%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL729^5 : 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 : n011.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 4.53s 4.88s % Output : Proof 4.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL729^5 : 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 % 0.10/0.37 % Computer : n011.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 08:38:13 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.44 %----Proving TH0 % 4.53/4.88 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 4.53/4.88 % SZS status Theorem % 4.53/4.88 % SZS output start Proof % 4.53/4.88 ( % 4.53/4.88 (declare-sort tptp.a 0) % 4.53/4.88 (define @t1 () (@var "X" (-> tptp.a Bool))) % 4.53/4.88 (define @t2 () (@var "Xf" (-> (-> tptp.a Bool) tptp.a))) % 4.53/4.88 (define @t3 () (_ @t2 @t1)) % 4.53/4.88 (define @t4 () (_ @t1 @t3)) % 4.53/4.88 (define @t5 () (@var "Xs" (-> (-> tptp.a Bool) Bool))) % 4.53/4.88 (define @t6 () (_ @t5 @t1)) % 4.53/4.88 (define @t7 () (@list @t1)) % 4.53/4.88 (define @t8 () (forall @t7 (=> @t6 @t4))) % 4.53/4.88 (define @t9 () (@list @t2)) % 4.53/4.88 (define @t10 () (exists @t9 @t8)) % 4.53/4.88 (define @t11 () (@var "Xt" tptp.a)) % 4.53/4.88 (define @t12 () (_ @t1 @t11)) % 4.53/4.88 (define @t13 () (@list @t11)) % 4.53/4.88 (define @t14 () (exists @t13 @t12)) % 4.53/4.88 (define @t15 () (=> @t6 @t14)) % 4.53/4.88 (define @t16 () (forall @t7 @t15)) % 4.53/4.88 (define @t17 () (=> @t16 @t10)) % 4.53/4.88 (define @t18 () (@list @t5)) % 4.53/4.88 (define @t19 () (forall @t18 @t17)) % 4.53/4.88 (define @t20 () (@var "Xx" (-> tptp.a Bool))) % 4.53/4.88 (define @t21 () (@var "Xg" (-> (-> tptp.a Bool) tptp.a))) % 4.53/4.88 (define @t22 () (_ @t21 @t20)) % 4.53/4.88 (define @t23 () (@var "Xr" (-> (-> tptp.a Bool) tptp.a Bool))) % 4.53/4.88 (define @t24 () (_ @t23 @t20)) % 4.53/4.88 (define @t25 () (_ @t24 @t22)) % 4.53/4.88 (define @t26 () (@var "Xy" tptp.a)) % 4.53/4.88 (define @t27 () (_ @t24 @t26)) % 4.53/4.88 (define @t28 () (@list @t26)) % 4.53/4.88 (define @t29 () (exists @t28 @t27)) % 4.53/4.88 (define @t30 () (=> @t29 @t25)) % 4.53/4.88 (define @t31 () (@list @t20)) % 4.53/4.88 (define @t32 () (forall @t31 @t30)) % 4.53/4.88 (define @t33 () (@list @t21)) % 4.53/4.88 (define @t34 () (exists @t33 @t32)) % 4.53/4.88 (define @t35 () (@list @t23)) % 4.53/4.88 (define @t36 () (forall @t35 @t34)) % 4.53/4.88 (define @t37 () (= @t36 @t19)) % 4.53/4.88 (define @t38 () (not @t37)) % 4.53/4.88 (define @t39 () (_ @t1 @t11)) % 4.53/4.88 (define @t40 () (not (forall @t13 (not @t39)))) % 4.53/4.88 (define @t41 () (_ @t2 @t1)) % 4.53/4.88 (define @t42 () (_ @t1 @t41)) % 4.53/4.88 (define @t43 () (_ @t5 @t1)) % 4.53/4.88 (define @t44 () (not @t43)) % 4.53/4.88 (define @t45 () (forall @t7 (or @t44 @t42))) % 4.53/4.88 (define @t46 () (not (forall @t9 (not @t45)))) % 4.53/4.88 (define @t47 () (forall @t7 (or @t44 @t40))) % 4.53/4.88 (define @t48 () (forall @t18 (or (not @t47) @t46))) % 4.53/4.88 (define @t49 () (@quantifiers_skolemize @t48 0)) % 4.53/4.88 (define @t50 () (not (_ @t49 @t1))) % 4.53/4.88 (define @t51 () (forall @t7 (or @t50 @t40))) % 4.53/4.88 (define @t52 () (forall @t9 (not (forall @t7 (or @t50 @t42))))) % 4.53/4.88 (define @t53 () (not @t52)) % 4.53/4.88 (define @t54 () (not @t51)) % 4.53/4.88 (define @t55 () (or @t54 @t53)) % 4.53/4.88 (define @t56 () (@const 0 (-> (-> tptp.a Bool) tptp.a))) % 4.53/4.88 (define @t57 () (_ @t56 @t1)) % 4.53/4.88 (define @t58 () (forall @t7 (or @t50 (_ @t1 @t57)))) % 4.53/4.88 (define @t59 () (@quantifiers_skolemize @t58 0)) % 4.53/4.88 (define @t60 () (@list @t59)) % 4.53/4.88 (define @t61 () (forall @t13 (not (_ @t59 @t11)))) % 4.53/4.88 (define @t62 () (not @t61)) % 4.53/4.88 (define @t63 () (_ @t49 @t59)) % 4.53/4.88 (define @t64 () (not @t63)) % 4.53/4.88 (define @t65 () (or @t64 @t62)) % 4.53/4.88 (define @t66 () (@var "BOUND_VARIABLE_51216" (-> tptp.a Bool))) % 4.53/4.88 (define @t67 () (_ @t56 @t66)) % 4.53/4.88 (define @t68 () (@list @t66)) % 4.53/4.88 (define @t69 () (lambda @t68 @t67)) % 4.53/4.88 (define @t70 () (_ @t69 @t1)) % 4.53/4.88 (define @t71 () (_ @t1 @t70)) % 4.53/4.88 (define @t72 () (or @t50 @t71)) % 4.53/4.88 (define @t73 () (forall @t7 @t72)) % 4.53/4.88 (define @t74 () (not @t73)) % 4.53/4.88 (define @t75 () (_ @t59 (_ @t56 @t59))) % 4.53/4.88 (define @t76 () (or @t64 @t75)) % 4.53/4.88 (define @t77 () (not @t76)) % 4.53/4.88 (define @t78 () (not @t58)) % 4.53/4.88 (define @t79 () (@var "x" tptp.a)) % 4.53/4.88 (define @t80 () (@list @t79)) % 4.53/4.88 (define @t81 () (forall @t80 (not (_ @t59 @t79)))) % 4.53/4.88 (define @t82 () (or @t81 @t75)) % 4.53/4.88 (define @t83 () (@list @t79)) % 4.53/4.88 (define @t84 () (not @t55)) % 4.53/4.88 (define @t85 () (not @t48)) % 4.53/4.88 (define @t86 () (@list false)) % 4.53/4.88 (define @t87 () (not @t6)) % 4.53/4.88 (define @t88 () (or @t87 @t4)) % 4.53/4.88 (define @t89 () (or @t87 @t40)) % 4.53/4.88 (define @t90 () (not @t12)) % 4.53/4.88 (define @t91 () (forall @t13 @t90)) % 4.53/4.88 (define @t92 () (not @t91)) % 4.53/4.88 (define @t93 () (_ @t21 @t20)) % 4.53/4.88 (define @t94 () (_ @t23 @t20 @t93)) % 4.53/4.88 (define @t95 () (@var "BOUND_VARIABLE_7466" tptp.a)) % 4.53/4.88 (define @t96 () (not (_ @t23 @t20 @t95))) % 4.53/4.88 (define @t97 () (or @t96 @t94)) % 4.53/4.88 (define @t98 () (@list @t20 @t95)) % 4.53/4.88 (define @t99 () (forall @t98 @t97)) % 4.53/4.88 (define @t100 () (not (forall @t33 (not @t99)))) % 4.53/4.88 (define @t101 () (@list @t95)) % 4.53/4.88 (define @t102 () (forall @t101 @t97)) % 4.53/4.88 (define @t103 () (forall @t101 @t96)) % 4.53/4.88 (define @t104 () (or @t103 @t94)) % 4.53/4.88 (define @t105 () (_ @t23 @t20 @t26)) % 4.53/4.88 (define @t106 () (forall @t28 (not @t105))) % 4.53/4.88 (define @t107 () (or @t106 @t25)) % 4.53/4.88 (define @t108 () (not @t106)) % 4.53/4.88 (define @t109 () (not @t27)) % 4.53/4.88 (define @t110 () (forall @t28 @t109)) % 4.53/4.88 (define @t111 () (not @t110)) % 4.53/4.88 (define @t112 () (forall @t35 @t100)) % 4.53/4.88 (define @t113 () (not @t112)) % 4.53/4.88 (define @t114 () (@quantifiers_skolemize @t112 0)) % 4.53/4.88 (define @t115 () (not (_ @t114 @t20 @t95))) % 4.53/4.88 (define @t116 () (forall @t33 (not (forall @t98 (or @t115 (_ @t114 @t20 @t93)))))) % 4.53/4.88 (define @t117 () (not (not @t116))) % 4.53/4.88 (define @t118 () (@list true)) % 4.53/4.88 (define @t119 () (@const 1 (-> (-> tptp.a Bool) tptp.a))) % 4.53/4.88 (define @t120 () (_ @t119 @t20)) % 4.53/4.88 (define @t121 () (@var "BOUND_VARIABLE_278398" (-> tptp.a Bool))) % 4.53/4.88 (define @t122 () (_ @t119 @t121)) % 4.53/4.88 (define @t123 () (@list @t121)) % 4.53/4.88 (define @t124 () (lambda @t123 @t122)) % 4.53/4.88 (define @t125 () (_ @t124 @t20)) % 4.53/4.88 (define @t126 () (_ @t114 @t20 @t125)) % 4.53/4.88 (define @t127 () (or @t115 @t126)) % 4.53/4.88 (define @t128 () (forall @t98 @t127)) % 4.53/4.88 (define @t129 () (not @t128)) % 4.53/4.88 (define @t130 () (forall @t98 (or @t115 (_ @t114 @t20 @t120)))) % 4.53/4.88 (define @t131 () (not @t130)) % 4.53/4.88 (define @t132 () (@quantifiers_skolemize @t130 0)) % 4.53/4.88 (define @t133 () (_ @t114 @t132 (_ @t119 @t132))) % 4.53/4.88 (define @t134 () (@quantifiers_skolemize @t130 1)) % 4.53/4.88 (define @t135 () (_ @t114 @t132 @t134)) % 4.53/4.88 (define @t136 () (not @t135)) % 4.53/4.88 (define @t137 () (or @t136 @t133)) % 4.53/4.88 (define @t138 () (not @t137)) % 4.53/4.88 (define @t139 () (@list @t137)) % 4.53/4.88 (define @t140 () (@var "x" tptp.a)) % 4.53/4.88 (define @t141 () (@list @t140)) % 4.53/4.88 (define @t142 () (forall @t141 (not (_ @t114 @t132 @t140)))) % 4.53/4.88 (define @t143 () (or @t142 @t133)) % 4.53/4.88 (define @t144 () (forall @t80 (not (_ @t114 @t132 @t79)))) % 4.53/4.88 (assume @p1 @t38) % 4.53/4.88 (assume @p2 true) % 4.53/4.88 (step @p3 :rule bool-double-not-elim :args (@t51)) % 4.53/4.88 (step @p4 :rule refl :args (@t55)) % 4.53/4.88 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t55 (not @t54)))) % 4.53/4.88 (step @p6 :rule cnf_or_neg :args (@t55 0)) % 4.53/4.88 (step @p7 :rule eq_resolve :premises (@p6 @p5)) % 4.53/4.88 (step @p8 :rule reordering :premises (@p7) :args ((or @t51 @t55))) % 4.53/4.88 (step @p9 :rule bool-double-not-elim :args (@t52)) % 4.53/4.88 (step @p10 :rule nary_cong :premises (@p4 @p9) :args ((or @t55 (not @t53)))) % 4.53/4.88 (step @p11 :rule cnf_or_neg :args (@t55 1)) % 4.53/4.88 (step @p12 :rule eq_resolve :premises (@p11 @p10)) % 4.53/4.88 (step @p13 :rule reordering :premises (@p12) :args ((or @t52 @t55))) % 4.53/4.88 (assume-push @p246 @t51) % 4.53/4.88 (step @p15 :rule instantiate :premises (@p246) :args (@t60)) % 4.53/4.88 (step-pop @p247 :rule scope :premises (@p15)) % 4.53/4.88 (step @p16 :rule process_scope :premises (@p247) :args (@t65)) % 4.53/4.88 (step @p18 :rule implies_elim :premises (@p16)) % 4.53/4.88 (step @p19 :rule beta-reduce :args ((= @t70 @t57))) % 4.53/4.88 (step @p20 :rule cong :premises (@p19) :args (@t71)) % 4.53/4.88 (step @p21 :rule refl :args (@t50)) % 4.53/4.88 (step @p22 :rule nary_cong :premises (@p21 @p20) :args (@t72)) % 4.53/4.88 (step @p23 :rule cong :premises (@p22) :args (@t73)) % 4.53/4.88 (step @p24 :rule cong :premises (@p23) :args (@t74)) % 4.53/4.88 (step @p25 :rule refl :args (@t52)) % 4.53/4.88 (step @p26 :rule cong :premises (@p25 @p24) :args ((=> @t52 @t74))) % 4.53/4.88 (assume-push @p248 @t52) % 4.53/4.88 (step @p28 :rule instantiate :premises (@p248) :args ((@list @t69))) % 4.53/4.88 (step-pop @p249 :rule scope :premises (@p28)) % 4.53/4.88 (step @p29 :rule process_scope :premises (@p249) :args (@t74)) % 4.53/4.88 (step @p31 :rule eq_resolve :premises (@p29 @p26)) % 4.53/4.88 (step @p32 :rule implies_elim :premises (@p31)) % 4.53/4.88 (step @p33 :rule refl :args (@t77)) % 4.53/4.88 (step @p34 :rule bool-double-not-elim :args (@t58)) % 4.53/4.88 (step @p35 :rule nary_cong :premises (@p34 @p33) :args ((or (not @t78) @t77))) % 4.53/4.88 (assume-push @p250 @t78) % 4.53/4.88 (step @p37 :rule skolemize :premises (@p250)) % 4.53/4.88 (step-pop @p251 :rule scope :premises (@p37)) % 4.53/4.88 (step @p38 :rule process_scope :premises (@p251) :args (@t77)) % 4.53/4.88 (step @p40 :rule implies_elim :premises (@p38)) % 4.53/4.88 (step @p41 :rule eq_resolve :premises (@p40 @p35)) % 4.53/4.88 (step @p42 :rule bool-double-not-elim :args (@t63)) % 4.53/4.88 (step @p43 :rule refl :args (@t76)) % 4.53/4.88 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or @t76 (not @t64)))) % 4.53/4.88 (step @p45 :rule cnf_or_neg :args (@t76 0)) % 4.53/4.88 (step @p46 :rule eq_resolve :premises (@p45 @p44)) % 4.53/4.88 (step @p47 :rule reordering :premises (@p46) :args ((or @t63 @t76))) % 4.53/4.88 (step @p48 :rule cnf_or_neg :args (@t76 1)) % 4.53/4.88 (step @p49 :rule cnf_or_pos :args (@t65)) % 4.53/4.88 (step @p50 :rule reordering :premises (@p49) :args ((or @t64 @t62 (not @t65)))) % 4.53/4.88 ; WARNING: add trust step for TRUST % 4.53/4.88 ; trust TRUST THEORY_LEMMA % 4.53/4.88 (step @p51 :rule trust :premises () :args ((forall @t68 (or (forall @t80 (not (_ @t66 @t79))) (_ @t66 @t67))))) % 4.53/4.88 (step @p52 :rule instantiate :premises (@p51) :args (@t60)) % 4.53/4.88 (step @p53 :rule cnf_or_pos :args (@t82)) % 4.53/4.88 (step @p54 :rule reordering :premises (@p53) :args ((or @t75 @t81 (not @t82)))) % 4.53/4.88 (step @p55 :rule alpha_equiv :args (@t81 @t83 (@list @t11))) % 4.53/4.88 (step @p56 :rule equiv_elim1 :premises (@p55)) % 4.53/4.88 (step @p57 :rule reordering :premises (@p56) :args ((or @t61 (not @t81)))) % 4.53/4.88 (step @p58 :rule chain_m_resolution :premises (@p57 @p54 @p52 @p50 @p48 @p47 @p41 @p32 @p18 @p13 @p8) :args (@t55 (@list false false true true false true true false false false) (@list @t81 @t82 @t61 @t75 @t63 @t76 @t58 @t65 @t52 @t51))) % 4.53/4.88 (step @p59 :rule refl :args (@t84)) % 4.53/4.88 (step @p60 :rule bool-double-not-elim :args (@t48)) % 4.53/4.88 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or (not @t85) @t84))) % 4.53/4.88 (assume-push @p252 @t85) % 4.53/4.88 (step @p63 :rule skolemize :premises (@p252)) % 4.53/4.88 (step-pop @p253 :rule scope :premises (@p63)) % 4.53/4.88 (step @p64 :rule process_scope :premises (@p253) :args (@t84)) % 4.53/4.88 (step @p66 :rule implies_elim :premises (@p64)) % 4.53/4.88 (step @p67 :rule eq_resolve :premises (@p66 @p61)) % 4.53/4.88 (step @p68 :rule chain_m_resolution :premises (@p67 @p58) :args (@t48 @t86 (@list @t55))) % 4.53/4.88 (step @p69 :rule bool-impl-elim :args (@t47 @t46)) % 4.53/4.88 (step @p70 :rule cong :premises (@p69) :args ((forall @t18 (=> @t47 @t46)))) % 4.53/4.88 (step @p71 :rule exists-elim :args ((= (exists @t9 @t45) @t46))) % 4.53/4.88 (step @p72 :rule refl :args ((_ @t1 @t3))) % 4.53/4.88 (step @p73 :rule refl :args (@t41)) % 4.53/4.88 (step @p74 :rule cong :premises (@p73) :args (@t42)) % 4.53/4.88 (step @p75 :rule trans :premises (@p74 @p72)) % 4.53/4.88 (step @p76 :rule refl :args (@t1)) % 4.53/4.88 (step @p77 :rule ho_cong :premises (@p76 @p73)) % 4.53/4.88 (step @p78 :rule cong :premises (@p77 @p75) :args ((= (_ @t1 @t41) @t42))) % 4.53/4.88 (step @p79 :rule symm :premises (@p78)) % 4.53/4.88 (step @p80 :rule refl :args (@t4)) % 4.53/4.88 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 4.53/4.88 (step @p82 :rule refl :args (@t3)) % 4.53/4.88 (step @p83 :rule cong :premises (@p82 @p73) :args ((= @t3 @t41))) % 4.53/4.88 (step @p84 :rule symm :premises (@p83)) % 4.53/4.88 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 4.53/4.88 (step @p86 :rule ho_cong :premises (@p76 @p85)) % 4.53/4.88 (step @p87 :rule trans :premises (@p86 @p81)) % 4.53/4.88 (step @p88 :rule refl :args (@t43)) % 4.53/4.88 (step @p89 :rule refl :args (@t6)) % 4.53/4.88 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t6 @t43))) % 4.53/4.88 (step @p91 :rule symm :premises (@p90)) % 4.53/4.88 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 4.53/4.88 (step @p93 :rule cong :premises (@p92) :args (@t87)) % 4.53/4.88 (step @p94 :rule nary_cong :premises (@p93 @p87) :args (@t88)) % 4.53/4.88 (step @p95 :rule cong :premises (@p94) :args ((forall @t7 @t88))) % 4.53/4.88 (step @p96 :rule bool-impl-elim :args (@t6 @t4)) % 4.53/4.88 (step @p97 :rule cong :premises (@p96) :args (@t8)) % 4.53/4.88 (step @p98 :rule trans :premises (@p97 @p95)) % 4.53/4.88 (step @p99 :rule cong :premises (@p98) :args (@t10)) % 4.53/4.88 (step @p100 :rule trans :premises (@p99 @p71)) % 4.53/4.88 (step @p101 :rule refl :args (@t40)) % 4.53/4.88 (step @p102 :rule nary_cong :premises (@p93 @p101) :args (@t89)) % 4.53/4.88 (step @p103 :rule cong :premises (@p102) :args ((forall @t7 @t89))) % 4.53/4.88 (step @p104 :rule bool-impl-elim :args (@t6 @t40)) % 4.53/4.88 (step @p105 :rule cong :premises (@p104) :args ((forall @t7 (=> @t6 @t40)))) % 4.53/4.88 (step @p106 :rule trans :premises (@p105 @p103)) % 4.53/4.88 (step @p107 :rule refl :args (@t39)) % 4.53/4.88 (step @p108 :rule refl :args (@t12)) % 4.53/4.88 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t12 @t39))) % 4.53/4.88 (step @p110 :rule symm :premises (@p109)) % 4.53/4.88 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 4.53/4.88 (step @p112 :rule cong :premises (@p111) :args (@t90)) % 4.53/4.88 (step @p113 :rule cong :premises (@p112) :args (@t91)) % 4.53/4.88 (step @p114 :rule cong :premises (@p113) :args (@t92)) % 4.53/4.88 (step @p115 :rule exists-elim :args ((= @t14 @t92))) % 4.53/4.88 (step @p116 :rule trans :premises (@p115 @p114)) % 4.53/4.88 (step @p117 :rule refl :args (@t6)) % 4.53/4.88 (step @p118 :rule cong :premises (@p117 @p116) :args (@t15)) % 4.53/4.88 (step @p119 :rule cong :premises (@p118) :args (@t16)) % 4.53/4.88 (step @p120 :rule trans :premises (@p119 @p106)) % 4.53/4.88 (step @p121 :rule cong :premises (@p120 @p100) :args (@t17)) % 4.53/4.88 (step @p122 :rule cong :premises (@p121) :args (@t19)) % 4.53/4.88 (step @p123 :rule trans :premises (@p122 @p70)) % 4.53/4.88 (step @p124 :rule exists-elim :args ((= (exists @t33 @t99) @t100))) % 4.53/4.88 (step @p125 :rule quant-merge-prenex :args ((= (forall @t31 @t102) @t99))) % 4.53/4.88 (step @p126 :rule refl :args (@t94)) % 4.53/4.88 (step @p127 :rule alpha_equiv :args (@t103 (@list @t95) (@list @t26))) % 4.53/4.88 (step @p128 :rule nary_cong :premises (@p127 @p126) :args (@t104)) % 4.53/4.88 (step @p129 :rule quant-miniscope-or :args ((= @t102 @t104))) % 4.53/4.88 (step @p130 :rule trans :premises (@p129 @p128)) % 4.53/4.88 (step @p131 :rule symm :premises (@p130)) % 4.53/4.88 (step @p132 :rule cong :premises (@p131) :args ((forall @t31 (or @t106 @t94)))) % 4.53/4.88 (step @p133 :rule trans :premises (@p132 @p125)) % 4.53/4.88 (step @p134 :rule refl :args ((_ @t23 @t20 @t22))) % 4.53/4.88 (step @p135 :rule refl :args (@t93)) % 4.53/4.88 (step @p136 :rule refl :args (@t20)) % 4.53/4.88 (step @p137 :rule cong :premises (@p136 @p135) :args (@t94)) % 4.53/4.88 (step @p138 :rule trans :premises (@p137 @p134)) % 4.53/4.88 (step @p139 :rule refl :args (@t24)) % 4.53/4.88 (step @p140 :rule ho_cong :premises (@p139 @p135)) % 4.53/4.88 (step @p141 :rule cong :premises (@p140 @p138) :args ((= (_ @t24 @t93) @t94))) % 4.53/4.88 (step @p142 :rule symm :premises (@p141)) % 4.53/4.88 (step @p143 :rule refl :args (@t25)) % 4.53/4.88 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 4.53/4.88 (step @p145 :rule refl :args (@t22)) % 4.53/4.88 (step @p146 :rule cong :premises (@p145 @p135) :args ((= @t22 @t93))) % 4.53/4.88 (step @p147 :rule symm :premises (@p146)) % 4.53/4.88 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 4.53/4.88 (step @p149 :rule ho_cong :premises (@p139 @p148)) % 4.53/4.88 (step @p150 :rule trans :premises (@p149 @p144)) % 4.53/4.88 (step @p151 :rule refl :args (@t106)) % 4.53/4.88 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t107)) % 4.53/4.88 (step @p153 :rule cong :premises (@p152) :args ((forall @t31 @t107))) % 4.53/4.88 (step @p154 :rule trans :premises (@p153 @p133)) % 4.53/4.88 (step @p155 :rule bool-double-not-elim :args (@t106)) % 4.53/4.88 (step @p156 :rule nary_cong :premises (@p155 @p143) :args ((or (not @t108) @t25))) % 4.53/4.88 (step @p157 :rule bool-impl-elim :args (@t108 @t25)) % 4.53/4.88 (step @p158 :rule trans :premises (@p157 @p156)) % 4.53/4.88 (step @p159 :rule cong :premises (@p158) :args ((forall @t31 (=> @t108 @t25)))) % 4.53/4.88 (step @p160 :rule trans :premises (@p159 @p154)) % 4.53/4.88 (step @p161 :rule refl :args (@t25)) % 4.53/4.88 (step @p162 :rule refl :args (@t105)) % 4.53/4.88 (step @p163 :rule refl :args (@t27)) % 4.53/4.88 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t27 @t105))) % 4.53/4.88 (step @p165 :rule symm :premises (@p164)) % 4.53/4.88 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 4.53/4.88 (step @p167 :rule cong :premises (@p166) :args (@t109)) % 4.53/4.88 (step @p168 :rule cong :premises (@p167) :args (@t110)) % 4.53/4.88 (step @p169 :rule cong :premises (@p168) :args (@t111)) % 4.53/4.88 (step @p170 :rule exists-elim :args ((= @t29 @t111))) % 4.53/4.88 (step @p171 :rule trans :premises (@p170 @p169)) % 4.53/4.88 (step @p172 :rule cong :premises (@p171 @p161) :args (@t30)) % 4.53/4.88 (step @p173 :rule cong :premises (@p172) :args (@t32)) % 4.53/4.88 (step @p174 :rule trans :premises (@p173 @p160)) % 4.53/4.88 (step @p175 :rule cong :premises (@p174) :args (@t34)) % 4.53/4.88 (step @p176 :rule trans :premises (@p175 @p124)) % 4.53/4.88 (step @p177 :rule cong :premises (@p176) :args (@t36)) % 4.53/4.88 (step @p178 :rule cong :premises (@p177 @p123) :args (@t37)) % 4.53/4.88 (step @p179 :rule cong :premises (@p178) :args (@t38)) % 4.53/4.88 (step @p180 :rule eq_resolve :premises (@p1 @p179)) % 4.53/4.88 (step @p181 :rule not_equiv_elim2 :premises (@p180)) % 4.53/4.88 (step @p182 :rule chain_m_resolution :premises (@p181 @p68) :args (@t113 @t86 (@list @t48))) % 4.53/4.88 (step @p183 :rule refl :args (@t116)) % 4.53/4.88 (step @p184 :rule bool-double-not-elim :args (@t112)) % 4.53/4.88 (step @p185 :rule nary_cong :premises (@p184 @p183) :args ((or (not @t113) @t116))) % 4.53/4.88 (step @p186 :rule bool-double-not-elim :args (@t116)) % 4.53/4.88 (step @p187 :rule refl :args (@t113)) % 4.53/4.88 (step @p188 :rule cong :premises (@p187 @p186) :args ((=> @t113 @t117))) % 4.53/4.88 (assume-push @p254 @t113) % 4.53/4.88 (step @p190 :rule skolemize :premises (@p254)) % 4.53/4.88 (step-pop @p255 :rule scope :premises (@p190)) % 4.53/4.88 (step @p191 :rule process_scope :premises (@p255) :args (@t117)) % 4.53/4.88 (step @p193 :rule eq_resolve :premises (@p191 @p188)) % 4.53/4.88 (step @p194 :rule implies_elim :premises (@p193)) % 4.53/4.88 (step @p195 :rule eq_resolve :premises (@p194 @p185)) % 4.53/4.88 (step @p196 :rule chain_m_resolution :premises (@p195 @p182) :args (@t116 @t118 (@list @t112))) % 4.53/4.88 (step @p197 :rule beta-reduce :args ((= @t125 @t120))) % 4.53/4.88 (step @p198 :rule refl :args (@t20)) % 4.53/4.88 (step @p199 :rule cong :premises (@p198 @p197) :args (@t126)) % 4.53/4.89 (step @p200 :rule refl :args (@t115)) % 4.53/4.89 (step @p201 :rule nary_cong :premises (@p200 @p199) :args (@t127)) % 4.53/4.89 (step @p202 :rule cong :premises (@p201) :args (@t128)) % 4.53/4.89 (step @p203 :rule cong :premises (@p202) :args (@t129)) % 4.53/4.89 (step @p204 :rule cong :premises (@p183 @p203) :args ((=> @t116 @t129))) % 4.53/4.89 (assume-push @p256 @t116) % 4.53/4.89 (step @p206 :rule instantiate :premises (@p256) :args ((@list @t124))) % 4.53/4.89 (step-pop @p257 :rule scope :premises (@p206)) % 4.53/4.89 (step @p207 :rule process_scope :premises (@p257) :args (@t129)) % 4.53/4.89 (step @p209 :rule eq_resolve :premises (@p207 @p204)) % 4.53/4.89 (step @p210 :rule implies_elim :premises (@p209)) % 4.53/4.89 (step @p211 :rule chain_m_resolution :premises (@p210 @p196) :args (@t131 @t86 (@list @t116))) % 4.53/4.89 (step @p212 :rule refl :args (@t138)) % 4.53/4.89 (step @p213 :rule bool-double-not-elim :args (@t130)) % 4.53/4.89 (step @p214 :rule nary_cong :premises (@p213 @p212) :args ((or (not @t131) @t138))) % 4.53/4.89 (assume-push @p258 @t131) % 4.53/4.89 (step @p216 :rule skolemize :premises (@p258)) % 4.53/4.89 (step-pop @p259 :rule scope :premises (@p216)) % 4.53/4.89 (step @p217 :rule process_scope :premises (@p259) :args (@t138)) % 4.53/4.89 (step @p219 :rule implies_elim :premises (@p217)) % 4.53/4.89 (step @p220 :rule eq_resolve :premises (@p219 @p214)) % 4.53/4.89 (step @p221 :rule chain_m_resolution :premises (@p220 @p211) :args (@t138 @t118 (@list @t130))) % 4.53/4.89 (step @p222 :rule bool-double-not-elim :args (@t135)) % 4.53/4.89 (step @p223 :rule refl :args (@t137)) % 4.53/4.89 (step @p224 :rule nary_cong :premises (@p223 @p222) :args ((or @t137 (not @t136)))) % 4.53/4.89 (step @p225 :rule cnf_or_neg :args (@t137 0)) % 4.53/4.89 (step @p226 :rule eq_resolve :premises (@p225 @p224)) % 4.53/4.89 (step @p227 :rule reordering :premises (@p226) :args ((or @t135 @t137))) % 4.53/4.89 (step @p228 :rule chain_m_resolution :premises (@p227 @p221) :args (@t135 @t118 @t139)) % 4.53/4.89 ; trust TRUST THEORY_LEMMA % 4.53/4.89 (step @p229 :rule trust :premises () :args ((forall @t123 (or (forall @t141 (not (_ @t114 @t121 @t140))) (_ @t114 @t121 @t122))))) % 4.53/4.89 (step @p230 :rule instantiate :premises (@p229) :args ((@list @t132))) % 4.53/4.89 (step @p231 :rule cnf_or_neg :args (@t137 1)) % 4.53/4.89 (step @p232 :rule chain_m_resolution :premises (@p231 @p221) :args ((not @t133) @t118 @t139)) % 4.53/4.89 (step @p233 :rule cnf_or_pos :args (@t143)) % 4.53/4.89 (step @p234 :rule reordering :premises (@p233) :args ((or @t133 @t142 (not @t143)))) % 4.53/4.89 (step @p235 :rule chain_m_resolution :premises (@p234 @p232 @p230) :args (@t142 (@list true false) (@list @t133 @t143))) % 4.53/4.89 (step @p236 :rule alpha_equiv :args (@t144 @t83 (@list @t140))) % 4.53/4.89 (step @p237 :rule equiv_elim2 :premises (@p236)) % 4.53/4.89 (step @p238 :rule chain_m_resolution :premises (@p237 @p235) :args (@t144 @t86 (@list @t142))) % 4.53/4.89 (assume-push @p260 @t144) % 4.53/4.89 (step @p240 :rule instantiate :premises (@p260) :args ((@list @t134))) % 4.53/4.89 (step-pop @p261 :rule scope :premises (@p240)) % 4.53/4.89 (step @p241 :rule process_scope :premises (@p261) :args (@t136)) % 4.53/4.89 (step @p243 :rule implies_elim :premises (@p241)) % 4.53/4.89 (step @p244 :rule reordering :premises (@p243) :args ((or @t136 (not @t144)))) % 4.53/4.89 (step @p245 false :rule chain_m_resolution :premises (@p244 @p238 @p228) :args (false (@list false false) (@list @t144 @t135))) % 4.53/4.89 ) % 4.53/4.89 % SZS output end Proof % 4.53/4.89 % cvc5 exiting %------------------------------------------------------------------------------