%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO548^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n020.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 09:13:06 AM UTC 2026 % Result : Theorem 0.96s 1.13s % Output : Proof 0.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO548^1 : TPTP v9.2.1. Released v5.2.0. % 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 : n020.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 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 00:20:40 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.96/1.13 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.96/1.13 % SZS status Theorem % 0.96/1.13 % SZS output start Proof % 0.96/1.13 ( % 0.96/1.13 (declare-sort $$unsorted 0) % 0.96/1.13 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 0.96/1.13 (define @t2 () (@var "E" (-> (-> $$unsorted Bool) $$unsorted))) % 0.96/1.13 (define @t3 () (_ @t2 @t1)) % 0.96/1.13 (define @t4 () (_ @t1 @t3)) % 0.96/1.13 (define @t5 () (not @t4)) % 0.96/1.13 (define @t6 () (@var "X" $$unsorted)) % 0.96/1.13 (define @t7 () (_ @t1 @t6)) % 0.96/1.13 (define @t8 () (not @t7)) % 0.96/1.13 (define @t9 () (@list @t6)) % 0.96/1.13 (define @t10 () (exists @t9 @t8)) % 0.96/1.13 (define @t11 () (=> @t10 @t5)) % 0.96/1.13 (define @t12 () (@list @t1)) % 0.96/1.13 (define @t13 () (forall @t12 @t11)) % 0.96/1.13 (define @t14 () (@list @t2)) % 0.96/1.13 (define @t15 () (exists @t14 @t13)) % 0.96/1.13 (define @t16 () (not @t15)) % 0.96/1.13 (define @t17 () (_ @t2 @t1)) % 0.96/1.13 (define @t18 () (_ @t1 @t17)) % 0.96/1.13 (define @t19 () (not @t18)) % 0.96/1.13 (define @t20 () (@var "BOUND_VARIABLE_7441" $$unsorted)) % 0.96/1.13 (define @t21 () (_ @t1 @t20)) % 0.96/1.13 (define @t22 () (or @t21 @t19)) % 0.96/1.13 (define @t23 () (@list @t1 @t20)) % 0.96/1.13 (define @t24 () (forall @t23 @t22)) % 0.96/1.13 (define @t25 () (forall @t14 (not @t24))) % 0.96/1.13 (define @t26 () (@list @t20)) % 0.96/1.13 (define @t27 () (forall @t26 @t22)) % 0.96/1.13 (define @t28 () (forall @t26 @t21)) % 0.96/1.13 (define @t29 () (or @t28 @t19)) % 0.96/1.13 (define @t30 () (_ @t1 @t6)) % 0.96/1.13 (define @t31 () (forall @t9 @t30)) % 0.96/1.13 (define @t32 () (or @t31 @t5)) % 0.96/1.13 (define @t33 () (not @t31)) % 0.96/1.13 (define @t34 () (forall @t9 (not @t8))) % 0.96/1.13 (define @t35 () (not @t34)) % 0.96/1.13 (define @t36 () (@const 0 (-> (-> $$unsorted Bool) $$unsorted))) % 0.96/1.13 (define @t37 () (_ @t36 @t1)) % 0.96/1.13 (define @t38 () (@var "BOUND_VARIABLE_21498" (-> $$unsorted Bool))) % 0.96/1.13 (define @t39 () (_ @t36 @t38)) % 0.96/1.13 (define @t40 () (@list @t38)) % 0.96/1.13 (define @t41 () (lambda @t40 @t39)) % 0.96/1.13 (define @t42 () (_ @t41 @t1)) % 0.96/1.13 (define @t43 () (_ @t1 @t42)) % 0.96/1.13 (define @t44 () (not @t43)) % 0.96/1.13 (define @t45 () (or @t21 @t44)) % 0.96/1.13 (define @t46 () (forall @t23 @t45)) % 0.96/1.13 (define @t47 () (not @t46)) % 0.96/1.13 (define @t48 () (forall @t23 (or @t21 (not (_ @t1 @t37))))) % 0.96/1.13 (define @t49 () (@quantifiers_skolemize @t48 0)) % 0.96/1.13 (define @t50 () (_ @t49 (_ @t36 @t49))) % 0.96/1.13 (define @t51 () (not @t50)) % 0.96/1.13 (define @t52 () (@quantifiers_skolemize @t48 1)) % 0.96/1.13 (define @t53 () (_ @t49 @t52)) % 0.96/1.13 (define @t54 () (or @t53 @t51)) % 0.96/1.13 (define @t55 () (@list true)) % 0.96/1.13 (define @t56 () (@list @t54)) % 0.96/1.13 (define @t57 () (_ @t38 @t39)) % 0.96/1.13 (define @t58 () (= @t57 true)) % 0.96/1.13 (define @t59 () (not @t58)) % 0.96/1.13 (define @t60 () (@var "BOUND_VARIABLE_64251" Bool)) % 0.96/1.13 (define @t61 () (lambda (@list @t60) (ite (= @t60 true) false true))) % 0.96/1.13 (define @t62 () (_ @t61 @t57)) % 0.96/1.13 (define @t63 () (@var "x" $$unsorted)) % 0.96/1.13 (define @t64 () (_ @t38 @t63)) % 0.96/1.13 (define @t65 () (= @t64 true)) % 0.96/1.13 (define @t66 () (not @t65)) % 0.96/1.13 (define @t67 () (_ @t61 @t64)) % 0.96/1.13 (define @t68 () (not @t67)) % 0.96/1.13 (define @t69 () (@list @t63)) % 0.96/1.13 (define @t70 () (forall @t69 @t68)) % 0.96/1.13 (define @t71 () (or @t70 @t62)) % 0.96/1.13 (define @t72 () (forall @t40 @t71)) % 0.96/1.13 (define @t73 () (forall @t69 (_ @t49 @t63))) % 0.96/1.13 (define @t74 () (or @t73 @t51)) % 0.96/1.13 (assume @p1 @t16) % 0.96/1.13 (assume @p2 true) % 0.96/1.13 (step @p3 :rule bool-double-not-elim :args (@t25)) % 0.96/1.13 (step @p4 :rule exists-elim :args ((= (exists @t14 @t24) (not @t25)))) % 0.96/1.13 (step @p5 :rule quant-merge-prenex :args ((= (forall @t12 @t27) @t24))) % 0.96/1.13 (step @p6 :rule refl :args (@t19)) % 0.96/1.13 (step @p7 :rule alpha_equiv :args (@t28 (@list @t20) (@list @t6))) % 0.96/1.13 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t29)) % 0.96/1.13 (step @p9 :rule quant-miniscope-or :args ((= @t27 @t29))) % 0.96/1.13 (step @p10 :rule trans :premises (@p9 @p8)) % 0.96/1.13 (step @p11 :rule symm :premises (@p10)) % 0.96/1.13 (step @p12 :rule cong :premises (@p11) :args ((forall @t12 (or @t31 @t19)))) % 0.96/1.13 (step @p13 :rule trans :premises (@p12 @p5)) % 0.96/1.13 (step @p14 :rule refl :args ((_ @t1 @t3))) % 0.96/1.13 (step @p15 :rule refl :args (@t17)) % 0.96/1.13 (step @p16 :rule cong :premises (@p15) :args (@t18)) % 0.96/1.13 (step @p17 :rule trans :premises (@p16 @p14)) % 0.96/1.13 (step @p18 :rule refl :args (@t1)) % 0.96/1.13 (step @p19 :rule ho_cong :premises (@p18 @p15)) % 0.96/1.13 (step @p20 :rule cong :premises (@p19 @p17) :args ((= (_ @t1 @t17) @t18))) % 0.96/1.13 (step @p21 :rule symm :premises (@p20)) % 0.96/1.13 (step @p22 :rule refl :args (@t4)) % 0.96/1.13 (step @p23 :rule eq_resolve :premises (@p22 @p21)) % 0.96/1.13 (step @p24 :rule refl :args (@t3)) % 0.96/1.13 (step @p25 :rule cong :premises (@p24 @p15) :args ((= @t3 @t17))) % 0.96/1.13 (step @p26 :rule symm :premises (@p25)) % 0.96/1.13 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.96/1.13 (step @p28 :rule ho_cong :premises (@p18 @p27)) % 0.96/1.13 (step @p29 :rule trans :premises (@p28 @p23)) % 0.96/1.13 (step @p30 :rule cong :premises (@p29) :args (@t5)) % 0.96/1.13 (step @p31 :rule refl :args (@t31)) % 0.96/1.13 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t32)) % 0.96/1.13 (step @p33 :rule cong :premises (@p32) :args ((forall @t12 @t32))) % 0.96/1.13 (step @p34 :rule trans :premises (@p33 @p13)) % 0.96/1.13 (step @p35 :rule refl :args (@t5)) % 0.96/1.13 (step @p36 :rule bool-double-not-elim :args (@t31)) % 0.96/1.13 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t33) @t5))) % 0.96/1.13 (step @p38 :rule bool-impl-elim :args (@t33 @t5)) % 0.96/1.13 (step @p39 :rule trans :premises (@p38 @p37)) % 0.96/1.13 (step @p40 :rule cong :premises (@p39) :args ((forall @t12 (=> @t33 @t5)))) % 0.96/1.13 (step @p41 :rule trans :premises (@p40 @p34)) % 0.96/1.13 (step @p42 :rule refl :args (@t5)) % 0.96/1.13 (step @p43 :rule refl :args (@t30)) % 0.96/1.13 (step @p44 :rule refl :args (@t7)) % 0.96/1.13 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t7 @t30))) % 0.96/1.13 (step @p46 :rule symm :premises (@p45)) % 0.96/1.13 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.96/1.13 (step @p48 :rule cong :premises (@p47) :args ((forall @t9 @t7))) % 0.96/1.13 (step @p49 :rule bool-double-not-elim :args (@t7)) % 0.96/1.13 (step @p50 :rule cong :premises (@p49) :args (@t34)) % 0.96/1.13 (step @p51 :rule trans :premises (@p50 @p48)) % 0.96/1.13 (step @p52 :rule cong :premises (@p51) :args (@t35)) % 0.96/1.13 (step @p53 :rule exists-elim :args ((= @t10 @t35))) % 0.96/1.13 (step @p54 :rule trans :premises (@p53 @p52)) % 0.96/1.13 (step @p55 :rule cong :premises (@p54 @p42) :args (@t11)) % 0.96/1.13 (step @p56 :rule cong :premises (@p55) :args (@t13)) % 0.96/1.13 (step @p57 :rule trans :premises (@p56 @p41)) % 0.96/1.13 (step @p58 :rule cong :premises (@p57) :args (@t15)) % 0.96/1.13 (step @p59 :rule trans :premises (@p58 @p4)) % 0.96/1.13 (step @p60 :rule cong :premises (@p59) :args (@t16)) % 0.96/1.13 (step @p61 :rule trans :premises (@p60 @p3)) % 0.96/1.13 (step @p62 :rule eq_resolve :premises (@p1 @p61)) % 0.96/1.13 (step @p63 :rule beta-reduce :args ((= @t42 @t37))) % 0.96/1.13 (step @p64 :rule cong :premises (@p63) :args (@t43)) % 0.96/1.13 (step @p65 :rule cong :premises (@p64) :args (@t44)) % 0.96/1.13 (step @p66 :rule refl :args (@t21)) % 0.96/1.13 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t45)) % 0.96/1.13 (step @p68 :rule cong :premises (@p67) :args (@t46)) % 0.96/1.13 (step @p69 :rule cong :premises (@p68) :args (@t47)) % 0.96/1.13 (step @p70 :rule refl :args (@t25)) % 0.96/1.13 (step @p71 :rule cong :premises (@p70 @p69) :args ((=> @t25 @t47))) % 0.96/1.13 (assume-push @p124 @t25) % 0.96/1.13 (step @p73 :rule instantiate :premises (@p62) :args ((@list @t41))) % 0.96/1.13 (step-pop @p125 :rule scope :premises (@p73)) % 0.96/1.13 (step @p74 :rule process_scope :premises (@p125) :args (@t47)) % 0.96/1.13 (step @p76 :rule eq_resolve :premises (@p74 @p71)) % 0.96/1.13 (step @p77 :rule implies_elim :premises (@p76)) % 0.96/1.13 (step @p78 :rule chain_m_resolution :premises (@p77 @p62) :args ((not @t48) (@list false) (@list @t25))) % 0.96/1.13 (step @p79 :rule skolemize :premises (@p78)) % 0.96/1.13 (step @p80 :rule cnf_or_neg :args (@t54 0)) % 0.96/1.13 (step @p81 :rule chain_m_resolution :premises (@p80 @p79) :args ((not @t53) @t55 @t56)) % 0.96/1.13 (step @p82 :rule bool-eq-true :args (@t57)) % 0.96/1.13 (step @p83 :rule cong :premises (@p82) :args (@t59)) % 0.96/1.13 (step @p84 :rule aci_norm :args ((= (and @t59 true) @t59))) % 0.96/1.13 (step @p85 :rule ite-then-false :args (@t58 true)) % 0.96/1.13 (step @p86 :rule trans :premises (@p85 @p84)) % 0.96/1.13 (step @p87 :rule trans :premises (@p86 @p83)) % 0.96/1.13 (step @p88 :rule beta-reduce :args ((= @t62 (ite @t58 false true)))) % 0.96/1.13 (step @p89 :rule trans :premises (@p88 @p87)) % 0.96/1.13 (step @p90 :rule bool-double-not-elim :args (@t64)) % 0.96/1.13 (step @p91 :rule bool-eq-true :args (@t64)) % 0.96/1.13 (step @p92 :rule cong :premises (@p91) :args (@t66)) % 0.96/1.13 (step @p93 :rule aci_norm :args ((= (and @t66 true) @t66))) % 0.96/1.13 (step @p94 :rule ite-then-false :args (@t65 true)) % 0.96/1.13 (step @p95 :rule trans :premises (@p94 @p93)) % 0.96/1.13 (step @p96 :rule trans :premises (@p95 @p92)) % 0.96/1.13 (step @p97 :rule beta-reduce :args ((= @t67 (ite @t65 false true)))) % 0.96/1.13 (step @p98 :rule trans :premises (@p97 @p96)) % 0.96/1.13 (step @p99 :rule cong :premises (@p98) :args (@t68)) % 0.96/1.13 (step @p100 :rule trans :premises (@p99 @p90)) % 0.96/1.13 (step @p101 :rule cong :premises (@p100) :args (@t70)) % 0.96/1.13 (step @p102 :rule nary_cong :premises (@p101 @p89) :args (@t71)) % 0.96/1.13 (step @p103 :rule cong :premises (@p102) :args (@t72)) % 0.96/1.13 ; WARNING: add trust step for TRUST % 0.96/1.13 ; trust TRUST THEORY_LEMMA % 0.96/1.13 (step @p104 :rule trust :premises () :args (@t72)) % 0.96/1.13 (step @p105 :rule eq_resolve :premises (@p104 @p103)) % 0.96/1.13 (step @p106 :rule instantiate :premises (@p105) :args ((@list @t49))) % 0.96/1.13 (step @p107 :rule bool-double-not-elim :args (@t50)) % 0.96/1.13 (step @p108 :rule refl :args (@t54)) % 0.96/1.13 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or @t54 (not @t51)))) % 0.96/1.13 (step @p110 :rule cnf_or_neg :args (@t54 1)) % 0.96/1.13 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.96/1.13 (step @p112 :rule reordering :premises (@p111) :args ((or @t50 @t54))) % 0.96/1.13 (step @p113 :rule chain_m_resolution :premises (@p112 @p79) :args (@t50 @t55 @t56)) % 0.96/1.13 (step @p114 :rule cnf_or_pos :args (@t74)) % 0.96/1.13 (step @p115 :rule reordering :premises (@p114) :args ((or @t51 @t73 (not @t74)))) % 0.96/1.13 (step @p116 :rule chain_m_resolution :premises (@p115 @p113 @p106) :args (@t73 (@list false false) (@list @t50 @t74))) % 0.96/1.13 (assume-push @p126 @t73) % 0.96/1.13 (step @p118 :rule instantiate :premises (@p116) :args ((@list @t52))) % 0.96/1.13 (step-pop @p127 :rule scope :premises (@p118)) % 0.96/1.13 (step @p119 :rule process_scope :premises (@p127) :args (@t53)) % 0.96/1.13 (step @p121 :rule implies_elim :premises (@p119)) % 0.96/1.13 (step @p122 :rule reordering :premises (@p121) :args ((or @t53 (not @t73)))) % 0.96/1.13 (step @p123 false :rule chain_m_resolution :premises (@p122 @p116 @p81) :args (false (@list false true) (@list @t73 @t53))) % 0.96/1.13 ) % 0.96/1.13 % SZS output end Proof % 0.96/1.13 % cvc5 exiting %------------------------------------------------------------------------------