%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV164^5 : 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 : n024.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 08:55:32 AM UTC 2026 % Result : Theorem 0.34s 0.56s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEV164^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n024.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 13:16:45 EDT 2026 % 0.07/0.25 % CPUTime : % 0.07/0.33 %----Proving TH0 % 0.34/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.34/0.56 % SZS status Theorem % 0.34/0.56 % SZS output start Proof % 0.34/0.56 ( % 0.34/0.56 (declare-sort tptp.a 0) % 0.34/0.56 (define @t1 () (@var "Xy" tptp.a)) % 0.34/0.56 (define @t2 () (@var "Xx" tptp.a)) % 0.34/0.56 (define @t3 () (@list @t2 @t1)) % 0.34/0.56 (define @t4 () (lambda @t3 @t1)) % 0.34/0.56 (define @t5 () (@var "Xp" (-> (-> tptp.a tptp.a tptp.a) tptp.a))) % 0.34/0.56 (define @t6 () (_ @t5 @t4)) % 0.34/0.56 (define @t7 () (lambda @t3 @t2)) % 0.34/0.56 (define @t8 () (_ @t5 @t7)) % 0.34/0.56 (define @t9 () (@var "Xr" (-> tptp.a tptp.a Bool))) % 0.34/0.56 (define @t10 () (_ (_ @t9 @t8) @t6)) % 0.34/0.56 (define @t11 () (@list @t5)) % 0.34/0.56 (define @t12 () (exists @t11 @t10)) % 0.34/0.56 (define @t13 () (_ (_ @t9 @t2) @t1)) % 0.34/0.56 (define @t14 () (exists @t3 @t13)) % 0.34/0.56 (define @t15 () (= @t14 @t12)) % 0.34/0.56 (define @t16 () (@list @t9)) % 0.34/0.56 (define @t17 () (forall @t16 @t15)) % 0.34/0.56 (define @t18 () (not @t17)) % 0.34/0.56 (define @t19 () (_ @t5 @t4)) % 0.34/0.56 (define @t20 () (_ @t5 @t7)) % 0.34/0.56 (define @t21 () (_ @t9 @t20 @t19)) % 0.34/0.56 (define @t22 () (not @t10)) % 0.34/0.56 (define @t23 () (forall @t11 @t22)) % 0.34/0.56 (define @t24 () (not @t23)) % 0.34/0.56 (define @t25 () (_ @t9 @t2 @t1)) % 0.34/0.56 (define @t26 () (not @t13)) % 0.34/0.56 (define @t27 () (forall @t3 @t26)) % 0.34/0.56 (define @t28 () (not @t27)) % 0.34/0.56 (define @t29 () (@quantifiers_skolemize (forall @t16 (= (not (forall @t3 (not @t25))) (not (forall @t11 (not @t21))))) 0)) % 0.34/0.56 (define @t30 () (forall @t11 (not (_ @t29 @t20 @t19)))) % 0.34/0.56 (define @t31 () (forall @t3 (not (_ @t29 @t2 @t1)))) % 0.34/0.56 (define @t32 () (not @t30)) % 0.34/0.56 (define @t33 () (not @t31)) % 0.34/0.56 (define @t34 () (= @t33 @t32)) % 0.34/0.56 (define @t35 () (not @t32)) % 0.34/0.56 (define @t36 () (not @t33)) % 0.34/0.56 (define @t37 () (@quantifiers_skolemize @t31 1)) % 0.34/0.56 (define @t38 () (@quantifiers_skolemize @t31 0)) % 0.34/0.56 (define @t39 () (_ @t29 @t38 @t37)) % 0.34/0.56 (define @t40 () (not @t39)) % 0.34/0.56 (define @t41 () (not @t40)) % 0.34/0.56 (define @t42 () (lambda (@list (@var "BOUND_VARIABLE_14739" (-> tptp.a tptp.a tptp.a))) @t37)) % 0.34/0.56 (define @t43 () (_ @t42 @t4)) % 0.34/0.56 (define @t44 () (_ @t42 @t7)) % 0.34/0.56 (define @t45 () (_ @t29 @t44 @t43)) % 0.34/0.56 (define @t46 () (not @t45)) % 0.34/0.56 (define @t47 () (= @t38 @t37)) % 0.34/0.56 (define @t48 () (not @t47)) % 0.34/0.56 (define @t49 () (_ @t29 @t37 @t37)) % 0.34/0.56 (define @t50 () (not @t49)) % 0.34/0.56 (define @t51 () (not @t50)) % 0.34/0.56 (define @t52 () (and @t50 @t47 @t39)) % 0.34/0.56 (define @t53 () (forall @t3 (= @t2 @t1))) % 0.34/0.56 (define @t54 () (= @t37 @t38)) % 0.34/0.56 (define @t55 () (@purify @t4)) % 0.34/0.56 (define @t56 () (@purify @t7)) % 0.34/0.56 (define @t57 () (= @t56 @t55)) % 0.34/0.56 (define @t58 () (@const 0 tptp.a)) % 0.34/0.56 (define @t59 () (= @t7 @t4)) % 0.34/0.56 (define @t60 () (ite @t59 @t58 @t37)) % 0.34/0.56 (define @t61 () (@purify @t60)) % 0.34/0.56 (define @t62 () (= @t37 @t61)) % 0.34/0.56 (define @t63 () (= @t58 @t61)) % 0.34/0.56 (define @t64 () (= @t60 @t37)) % 0.34/0.56 (define @t65 () (= @t60 @t58)) % 0.34/0.56 (define @t66 () (@const 1 tptp.a)) % 0.34/0.56 (define @t67 () (ite @t59 @t66 @t61)) % 0.34/0.56 (define @t68 () (@purify @t67)) % 0.34/0.56 (define @t69 () (_ @t29 @t67 @t66)) % 0.34/0.56 (define @t70 () (not @t69)) % 0.34/0.56 (define @t71 () (ite @t59 @t61 @t38)) % 0.34/0.56 (define @t72 () (= @t4 @t4)) % 0.34/0.56 (define @t73 () (ite @t72 @t66 @t71)) % 0.34/0.56 (define @t74 () (@var "BOUND_VARIABLE_42889" (-> tptp.a tptp.a tptp.a))) % 0.34/0.56 (define @t75 () (lambda (@list @t74) (ite (= @t4 @t74) @t66 (ite (= @t7 @t74) @t61 @t38)))) % 0.34/0.56 (define @t76 () (_ @t75 @t4)) % 0.34/0.56 (define @t77 () (ite (= @t7 @t7) @t61 @t38)) % 0.34/0.56 (define @t78 () (= @t4 @t7)) % 0.34/0.56 (define @t79 () (ite @t78 @t66 @t77)) % 0.34/0.56 (define @t80 () (_ @t75 @t7)) % 0.34/0.56 (define @t81 () (_ @t29 @t80 @t76)) % 0.34/0.56 (define @t82 () (not @t81)) % 0.34/0.56 (define @t83 () (= @t61 @t68)) % 0.34/0.56 (define @t84 () (= @t66 @t68)) % 0.34/0.56 (define @t85 () (= @t67 @t61)) % 0.34/0.56 (define @t86 () (= @t67 @t66)) % 0.34/0.56 (define @t87 () (_ @t29 @t61 @t66)) % 0.34/0.56 (define @t88 () (not @t87)) % 0.34/0.56 (define @t89 () (not @t83)) % 0.34/0.56 (define @t90 () (_ @t29 @t68 @t66)) % 0.34/0.56 (define @t91 () (not @t90)) % 0.34/0.56 (define @t92 () (and @t91 @t83)) % 0.34/0.56 (define @t93 () (= (_ @t29 @t38) (_ @t29 @t61))) % 0.34/0.56 (define @t94 () (not @t93)) % 0.34/0.56 (define @t95 () (not @t62)) % 0.34/0.56 (define @t96 () (= false true)) % 0.34/0.56 (define @t97 () (and @t93 @t62 @t50 @t39)) % 0.34/0.56 (define @t98 () (_ @t29 @t38 @t66)) % 0.34/0.56 (define @t99 () (= @t98 @t87)) % 0.34/0.56 (define @t100 () (ite @t59 @t66 @t38)) % 0.34/0.56 (define @t101 () (@purify @t100)) % 0.34/0.56 (define @t102 () (_ @t29 @t100 @t66)) % 0.34/0.56 (define @t103 () (not @t102)) % 0.34/0.56 (define @t104 () (ite @t72 @t66 @t38)) % 0.34/0.56 (define @t105 () (@var "BOUND_VARIABLE_58036" (-> tptp.a tptp.a tptp.a))) % 0.34/0.56 (define @t106 () (lambda (@list @t105) (ite (= @t4 @t105) @t66 @t38))) % 0.34/0.56 (define @t107 () (_ @t106 @t4)) % 0.34/0.56 (define @t108 () (ite @t78 @t66 @t38)) % 0.34/0.56 (define @t109 () (_ @t106 @t7)) % 0.34/0.56 (define @t110 () (_ @t29 @t109 @t107)) % 0.34/0.56 (define @t111 () (not @t110)) % 0.34/0.56 (define @t112 () (= @t38 @t101)) % 0.34/0.56 (define @t113 () (= @t66 @t101)) % 0.34/0.56 (define @t114 () (= @t100 @t38)) % 0.34/0.56 (define @t115 () (= @t100 @t66)) % 0.34/0.56 (define @t116 () (not @t112)) % 0.34/0.56 (define @t117 () (_ @t29 @t101 @t66)) % 0.34/0.56 (define @t118 () (not @t98)) % 0.34/0.56 (define @t119 () (not @t117)) % 0.34/0.56 (define @t120 () (and @t98 @t112 @t119)) % 0.34/0.56 (define @t121 () (@quantifiers_skolemize @t30 0)) % 0.34/0.56 (define @t122 () (_ @t121 @t55)) % 0.34/0.56 (define @t123 () (_ @t121 @t56)) % 0.34/0.56 (define @t124 () (_ @t29 @t123 @t122)) % 0.34/0.56 (define @t125 () (_ @t121 @t4)) % 0.34/0.56 (define @t126 () (_ @t121 @t7)) % 0.34/0.56 (define @t127 () (_ @t29 @t126 @t125)) % 0.34/0.56 (define @t128 () (not (not @t127))) % 0.34/0.56 (assume @p1 @t18) % 0.34/0.56 (assume @p2 true) % 0.34/0.56 (step @p3 :rule refl :args ((_ @t9 @t8 @t6))) % 0.34/0.56 (step @p4 :rule refl :args (@t19)) % 0.34/0.56 (step @p5 :rule refl :args (@t20)) % 0.34/0.56 (step @p6 :rule cong :premises (@p5 @p4) :args (@t21)) % 0.34/0.56 (step @p7 :rule trans :premises (@p6 @p3)) % 0.34/0.56 (step @p8 :rule refl :args (@t9)) % 0.34/0.56 (step @p9 :rule ho_cong :premises (@p8 @p5)) % 0.34/0.56 (step @p10 :rule ho_cong :premises (@p9 @p4)) % 0.34/0.56 (step @p11 :rule cong :premises (@p10 @p7) :args ((= (_ (_ @t9 @t20) @t19) @t21))) % 0.34/0.56 (step @p12 :rule symm :premises (@p11)) % 0.34/0.56 (step @p13 :rule refl :args (@t10)) % 0.34/0.56 (step @p14 :rule eq_resolve :premises (@p13 @p12)) % 0.34/0.56 (step @p15 :rule refl :args (@t6)) % 0.34/0.56 (step @p16 :rule cong :premises (@p15 @p4) :args ((= @t6 @t19))) % 0.34/0.56 (step @p17 :rule symm :premises (@p16)) % 0.34/0.56 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 0.34/0.56 (step @p19 :rule refl :args (@t8)) % 0.34/0.56 (step @p20 :rule cong :premises (@p19 @p5) :args ((= @t8 @t20))) % 0.34/0.56 (step @p21 :rule symm :premises (@p20)) % 0.34/0.56 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.34/0.56 (step @p23 :rule ho_cong :premises (@p8 @p22)) % 0.34/0.56 (step @p24 :rule ho_cong :premises (@p23 @p18)) % 0.34/0.56 (step @p25 :rule trans :premises (@p24 @p14)) % 0.34/0.56 (step @p26 :rule cong :premises (@p25) :args (@t22)) % 0.34/0.56 (step @p27 :rule cong :premises (@p26) :args (@t23)) % 0.34/0.56 (step @p28 :rule cong :premises (@p27) :args (@t24)) % 0.34/0.56 (step @p29 :rule exists-elim :args ((= @t12 @t24))) % 0.34/0.56 (step @p30 :rule trans :premises (@p29 @p28)) % 0.34/0.56 (step @p31 :rule refl :args (@t25)) % 0.34/0.56 (step @p32 :rule refl :args (@t13)) % 0.34/0.56 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t13 @t25))) % 0.34/0.56 (step @p34 :rule symm :premises (@p33)) % 0.34/0.56 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.34/0.56 (step @p36 :rule cong :premises (@p35) :args (@t26)) % 0.34/0.56 (step @p37 :rule cong :premises (@p36) :args (@t27)) % 0.34/0.56 (step @p38 :rule cong :premises (@p37) :args (@t28)) % 0.34/0.56 (step @p39 :rule exists-elim :args ((= @t14 @t28))) % 0.34/0.56 (step @p40 :rule trans :premises (@p39 @p38)) % 0.34/0.56 (step @p41 :rule cong :premises (@p40 @p30) :args (@t15)) % 0.34/0.56 (step @p42 :rule cong :premises (@p41) :args (@t17)) % 0.34/0.56 (step @p43 :rule cong :premises (@p42) :args (@t18)) % 0.34/0.56 (step @p44 :rule eq_resolve :premises (@p1 @p43)) % 0.34/0.56 (step @p45 :rule skolemize :premises (@p44)) % 0.34/0.56 (step @p46 :rule bool-double-not-elim :args (@t30)) % 0.34/0.56 (step @p47 :rule bool-double-not-elim :args (@t31)) % 0.34/0.56 (step @p48 :rule refl :args (@t34)) % 0.34/0.56 (step @p49 :rule nary_cong :premises (@p48 @p47 @p46) :args ((or @t34 @t36 @t35))) % 0.34/0.56 (step @p50 :rule cnf_equiv_neg2 :args (@t34)) % 0.34/0.56 (step @p51 :rule eq_resolve :premises (@p50 @p49)) % 0.34/0.56 (step @p52 :rule reordering :premises (@p51) :args ((or @t31 @t30 @t34))) % 0.34/0.56 (step @p53 :rule refl :args (@t39)) % 0.34/0.56 (step @p54 :rule nary_cong :premises (@p47 @p53) :args ((or @t36 @t39))) % 0.34/0.56 (step @p55 :rule bool-double-not-elim :args (@t39)) % 0.34/0.56 (step @p56 :rule refl :args (@t33)) % 0.34/0.56 (step @p57 :rule cong :premises (@p56 @p55) :args ((=> @t33 @t41))) % 0.34/0.56 (assume-push @p370 @t33) % 0.34/0.56 (step @p59 :rule skolemize :premises (@p370)) % 0.34/0.56 (step-pop @p371 :rule scope :premises (@p59)) % 0.34/0.56 (step @p60 :rule process_scope :premises (@p371) :args (@t41)) % 0.34/0.56 (step @p62 :rule eq_resolve :premises (@p60 @p57)) % 0.34/0.56 (step @p63 :rule implies_elim :premises (@p62)) % 0.34/0.56 (step @p64 :rule eq_resolve :premises (@p63 @p54)) % 0.34/0.56 (step @p65 :rule beta-reduce :args ((= @t43 @t37))) % 0.34/0.56 (step @p66 :rule beta-reduce :args ((= @t44 @t37))) % 0.34/0.56 (step @p67 :rule cong :premises (@p66 @p65) :args (@t45)) % 0.34/0.56 (step @p68 :rule cong :premises (@p67) :args (@t46)) % 0.34/0.56 (step @p69 :rule refl :args (@t30)) % 0.34/0.56 (step @p70 :rule cong :premises (@p69 @p68) :args ((=> @t30 @t46))) % 0.34/0.56 (assume-push @p372 @t30) % 0.34/0.56 (step @p72 :rule instantiate :premises (@p372) :args ((@list @t42))) % 0.34/0.56 (step-pop @p373 :rule scope :premises (@p72)) % 0.34/0.56 (step @p73 :rule process_scope :premises (@p373) :args (@t46)) % 0.34/0.56 (step @p75 :rule eq_resolve :premises (@p73 @p70)) % 0.34/0.56 (step @p76 :rule implies_elim :premises (@p75)) % 0.34/0.56 (step @p77 :rule refl :args (@t48)) % 0.34/0.56 (step @p78 :rule bool-double-not-elim :args (@t49)) % 0.34/0.56 (step @p79 :rule refl :args (@t40)) % 0.34/0.56 (step @p80 :rule nary_cong :premises (@p79 @p78 @p77) :args ((or @t40 @t51 @t48))) % 0.34/0.56 (assume-push @p374 @t50) % 0.34/0.56 (assume-push @p375 @t47) % 0.34/0.56 (assume-push @p376 @t39) % 0.34/0.56 (step @p84 :rule evaluate :args ((= true false))) % 0.34/0.56 (step @p85 :rule false_intro :premises (@p374)) % 0.34/0.56 (step @p86 :rule refl :args (@t37)) % 0.34/0.56 (step @p87 :rule cong :premises (@p375 @p86) :args (@t39)) % 0.34/0.56 (step @p88 :rule true_intro :premises (@p376)) % 0.34/0.56 (step @p89 :rule symm :premises (@p88)) % 0.34/0.56 (step @p90 :rule trans :premises (@p89 @p87 @p85)) % 0.34/0.56 (step @p91 false :rule eq_resolve :premises (@p90 @p84)) % 0.34/0.56 (step-pop @p377 :rule scope :premises (@p91)) % 0.34/0.56 (step-pop @p378 :rule scope :premises (@p377)) % 0.34/0.56 (step-pop @p379 :rule scope :premises (@p378)) % 0.34/0.56 (step @p92 :rule process_scope :premises (@p379) :args (false)) % 0.34/0.56 (assume-push @p380 @t39) % 0.34/0.56 (assume-push @p381 @t50) % 0.34/0.56 (assume-push @p382 @t47) % 0.34/0.56 (step @p99 :rule and_intro :premises (@p381 @p382 @p380)) % 0.34/0.56 (step-pop @p383 :rule scope :premises (@p99)) % 0.34/0.56 (step-pop @p384 :rule scope :premises (@p383)) % 0.34/0.56 (step-pop @p385 :rule scope :premises (@p384)) % 0.34/0.56 (step @p100 :rule process_scope :premises (@p385) :args (@t52)) % 0.34/0.56 (step @p104 :rule implies_elim :premises (@p100)) % 0.34/0.56 (step @p105 :rule resolution :premises (@p104 @p92) :args (true @t52)) % 0.34/0.56 (step @p106 :rule not_and :premises (@p105)) % 0.34/0.56 (step @p107 :rule eq_resolve :premises (@p106 @p80)) % 0.34/0.56 (step @p108 :rule eq-symm :args (@t37 @t38)) % 0.34/0.56 (step @p109 :rule refl :args (@t53)) % 0.34/0.56 (step @p110 :rule cong :premises (@p109 @p108) :args ((=> @t53 @t54))) % 0.34/0.56 (assume-push @p386 @t53) % 0.34/0.56 (step @p112 :rule instantiate :premises (@p386) :args ((@list @t37 @t38))) % 0.34/0.56 (step-pop @p387 :rule scope :premises (@p112)) % 0.34/0.56 (step @p113 :rule process_scope :premises (@p387) :args (@t54)) % 0.34/0.56 (step @p115 :rule eq_resolve :premises (@p113 @p110)) % 0.34/0.56 (step @p116 :rule implies_elim :premises (@p115)) % 0.34/0.56 ; WARNING: add trust step for TRUST % 0.34/0.56 ; trust TRUST THEORY_LEMMA % 0.34/0.56 (step @p117 :rule trust :premises () :args ((=> @t57 @t53))) % 0.34/0.56 (step @p118 :rule implies_elim :premises (@p117)) % 0.34/0.56 (step @p119 :rule refl :args (@t62)) % 0.34/0.56 (step @p120 :rule refl :args (@t63)) % 0.34/0.56 (step @p121 :rule eq-refl :args (@t4)) % 0.34/0.56 (step @p122 :rule skolem_intro :args (@t55)) % 0.34/0.56 (step @p123 :rule refl :args (@t4)) % 0.34/0.56 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t4 @t55))) % 0.34/0.56 (step @p125 :rule trans :premises (@p124 @p121)) % 0.34/0.56 (step @p126 :rule true_elim :premises (@p125)) % 0.34/0.56 (step @p127 :rule eq-refl :args (@t7)) % 0.34/0.56 (step @p128 :rule skolem_intro :args (@t56)) % 0.34/0.56 (step @p129 :rule refl :args (@t7)) % 0.34/0.56 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t7 @t56))) % 0.34/0.56 (step @p131 :rule trans :premises (@p130 @p127)) % 0.34/0.56 (step @p132 :rule true_elim :premises (@p131)) % 0.34/0.56 (step @p133 :rule cong :premises (@p132 @p126) :args (@t59)) % 0.34/0.56 (step @p134 :rule cong :premises (@p133 @p120 @p119) :args ((ite @t59 @t63 @t62))) % 0.34/0.56 (step @p135 :rule eq-symm :args (@t61 @t37)) % 0.34/0.56 (step @p136 :rule eq-symm :args (@t61 @t58)) % 0.34/0.56 (step @p137 :rule refl :args (@t59)) % 0.34/0.56 (step @p138 :rule cong :premises (@p137 @p136 @p135) :args ((ite @t59 (= @t61 @t58) (= @t61 @t37)))) % 0.34/0.56 (step @p139 :rule trans :premises (@p138 @p134)) % 0.34/0.56 (step @p86 :rule refl :args (@t37)) % 0.34/0.56 (step @p140 :rule eq-refl :args (@t60)) % 0.34/0.56 (step @p141 :rule skolem_intro :args (@t61)) % 0.34/0.56 (step @p142 :rule refl :args (@t60)) % 0.34/0.56 (step @p143 :rule cong :premises (@p142 @p141) :args ((= @t60 @t61))) % 0.34/0.56 (step @p144 :rule trans :premises (@p143 @p140)) % 0.34/0.56 (step @p145 :rule true_elim :premises (@p144)) % 0.34/0.56 (step @p146 :rule cong :premises (@p145 @p86) :args (@t64)) % 0.34/0.56 (step @p147 :rule refl :args (@t58)) % 0.34/0.56 (step @p148 :rule cong :premises (@p145 @p147) :args (@t65)) % 0.34/0.56 (step @p149 :rule cong :premises (@p137 @p148 @p146) :args ((ite @t59 @t65 @t64))) % 0.34/0.56 (step @p150 :rule ite_eq :args (@t60)) % 0.34/0.56 (step @p151 :rule eq_resolve :premises (@p150 @p149)) % 0.34/0.56 (step @p152 :rule eq_resolve :premises (@p151 @p139)) % 0.34/0.56 (step @p153 :rule ite_elim2 :premises (@p152)) % 0.34/0.56 (step @p154 :rule refl :args (@t66)) % 0.34/0.56 (step @p155 :rule eq-refl :args ((ite @t59 @t66 @t60))) % 0.34/0.56 (step @p156 :rule cong :premises (@p137 @p154 @p141) :args (@t67)) % 0.34/0.56 (step @p157 :rule skolem_intro :args (@t68)) % 0.34/0.56 (step @p158 :rule trans :premises (@p157 @p156)) % 0.34/0.56 (step @p159 :rule cong :premises (@p156 @p158) :args ((= @t67 @t68))) % 0.34/0.56 (step @p160 :rule trans :premises (@p159 @p155)) % 0.34/0.56 (step @p161 :rule true_elim :premises (@p160)) % 0.34/0.56 (step @p162 :rule cong :premises (@p161 @p154) :args (@t69)) % 0.34/0.56 (step @p163 :rule cong :premises (@p162) :args (@t70)) % 0.34/0.56 (step @p164 :rule cong :premises (@p69 @p163) :args ((=> @t30 @t70))) % 0.34/0.56 (step @p165 :rule ite-true-cond :args (@t66 @t71)) % 0.34/0.56 (step @p166 :rule refl :args (@t71)) % 0.34/0.56 (step @p167 :rule cong :premises (@p121 @p154 @p166) :args (@t73)) % 0.34/0.56 (step @p168 :rule trans :premises (@p167 @p165)) % 0.34/0.56 (step @p169 :rule beta-reduce :args ((= @t76 @t73))) % 0.34/0.56 (step @p170 :rule trans :premises (@p169 @p168)) % 0.34/0.56 (step @p171 :rule ite-true-cond :args (@t61 @t38)) % 0.34/0.56 (step @p172 :rule refl :args (@t38)) % 0.34/0.56 (step @p173 :rule refl :args (@t61)) % 0.34/0.56 (step @p174 :rule cong :premises (@p127 @p173 @p172) :args (@t77)) % 0.34/0.56 (step @p175 :rule trans :premises (@p174 @p171)) % 0.34/0.56 (step @p176 :rule eq-symm :args (@t4 @t7)) % 0.34/0.56 (step @p177 :rule cong :premises (@p176 @p154 @p175) :args (@t79)) % 0.34/0.56 (step @p178 :rule beta-reduce :args ((= @t80 @t79))) % 0.34/0.56 (step @p179 :rule trans :premises (@p178 @p177)) % 0.34/0.56 (step @p180 :rule cong :premises (@p179 @p170) :args (@t81)) % 0.34/0.56 (step @p181 :rule cong :premises (@p180) :args (@t82)) % 0.34/0.56 (step @p182 :rule cong :premises (@p69 @p181) :args ((=> @t30 @t82))) % 0.34/0.56 (assume-push @p388 @t30) % 0.34/0.56 (step @p184 :rule instantiate :premises (@p388) :args ((@list @t75))) % 0.34/0.56 (step-pop @p389 :rule scope :premises (@p184)) % 0.34/0.56 (step @p185 :rule process_scope :premises (@p389) :args (@t82)) % 0.34/0.56 (step @p187 :rule eq_resolve :premises (@p185 @p182)) % 0.34/0.56 (step @p188 :rule eq_resolve :premises (@p187 @p164)) % 0.34/0.56 (step @p189 :rule implies_elim :premises (@p188)) % 0.34/0.56 (step @p190 :rule refl :args (@t83)) % 0.34/0.56 (step @p191 :rule refl :args (@t84)) % 0.34/0.56 (step @p192 :rule cong :premises (@p133 @p191 @p190) :args ((ite @t59 @t84 @t83))) % 0.34/0.56 (step @p193 :rule eq-symm :args (@t68 @t61)) % 0.34/0.56 (step @p194 :rule eq-symm :args (@t68 @t66)) % 0.34/0.56 (step @p195 :rule cong :premises (@p137 @p194 @p193) :args ((ite @t59 (= @t68 @t66) (= @t68 @t61)))) % 0.34/0.56 (step @p196 :rule trans :premises (@p195 @p192)) % 0.34/0.56 (step @p197 :rule cong :premises (@p161 @p173) :args (@t85)) % 0.34/0.56 (step @p198 :rule cong :premises (@p161 @p154) :args (@t86)) % 0.34/0.56 (step @p199 :rule cong :premises (@p137 @p198 @p197) :args ((ite @t59 @t86 @t85))) % 0.34/0.56 (step @p200 :rule ite_eq :args (@t67)) % 0.34/0.56 (step @p201 :rule eq_resolve :premises (@p200 @p199)) % 0.34/0.56 (step @p202 :rule eq_resolve :premises (@p201 @p196)) % 0.34/0.56 (step @p203 :rule ite_elim2 :premises (@p202)) % 0.34/0.56 (step @p204 :rule refl :args (@t88)) % 0.34/0.56 (step @p205 :rule refl :args (@t89)) % 0.34/0.56 (step @p206 :rule bool-double-not-elim :args (@t90)) % 0.34/0.56 (step @p207 :rule nary_cong :premises (@p206 @p205 @p204) :args ((or (not @t91) @t89 @t88))) % 0.34/0.56 (assume-push @p390 @t91) % 0.34/0.56 (assume-push @p391 @t83) % 0.34/0.56 (assume-push @p392 @t91) % 0.34/0.56 (assume-push @p393 @t83) % 0.34/0.56 (step @p212 :rule false_intro :premises (@p390)) % 0.34/0.56 (step @p213 :rule cong :premises (@p391 @p154) :args (@t87)) % 0.34/0.56 (step @p214 :rule trans :premises (@p213 @p212)) % 0.34/0.56 (step @p215 :rule false_elim :premises (@p214)) % 0.34/0.56 (step-pop @p394 :rule scope :premises (@p215)) % 0.34/0.56 (step-pop @p395 :rule scope :premises (@p394)) % 0.34/0.56 (step @p216 :rule process_scope :premises (@p395) :args (@t88)) % 0.34/0.56 (step @p219 :rule and_intro :premises (@p390 @p391)) % 0.34/0.56 (step @p220 :rule modus_ponens :premises (@p219 @p216)) % 0.34/0.56 (step-pop @p396 :rule scope :premises (@p220)) % 0.34/0.56 (step-pop @p397 :rule scope :premises (@p396)) % 0.34/0.56 (step @p221 :rule process_scope :premises (@p397) :args (@t88)) % 0.34/0.56 (step @p224 :rule implies_elim :premises (@p221)) % 0.34/0.56 (step @p225 :rule cnf_and_neg :args (@t92)) % 0.34/0.56 (step @p226 :rule resolution :premises (@p225 @p224) :args (true @t92)) % 0.34/0.56 (step @p227 :rule eq_resolve :premises (@p226 @p207)) % 0.34/0.56 (step @p228 :rule refl :args (@t94)) % 0.34/0.56 (step @p229 :rule refl :args (@t95)) % 0.34/0.56 (step @p230 :rule nary_cong :premises (@p79 @p78 @p229 @p228) :args ((or @t40 @t51 @t95 @t94))) % 0.34/0.56 (assume-push @p398 @t93) % 0.34/0.56 (assume-push @p399 @t62) % 0.34/0.56 (assume-push @p400 @t50) % 0.34/0.56 (assume-push @p401 @t39) % 0.34/0.56 (step @p235 :rule evaluate :args (@t96)) % 0.34/0.56 (step @p236 :rule true_intro :premises (@p401)) % 0.34/0.56 (step @p237 :rule refl :args (@t39)) % 0.34/0.56 (step @p238 :rule symm :premises (@p237)) % 0.34/0.56 (step @p239 :rule symm :premises (@p398)) % 0.34/0.56 (step @p240 :rule refl :args (@t29)) % 0.34/0.56 (step @p241 :rule ho_cong :premises (@p240 @p399)) % 0.34/0.56 (step @p242 :rule trans :premises (@p241 @p239)) % 0.34/0.56 (step @p243 :rule ho_cong :premises (@p242 @p86)) % 0.34/0.56 (step @p244 :rule refl :args (@t49)) % 0.34/0.56 (step @p245 :rule false_intro :premises (@p400)) % 0.34/0.56 (step @p246 :rule symm :premises (@p245)) % 0.34/0.56 (step @p247 :rule trans :premises (@p246 @p244 @p243 @p238 @p236)) % 0.34/0.56 (step @p248 false :rule eq_resolve :premises (@p247 @p235)) % 0.34/0.56 (step-pop @p402 :rule scope :premises (@p248)) % 0.34/0.56 (step-pop @p403 :rule scope :premises (@p402)) % 0.34/0.56 (step-pop @p404 :rule scope :premises (@p403)) % 0.34/0.56 (step-pop @p405 :rule scope :premises (@p404)) % 0.34/0.56 (step @p249 :rule process_scope :premises (@p405) :args (false)) % 0.34/0.56 (assume-push @p406 @t39) % 0.34/0.56 (assume-push @p407 @t50) % 0.34/0.56 (assume-push @p408 @t62) % 0.34/0.56 (assume-push @p409 @t93) % 0.34/0.56 (step @p258 :rule and_intro :premises (@p409 @p408 @p407 @p406)) % 0.34/0.56 (step-pop @p410 :rule scope :premises (@p258)) % 0.34/0.56 (step-pop @p411 :rule scope :premises (@p410)) % 0.34/0.56 (step-pop @p412 :rule scope :premises (@p411)) % 0.34/0.56 (step-pop @p413 :rule scope :premises (@p412)) % 0.34/0.56 (step @p259 :rule process_scope :premises (@p413) :args (@t97)) % 0.34/0.56 (step @p264 :rule implies_elim :premises (@p259)) % 0.34/0.56 (step @p265 :rule resolution :premises (@p264 @p249) :args (true @t97)) % 0.34/0.56 (step @p266 :rule not_and :premises (@p265)) % 0.34/0.56 (step @p267 :rule eq_resolve :premises (@p266 @p230)) % 0.34/0.56 ; trust TRUST THEORY_LEMMA % 0.34/0.56 (step @p268 :rule trust :premises () :args ((or @t93 (not @t99)))) % 0.34/0.56 (step @p269 :rule cnf_equiv_neg1 :args (@t99)) % 0.34/0.56 (step @p270 :rule reordering :premises (@p269) :args ((or @t98 @t87 @t99))) % 0.34/0.56 (step @p271 :rule eq-refl :args (@t100)) % 0.34/0.56 (step @p272 :rule skolem_intro :args (@t101)) % 0.34/0.56 (step @p273 :rule refl :args (@t100)) % 0.34/0.56 (step @p274 :rule cong :premises (@p273 @p272) :args ((= @t100 @t101))) % 0.34/0.56 (step @p275 :rule trans :premises (@p274 @p271)) % 0.34/0.56 (step @p276 :rule true_elim :premises (@p275)) % 0.34/0.56 (step @p277 :rule cong :premises (@p276 @p154) :args (@t102)) % 0.34/0.56 (step @p278 :rule cong :premises (@p277) :args (@t103)) % 0.34/0.56 (step @p279 :rule cong :premises (@p69 @p278) :args ((=> @t30 @t103))) % 0.34/0.56 (step @p280 :rule ite-true-cond :args (@t66 @t38)) % 0.34/0.56 (step @p281 :rule cong :premises (@p121 @p154 @p172) :args (@t104)) % 0.34/0.56 (step @p282 :rule trans :premises (@p281 @p280)) % 0.34/0.56 (step @p283 :rule beta-reduce :args ((= @t107 @t104))) % 0.34/0.56 (step @p284 :rule trans :premises (@p283 @p282)) % 0.34/0.56 (step @p285 :rule cong :premises (@p176 @p154 @p172) :args (@t108)) % 0.34/0.56 (step @p286 :rule beta-reduce :args ((= @t109 @t108))) % 0.34/0.56 (step @p287 :rule trans :premises (@p286 @p285)) % 0.34/0.56 (step @p288 :rule cong :premises (@p287 @p284) :args (@t110)) % 0.34/0.56 (step @p289 :rule cong :premises (@p288) :args (@t111)) % 0.34/0.56 (step @p290 :rule cong :premises (@p69 @p289) :args ((=> @t30 @t111))) % 0.34/0.56 (assume-push @p414 @t30) % 0.34/0.56 (step @p292 :rule instantiate :premises (@p414) :args ((@list @t106))) % 0.34/0.56 (step-pop @p415 :rule scope :premises (@p292)) % 0.34/0.56 (step @p293 :rule process_scope :premises (@p415) :args (@t111)) % 0.34/0.56 (step @p295 :rule eq_resolve :premises (@p293 @p290)) % 0.34/0.56 (step @p296 :rule eq_resolve :premises (@p295 @p279)) % 0.34/0.56 (step @p297 :rule implies_elim :premises (@p296)) % 0.34/0.56 (step @p298 :rule refl :args (@t112)) % 0.34/0.56 (step @p299 :rule refl :args (@t113)) % 0.34/0.56 (step @p300 :rule cong :premises (@p133 @p299 @p298) :args ((ite @t59 @t113 @t112))) % 0.34/0.56 (step @p301 :rule eq-symm :args (@t101 @t38)) % 0.34/0.56 (step @p302 :rule eq-symm :args (@t101 @t66)) % 0.34/0.56 (step @p303 :rule cong :premises (@p137 @p302 @p301) :args ((ite @t59 (= @t101 @t66) (= @t101 @t38)))) % 0.34/0.56 (step @p304 :rule trans :premises (@p303 @p300)) % 0.34/0.56 (step @p305 :rule cong :premises (@p276 @p172) :args (@t114)) % 0.34/0.56 (step @p306 :rule cong :premises (@p276 @p154) :args (@t115)) % 0.34/0.56 (step @p307 :rule cong :premises (@p137 @p306 @p305) :args ((ite @t59 @t115 @t114))) % 0.34/0.56 (step @p308 :rule ite_eq :args (@t100)) % 0.34/0.56 (step @p309 :rule eq_resolve :premises (@p308 @p307)) % 0.34/0.56 (step @p310 :rule eq_resolve :premises (@p309 @p304)) % 0.34/0.56 (step @p311 :rule ite_elim2 :premises (@p310)) % 0.34/0.56 (step @p312 :rule refl :args (@t116)) % 0.34/0.56 (step @p313 :rule bool-double-not-elim :args (@t117)) % 0.34/0.56 (step @p314 :rule refl :args (@t118)) % 0.34/0.56 (step @p315 :rule nary_cong :premises (@p314 @p313 @p312) :args ((or @t118 (not @t119) @t116))) % 0.34/0.56 (assume-push @p416 @t98) % 0.34/0.56 (assume-push @p417 @t112) % 0.34/0.56 (assume-push @p418 @t119) % 0.34/0.56 (step @p235 :rule evaluate :args (@t96)) % 0.34/0.56 (step @p319 :rule true_intro :premises (@p416)) % 0.34/0.56 (step @p320 :rule symm :premises (@p417)) % 0.34/0.56 (step @p321 :rule cong :premises (@p320 @p154) :args (@t117)) % 0.34/0.56 (step @p322 :rule false_intro :premises (@p418)) % 0.34/0.56 (step @p323 :rule symm :premises (@p322)) % 0.34/0.56 (step @p324 :rule trans :premises (@p323 @p321 @p319)) % 0.34/0.56 (step @p325 false :rule eq_resolve :premises (@p324 @p235)) % 0.34/0.56 (step-pop @p419 :rule scope :premises (@p325)) % 0.34/0.56 (step-pop @p420 :rule scope :premises (@p419)) % 0.34/0.56 (step-pop @p421 :rule scope :premises (@p420)) % 0.34/0.56 (step @p326 :rule process_scope :premises (@p421) :args (false)) % 0.34/0.56 (assume-push @p422 @t98) % 0.34/0.56 (assume-push @p423 @t119) % 0.34/0.56 (assume-push @p424 @t112) % 0.34/0.56 (step @p333 :rule and_intro :premises (@p422 @p424 @p423)) % 0.34/0.56 (step-pop @p425 :rule scope :premises (@p333)) % 0.34/0.56 (step-pop @p426 :rule scope :premises (@p425)) % 0.34/0.56 (step-pop @p427 :rule scope :premises (@p426)) % 0.34/0.56 (step @p334 :rule process_scope :premises (@p427) :args (@t120)) % 0.34/0.56 (step @p338 :rule implies_elim :premises (@p334)) % 0.34/0.56 (step @p339 :rule resolution :premises (@p338 @p326) :args (true @t120)) % 0.34/0.56 (step @p340 :rule not_and :premises (@p339)) % 0.34/0.56 (step @p341 :rule eq_resolve :premises (@p340 @p315)) % 0.34/0.56 (step @p342 :rule chain_m_resolution :premises (@p341 @p311 @p297 @p270 @p268 @p267 @p227 @p203 @p189 @p153 @p118 @p116 @p107 @p76 @p64 @p52 @p45) :args (@t31 (@list false true false true true true false true false true true true true false false true) (@list @t112 @t117 @t98 @t99 @t93 @t87 @t83 @t90 @t62 @t57 @t53 @t47 @t49 @t39 @t30 @t34))) % 0.34/0.56 (step @p343 :rule cnf_equiv_neg1 :args (@t34)) % 0.34/0.56 (step @p344 :rule reordering :premises (@p343) :args ((or @t33 @t32 @t34))) % 0.34/0.56 (step @p345 :rule chain_m_resolution :premises (@p344 @p342 @p45) :args (@t32 (@list false true) (@list @t31 @t34))) % 0.34/0.56 (step @p346 :rule refl :args (@t124)) % 0.34/0.56 (step @p347 :rule nary_cong :premises (@p46 @p346) :args ((or @t35 @t124))) % 0.34/0.56 (step @p348 :rule cong :premises (@p126) :args (@t125)) % 0.34/0.56 (step @p349 :rule cong :premises (@p132) :args (@t126)) % 0.34/0.56 (step @p350 :rule cong :premises (@p349 @p348) :args (@t127)) % 0.34/0.56 (step @p351 :rule refl :args (@t32)) % 0.34/0.56 (step @p352 :rule cong :premises (@p351 @p350) :args ((=> @t32 @t127))) % 0.34/0.56 (step @p353 :rule bool-double-not-elim :args (@t127)) % 0.34/0.56 (step @p354 :rule cong :premises (@p351 @p353) :args ((=> @t32 @t128))) % 0.34/0.56 (step @p355 :rule trans :premises (@p354 @p352)) % 0.34/0.56 (assume-push @p428 @t32) % 0.34/0.56 (step @p357 :rule skolemize :premises (@p428)) % 0.34/0.56 (step-pop @p429 :rule scope :premises (@p357)) % 0.34/0.56 (step @p358 :rule process_scope :premises (@p429) :args (@t128)) % 0.34/0.56 (step @p360 :rule eq_resolve :premises (@p358 @p355)) % 0.34/0.56 (step @p361 :rule implies_elim :premises (@p360)) % 0.34/0.56 (step @p362 :rule eq_resolve :premises (@p361 @p347)) % 0.34/0.56 (step @p363 :rule chain_m_resolution :premises (@p362 @p345) :args (@t124 (@list true) (@list @t30))) % 0.34/0.56 (assume-push @p430 @t31) % 0.34/0.56 (step @p365 :rule instantiate :premises (@p430) :args ((@list @t123 @t122))) % 0.34/0.56 (step-pop @p431 :rule scope :premises (@p365)) % 0.34/0.56 (step @p366 :rule process_scope :premises (@p431) :args ((not @t124))) % 0.34/0.56 (step @p368 :rule implies_elim :premises (@p366)) % 0.34/0.56 (step @p369 false :rule chain_m_resolution :premises (@p368 @p363 @p342) :args (false (@list false false) (@list @t124 @t31))) % 0.34/0.56 ) % 0.34/0.56 % SZS output end Proof % 0.34/0.56 % cvc5 exiting %------------------------------------------------------------------------------