 @p222)) % 0.94/1.16 (step @p427 :rule trans :premises (@p426 @p425)) % 0.94/1.16 (step @p428 :rule alpha_equiv :args (@t23 @t32 @t95)) % 0.94/1.16 (step @p429 :rule trans :premises (@p428 @p204)) % 0.94/1.16 (step @p430 :rule trans :premises (@p429 @p187)) % 0.94/1.16 (step @p431 :rule ho_cong :premises (@p23 @p430)) % 0.94/1.16 (step @p432 :rule trans :premises (@p431 @p427)) % 0.94/1.16 (step @p433 :rule eq_resolve :premises (@p5 @p432)) % 0.94/1.16 (step @p434 :rule refl :args (@t150)) % 0.94/1.16 (step @p435 :rule refl :args (@t151)) % 0.94/1.16 (step @p436 :rule nary_cong :premises (@p435 @p40 @p434) :args ((or @t151 @t38 @t150))) % 0.94/1.16 (assume-push @p620 @t37) % 0.94/1.16 (assume-push @p621 @t149) % 0.94/1.16 (assume-push @p622 @t147) % 0.94/1.16 (step @p324 :rule evaluate :args (@t133)) % 0.94/1.16 (step @p49 :rule false_intro :premises (@p38)) % 0.94/1.16 (step @p440 :rule symm :premises (@p621)) % 0.94/1.16 (step @p441 :rule cong :premises (@p440) :args (@t147)) % 0.94/1.16 (step @p442 :rule true_intro :premises (@p433)) % 0.94/1.16 (step @p443 :rule symm :premises (@p442)) % 0.94/1.16 (step @p444 :rule trans :premises (@p443 @p441 @p49)) % 0.94/1.16 (step @p445 false :rule eq_resolve :premises (@p444 @p324)) % 0.94/1.16 (step-pop @p623 :rule scope :premises (@p445)) % 0.94/1.16 (step-pop @p624 :rule scope :premises (@p623)) % 0.94/1.16 (step-pop @p625 :rule scope :premises (@p624)) % 0.94/1.16 (step @p446 :rule process_scope :premises (@p625) :args (false)) % 0.94/1.16 (assume-push @p626 @t147) % 0.94/1.16 (assume-push @p627 @t37) % 0.94/1.16 (assume-push @p628 @t149) % 0.94/1.16 (step @p453 :rule and_intro :premises (@p38 @p628 @p433)) % 0.94/1.16 (step-pop @p629 :rule scope :premises (@p453)) % 0.94/1.16 (step-pop @p630 :rule scope :premises (@p629)) % 0.94/1.16 (step-pop @p631 :rule scope :premises (@p630)) % 0.94/1.16 (step @p454 :rule process_scope :premises (@p631) :args (@t152)) % 0.94/1.16 (step @p458 :rule implies_elim :premises (@p454)) % 0.94/1.16 (step @p459 :rule resolution :premises (@p458 @p446) :args (true @t152)) % 0.94/1.16 (step @p460 :rule not_and :premises (@p459)) % 0.94/1.16 (step @p461 :rule eq_resolve :premises (@p460 @p436)) % 0.94/1.16 (step @p462 :rule reordering :premises (@p461) :args ((or @t33 @t151 @t150))) % 0.94/1.16 (step @p463 :rule chain_m_resolution :premises (@p462 @p38 @p433) :args (@t150 @t40 (@list @t33 @t147))) % 0.94/1.16 (step @p464 :rule eq-symm :args (@t155 @t154)) % 0.94/1.16 (step @p465 :rule eq-refl :args (@t153)) % 0.94/1.16 (step @p466 :rule bool-double-not-elim :args (@t153)) % 0.94/1.16 (step @p467 :rule bool-eq-false :args (@t153)) % 0.94/1.16 (step @p468 :rule cong :premises (@p467) :args (@t157)) % 0.94/1.16 (step @p469 :rule trans :premises (@p468 @p466)) % 0.94/1.16 (step @p470 :rule aci_norm :args ((= (and @t157 true) @t157))) % 0.94/1.16 (step @p471 :rule ite-then-false :args (@t156 true)) % 0.94/1.16 (step @p472 :rule trans :premises (@p471 @p470)) % 0.94/1.16 (step @p473 :rule trans :premises (@p472 @p469)) % 0.94/1.16 (step @p474 :rule beta-reduce :args ((= @t158 (ite @t156 false true)))) % 0.94/1.16 (step @p475 :rule trans :premises (@p474 @p473)) % 0.94/1.16 (step @p476 :rule refl :args (@t153)) % 0.94/1.16 (step @p477 :rule cong :premises (@p476 @p475) :args ((= @t153 @t158))) % 0.94/1.16 (step @p478 :rule trans :premises (@p477 @p465)) % 0.94/1.16 (step @p479 :rule skolem_intro :args (@t154)) % 0.94/1.16 (step @p480 :rule ho_cong :premises (@p219 @p479)) % 0.94/1.16 (step @p481 :rule cong :premises (@p479 @p480) :args ((= @t154 @t159))) % 0.94/1.16 (step @p482 :rule eq-symm :args (@t159 @t154)) % 0.94/1.16 (step @p483 :rule trans :premises (@p482 @p481 @p478)) % 0.94/1.16 (step @p484 :rule true_elim :premises (@p483)) % 0.94/1.16 (step @p485 :rule cong :premises (@p476 @p479) :args ((= @t153 @t154))) % 0.94/1.16 (step @p486 :rule trans :premises (@p485 @p465)) % 0.94/1.16 (step @p487 :rule true_elim :premises (@p486)) % 0.94/1.16 (step @p488 :rule cong :premises (@p487) :args (@t160)) % 0.94/1.16 (step @p489 :rule trans :premises (@p488 @p484)) % 0.94/1.16 (step @p490 :rule cong :premises (@p85 @p487) :args (@t161)) % 0.94/1.16 (step @p491 :rule cong :premises (@p490 @p489) :args (@t162)) % 0.94/1.16 (step @p492 :rule trans :premises (@p491 @p464)) % 0.94/1.16 (step @p493 :rule cong :premises (@p492) :args (@t163)) % 0.94/1.16 (step @p494 :rule refl :args (@t149)) % 0.94/1.16 (step @p495 :rule nary_cong :premises (@p494 @p493) :args (@t164)) % 0.94/1.16 ; trust TRUST THEORY_LEMMA % 0.94/1.16 (step @p496 :rule trust :premises () :args (@t164)) % 0.94/1.16 (step @p497 :rule eq_resolve :premises (@p496 @p495)) % 0.94/1.16 (step @p498 :rule chain_m_resolution :premises (@p497 @p463) :args ((not @t165) @t50 (@list @t149))) % 0.94/1.16 (step @p499 :rule cnf_equiv_neg2 :args (@t165)) % 0.94/1.16 (step @p500 :rule reordering :premises (@p499) :args ((or @t167 @t165 @t166))) % 0.94/1.16 (step @p501 :rule bool-eq-true :args (@t168)) % 0.94/1.16 (step @p502 :rule skolem_intro :args (@t168)) % 0.94/1.16 (step @p503 :rule eq_resolve :premises (@p502 @p501)) % 0.94/1.16 (assume-push @p632 @t154) % 0.94/1.16 (assume-push @p633 @t108) % 0.94/1.16 (assume-push @p634 @t109) % 0.94/1.16 (assume-push @p635 @t168) % 0.94/1.16 (assume-push @p636 @t109) % 0.94/1.16 (assume-push @p637 @t108) % 0.94/1.16 (assume-push @p638 @t168) % 0.94/1.16 (assume-push @p639 @t154) % 0.94/1.16 (step @p512 :rule true_intro :premises (@p634)) % 0.94/1.16 (step @p393 :rule true_intro :premises (@p256)) % 0.94/1.16 (step @p513 :rule symm :premises (@p393)) % 0.94/1.16 (step @p514 :rule trans :premises (@p502 @p513)) % 0.94/1.16 (step @p515 :rule cong :premises (@p85 @p514) :args ((tptp.epsoo tptp.epso @t168))) % 0.94/1.16 (step @p516 :rule symm :premises (@p502)) % 0.94/1.16 (step @p517 :rule true_intro :premises (@p632)) % 0.94/1.16 (step @p518 :rule trans :premises (@p517 @p516)) % 0.94/1.16 (step @p519 :rule cong :premises (@p85 @p518) :args (@t155)) % 0.94/1.16 (step @p520 :rule trans :premises (@p519 @p515 @p512)) % 0.94/1.16 (step @p521 :rule true_elim :premises (@p520)) % 0.94/1.16 (step-pop @p640 :rule scope :premises (@p521)) % 0.94/1.16 (step-pop @p641 :rule scope :premises (@p640)) % 0.94/1.16 (step-pop @p642 :rule scope :premises (@p641)) % 0.94/1.16 (step-pop @p643 :rule scope :premises (@p642)) % 0.94/1.16 (step @p522 :rule process_scope :premises (@p643) :args (@t155)) % 0.94/1.16 (step @p527 :rule and_intro :premises (@p634 @p256 @p503 @p632)) % 0.94/1.16 (step @p528 :rule modus_ponens :premises (@p527 @p522)) % 0.94/1.16 (step-pop @p644 :rule scope :premises (@p528)) % 0.94/1.16 (step-pop @p645 :rule scope :premises (@p644)) % 0.94/1.16 (step-pop @p646 :rule scope :premises (@p645)) % 0.94/1.16 (step-pop @p647 :rule scope :premises (@p646)) % 0.94/1.16 (step @p529 :rule process_scope :premises (@p647) :args (@t155)) % 0.94/1.16 (step @p534 :rule implies_elim :premises (@p529)) % 0.94/1.16 (step @p535 :rule cnf_and_neg :args (@t169)) % 0.94/1.16 (step @p536 :rule resolution :premises (@p535 @p534) :args (true @t169)) % 0.94/1.16 (step @p537 :rule reordering :premises (@p536) :args ((or @t167 @t155 @t142 @t143 (not @t168)))) % 0.94/1.16 (step @p538 :rule chain_m_resolution :premises (@p537 @p256 @p503 @p380 @p500 @p498) :args (@t167 (@list false false false true true) (@list @t108 @t168 @t109 @t155 @t165))) % 0.94/1.16 (step @p539 :rule cnf_equiv_neg1 :args (@t165)) % 0.94/1.16 (step @p540 :rule reordering :premises (@p539) :args ((or @t154 @t155 @t165))) % 0.94/1.16 (step @p541 :rule chain_m_resolution :premises (@p540 @p538 @p498) :args (@t155 (@list true true) (@list @t154 @t165))) % 0.94/1.16 (step @p542 :rule refl :args (@t166)) % 0.94/1.16 (step @p543 :rule bool-double-not-elim :args (@t154)) % 0.94/1.16 (step @p544 :rule bool-double-not-elim :args (@t42)) % 0.94/1.16 (step @p545 :rule nary_cong :premises (@p383 @p544 @p543 @p542) :args ((or @t145 (not @t144) (not @t167) @t166))) % 0.94/1.16 (assume-push @p648 @t49) % 0.94/1.16 (assume-push @p649 @t144) % 0.94/1.16 (assume-push @p650 @t167) % 0.94/1.16 (assume-push @p651 @t49) % 0.94/1.16 (assume-push @p652 @t144) % 0.94/1.16 (assume-push @p653 @t167) % 0.94/1.16 (step @p552 :rule false_intro :premises (@p648)) % 0.94/1.16 (step @p553 :rule false_intro :premises (@p649)) % 0.94/1.16 (step @p554 :rule symm :premises (@p553)) % 0.94/1.16 (step @p555 :rule false_intro :premises (@p650)) % 0.94/1.16 (step @p556 :rule trans :premises (@p555 @p554)) % 0.94/1.16 (step @p557 :rule cong :premises (@p85 @p556) :args (@t155)) % 0.94/1.16 (step @p558 :rule trans :premises (@p557 @p552)) % 0.94/1.16 (step @p559 :rule false_elim :premises (@p558)) % 0.94/1.16 (step-pop @p654 :rule scope :premises (@p559)) % 0.94/1.16 (step-pop @p655 :rule scope :premises (@p654)) % 0.94/1.16 (step-pop @p656 :rule scope :premises (@p655)) % 0.94/1.16 (step @p560 :rule process_scope :premises (@p656) :args (@t166)) % 0.94/1.16 (step @p564 :rule and_intro :premises (@p648 @p649 @p650)) % 0.94/1.16 (step @p565 :rule modus_ponens :premises (@p564 @p560)) % 0.94/1.16 (step-pop @p657 :rule scope :premises (@p565)) % 0.94/1.16 (step-pop @p658 :rule scope :premises (@p657)) % 0.94/1.16 (step-pop @p659 :rule scope :premises (@p658)) % 0.94/1.16 (step @p566 :rule process_scope :premises (@p659) :args (@t166)) % 0.94/1.16 (step @p570 :rule implies_elim :premises (@p566)) % 0.94/1.16 (step @p571 :rule cnf_and_neg :args (@t170)) % 0.94/1.16 (step @p572 :rule resolution :premises (@p571 @p570) :args (true @t170)) % 0.94/1.16 (step @p573 :rule eq_resolve :premises (@p572 @p545)) % 0.94/1.16 (step @p574 :rule reordering :premises (@p573) :args ((or @t42 @t43 @t154 @t166))) % 0.94/1.16 (step @p575 false :rule chain_m_resolution :premises (@p574 @p541 @p538 @p420 @p94) :args (false (@list false true true true) (@list @t155 @t154 @t42 @t43))) % 0.94/1.16 ) % 0.94/1.16 % SZS output end Proof % 0.94/1.16 % cvc5 exiting %------------------------------------------------------------------------------