%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET632^5 : 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 : n006.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 08:48:19 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET632^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 16:05:19 EDT 2026 % 0.16/0.35 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort tptp.a 0) % 0.37/0.56 (define @t1 () (@var "Xx" tptp.a)) % 0.37/0.56 (define @t2 () (@list @t1)) % 0.37/0.56 (define @t3 () (lambda @t2 false)) % 0.37/0.56 (define @t4 () (@var "X" (-> tptp.a Bool))) % 0.37/0.56 (define @t5 () (= @t4 @t3)) % 0.37/0.56 (define @t6 () (@var "Z" (-> tptp.a Bool))) % 0.37/0.56 (define @t7 () (_ @t6 @t1)) % 0.37/0.56 (define @t8 () (@var "Y" (-> tptp.a Bool))) % 0.37/0.56 (define @t9 () (_ @t8 @t1)) % 0.37/0.56 (define @t10 () (and @t9 @t7)) % 0.37/0.56 (define @t11 () (exists @t2 @t10)) % 0.37/0.56 (define @t12 () (not @t11)) % 0.37/0.56 (define @t13 () (_ @t4 @t1)) % 0.37/0.56 (define @t14 () (forall @t2 (=> @t13 @t7))) % 0.37/0.56 (define @t15 () (forall @t2 (=> @t13 @t9))) % 0.37/0.56 (define @t16 () (and @t15 @t14 @t12)) % 0.37/0.56 (define @t17 () (=> @t16 @t5)) % 0.37/0.56 (define @t18 () (@list @t4 @t8 @t6)) % 0.37/0.56 (define @t19 () (forall @t18 @t17)) % 0.37/0.56 (define @t20 () (not @t19)) % 0.37/0.56 (define @t21 () (@var "BOUND_VARIABLE_7529" tptp.a)) % 0.37/0.56 (define @t22 () (lambda (@list @t21) false)) % 0.37/0.56 (define @t23 () (= @t4 @t22)) % 0.37/0.56 (define @t24 () (_ @t6 @t1)) % 0.37/0.56 (define @t25 () (_ @t8 @t1)) % 0.37/0.56 (define @t26 () (forall @t2 (or (not @t25) (not @t24)))) % 0.37/0.56 (define @t27 () (not @t26)) % 0.37/0.56 (define @t28 () (_ @t4 @t1)) % 0.37/0.56 (define @t29 () (not @t28)) % 0.37/0.56 (define @t30 () (forall @t2 (or @t29 @t24))) % 0.37/0.56 (define @t31 () (not @t30)) % 0.37/0.56 (define @t32 () (forall @t2 (or @t29 @t25))) % 0.37/0.56 (define @t33 () (not @t32)) % 0.37/0.56 (define @t34 () (or @t33 @t31 @t27 @t23)) % 0.37/0.56 (define @t35 () (or @t33 @t31 @t27)) % 0.37/0.56 (define @t36 () (and @t32 @t30 @t26)) % 0.37/0.56 (define @t37 () (not @t7)) % 0.37/0.56 (define @t38 () (not @t9)) % 0.37/0.56 (define @t39 () (or @t38 @t37)) % 0.37/0.56 (define @t40 () (forall @t2 (not @t10))) % 0.37/0.56 (define @t41 () (not @t40)) % 0.37/0.56 (define @t42 () (not @t13)) % 0.37/0.56 (define @t43 () (or @t42 @t7)) % 0.37/0.56 (define @t44 () (or @t42 @t9)) % 0.37/0.56 (define @t45 () (@purify @t22)) % 0.37/0.56 (define @t46 () (forall @t18 @t34)) % 0.37/0.56 (define @t47 () (@quantifiers_skolemize @t46 0)) % 0.37/0.56 (define @t48 () (= @t47 @t45)) % 0.37/0.56 (define @t49 () (@quantifiers_skolemize @t46 2)) % 0.37/0.56 (define @t50 () (_ @t49 @t1)) % 0.37/0.56 (define @t51 () (@quantifiers_skolemize @t46 1)) % 0.37/0.56 (define @t52 () (_ @t51 @t1)) % 0.37/0.56 (define @t53 () (forall @t2 (or (not @t52) (not @t50)))) % 0.37/0.56 (define @t54 () (not @t53)) % 0.37/0.56 (define @t55 () (not (_ @t47 @t1))) % 0.37/0.56 (define @t56 () (forall @t2 (or @t55 @t50))) % 0.37/0.56 (define @t57 () (not @t56)) % 0.37/0.56 (define @t58 () (forall @t2 (or @t55 @t52))) % 0.37/0.56 (define @t59 () (not @t58)) % 0.37/0.56 (define @t60 () (or @t59 @t57 @t54 @t48)) % 0.37/0.56 (define @t61 () (not @t60)) % 0.37/0.56 (define @t62 () (not @t46)) % 0.37/0.56 (define @t63 () (= @t22 @t47)) % 0.37/0.56 (define @t64 () (or @t59 @t57 @t54 @t63)) % 0.37/0.56 (define @t65 () (not @t64)) % 0.37/0.56 (define @t66 () (or @t59 @t57 @t54 (= @t47 @t22))) % 0.37/0.56 (define @t67 () (not @t66)) % 0.37/0.56 (define @t68 () (@list true)) % 0.37/0.56 (define @t69 () (@list @t60)) % 0.37/0.56 (define @t70 () (@const 0 tptp.a)) % 0.37/0.56 (define @t71 () (@list @t70)) % 0.37/0.56 (define @t72 () (_ @t47 @t70)) % 0.37/0.56 (define @t73 () (_ @t22 @t70)) % 0.37/0.56 (define @t74 () (_ @t45 @t70)) % 0.37/0.56 (define @t75 () (= @t72 @t74)) % 0.37/0.56 (define @t76 () (not @t75)) % 0.37/0.56 (define @t77 () (or @t48 @t76)) % 0.37/0.56 (define @t78 () (_ @t49 @t70)) % 0.37/0.56 (define @t79 () (not @t72)) % 0.37/0.56 (define @t80 () (or @t79 @t78)) % 0.37/0.56 (define @t81 () (@list false false)) % 0.37/0.56 (define @t82 () (_ @t51 @t70)) % 0.37/0.56 (define @t83 () (or @t79 @t82)) % 0.37/0.56 (define @t84 () (not @t78)) % 0.37/0.56 (define @t85 () (not @t82)) % 0.37/0.56 (define @t86 () (or @t85 @t84)) % 0.37/0.56 (define @t87 () (not @t86)) % 0.37/0.56 (assume @p1 @t20) % 0.37/0.56 (assume @p2 true) % 0.37/0.56 (step @p3 :rule aci_norm :args ((= (or @t35 @t23) @t34))) % 0.37/0.56 (step @p4 :rule refl :args (@t23)) % 0.37/0.56 (step @p5 :rule aci_norm :args ((= (or @t33 (or @t31 @t27)) @t35))) % 0.37/0.56 (step @p6 :rule bool-and-de-morgan :args (@t30 @t26 true)) % 0.37/0.56 (step @p7 :rule refl :args (@t33)) % 0.37/0.56 (step @p8 :rule nary_cong :premises (@p7 @p6) :args ((or @t33 (not (and @t30 @t26))))) % 0.37/0.56 (step @p9 :rule bool-and-de-morgan :args (@t32 @t30 (and @t26))) % 0.37/0.56 (step @p10 :rule trans :premises (@p9 @p8)) % 0.37/0.56 (step @p11 :rule trans :premises (@p10 @p5)) % 0.37/0.56 (step @p12 :rule nary_cong :premises (@p11 @p4) :args ((or (not @t36) @t23))) % 0.37/0.56 (step @p13 :rule trans :premises (@p12 @p3)) % 0.37/0.56 (step @p14 :rule bool-impl-elim :args (@t36 @t23)) % 0.37/0.56 (step @p15 :rule trans :premises (@p14 @p13)) % 0.37/0.56 (step @p16 :rule cong :premises (@p15) :args ((forall @t18 (=> @t36 @t23)))) % 0.37/0.56 (step @p17 :rule refl :args (@t22)) % 0.37/0.56 (step @p18 :rule symm :premises (@p17)) % 0.37/0.56 (step @p19 :rule alpha_equiv :args (@t3 (@list @t1) (@list @t21))) % 0.37/0.56 (step @p20 :rule trans :premises (@p19 @p18)) % 0.37/0.56 (step @p21 :rule refl :args (@t4)) % 0.37/0.56 (step @p22 :rule cong :premises (@p21 @p20) :args (@t5)) % 0.37/0.56 (step @p23 :rule bool-double-not-elim :args (@t26)) % 0.37/0.56 (step @p24 :rule refl :args (@t24)) % 0.37/0.56 (step @p25 :rule refl :args (@t7)) % 0.37/0.56 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t7 @t24))) % 0.37/0.56 (step @p27 :rule symm :premises (@p26)) % 0.37/0.56 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.37/0.56 (step @p29 :rule cong :premises (@p28) :args (@t37)) % 0.37/0.56 (step @p30 :rule refl :args (@t25)) % 0.37/0.56 (step @p31 :rule refl :args (@t9)) % 0.37/0.56 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t9 @t25))) % 0.37/0.56 (step @p33 :rule symm :premises (@p32)) % 0.37/0.56 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.37/0.56 (step @p35 :rule cong :premises (@p34) :args (@t38)) % 0.37/0.56 (step @p36 :rule nary_cong :premises (@p35 @p29) :args (@t39)) % 0.37/0.56 (step @p37 :rule cong :premises (@p36) :args ((forall @t2 @t39))) % 0.37/0.56 (step @p38 :rule bool-and-de-morgan :args (@t9 @t7 true)) % 0.37/0.56 (step @p39 :rule cong :premises (@p38) :args (@t40)) % 0.37/0.56 (step @p40 :rule trans :premises (@p39 @p37)) % 0.37/0.56 (step @p41 :rule cong :premises (@p40) :args (@t41)) % 0.37/0.56 (step @p42 :rule exists-elim :args ((= @t11 @t41))) % 0.37/0.56 (step @p43 :rule trans :premises (@p42 @p41)) % 0.37/0.56 (step @p44 :rule cong :premises (@p43) :args (@t12)) % 0.37/0.56 (step @p45 :rule trans :premises (@p44 @p23)) % 0.37/0.56 (step @p46 :rule refl :args (@t28)) % 0.37/0.56 (step @p47 :rule refl :args (@t13)) % 0.37/0.56 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t13 @t28))) % 0.37/0.56 (step @p49 :rule symm :premises (@p48)) % 0.37/0.56 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.37/0.56 (step @p51 :rule cong :premises (@p50) :args (@t42)) % 0.37/0.56 (step @p52 :rule nary_cong :premises (@p51 @p28) :args (@t43)) % 0.37/0.56 (step @p53 :rule cong :premises (@p52) :args ((forall @t2 @t43))) % 0.37/0.56 (step @p54 :rule bool-impl-elim :args (@t13 @t7)) % 0.37/0.56 (step @p55 :rule cong :premises (@p54) :args (@t14)) % 0.37/0.56 (step @p56 :rule trans :premises (@p55 @p53)) % 0.37/0.56 (step @p57 :rule nary_cong :premises (@p51 @p34) :args (@t44)) % 0.37/0.56 (step @p58 :rule cong :premises (@p57) :args ((forall @t2 @t44))) % 0.37/0.56 (step @p59 :rule bool-impl-elim :args (@t13 @t9)) % 0.37/0.56 (step @p60 :rule cong :premises (@p59) :args (@t15)) % 0.37/0.56 (step @p61 :rule trans :premises (@p60 @p58)) % 0.37/0.56 (step @p62 :rule nary_cong :premises (@p61 @p56 @p45) :args (@t16)) % 0.37/0.56 (step @p63 :rule cong :premises (@p62 @p22) :args (@t17)) % 0.37/0.56 (step @p64 :rule cong :premises (@p63) :args (@t19)) % 0.37/0.56 (step @p65 :rule trans :premises (@p64 @p16)) % 0.37/0.56 (step @p66 :rule cong :premises (@p65) :args (@t20)) % 0.37/0.56 (step @p67 :rule eq_resolve :premises (@p1 @p66)) % 0.37/0.56 (step @p68 :rule refl :args (@t61)) % 0.37/0.56 (step @p69 :rule bool-double-not-elim :args (@t46)) % 0.37/0.56 (step @p70 :rule nary_cong :premises (@p69 @p68) :args ((or (not @t62) @t61))) % 0.37/0.56 (step @p71 :rule eq-symm :args (@t45 @t47)) % 0.37/0.56 (step @p72 :rule refl :args (@t47)) % 0.37/0.56 (step @p73 :rule eq-refl :args (@t22)) % 0.37/0.56 (step @p74 :rule refl :args (@t22)) % 0.37/0.56 (step @p75 :rule cong :premises (@p74 @p18) :args ((= @t22 @t22))) % 0.37/0.56 (step @p76 :rule trans :premises (@p75 @p73)) % 0.37/0.56 (step @p77 :rule skolem_intro :args (@t45)) % 0.37/0.56 (step @p78 :rule cong :premises (@p74 @p77) :args ((= @t22 @t45))) % 0.37/0.56 (step @p79 :rule trans :premises (@p78 @p76)) % 0.37/0.56 (step @p80 :rule true_elim :premises (@p79)) % 0.37/0.56 (step @p81 :rule cong :premises (@p80 @p72) :args (@t63)) % 0.37/0.56 (step @p82 :rule trans :premises (@p81 @p71)) % 0.37/0.56 (step @p83 :rule refl :args (@t54)) % 0.37/0.56 (step @p84 :rule refl :args (@t57)) % 0.37/0.56 (step @p85 :rule refl :args (@t59)) % 0.37/0.56 (step @p86 :rule nary_cong :premises (@p85 @p84 @p83 @p82) :args (@t64)) % 0.37/0.56 (step @p87 :rule cong :premises (@p86) :args (@t65)) % 0.37/0.56 (step @p88 :rule refl :args (@t62)) % 0.37/0.56 (step @p89 :rule cong :premises (@p88 @p87) :args ((=> @t62 @t65))) % 0.37/0.56 (step @p90 :rule eq-symm :args (@t47 @t22)) % 0.37/0.56 (step @p91 :rule nary_cong :premises (@p85 @p84 @p83 @p90) :args (@t66)) % 0.37/0.56 (step @p92 :rule cong :premises (@p91) :args (@t67)) % 0.37/0.56 (step @p93 :rule cong :premises (@p88 @p92) :args ((=> @t62 @t67))) % 0.37/0.56 (step @p94 :rule trans :premises (@p93 @p89)) % 0.37/0.56 (assume-push @p163 @t62) % 0.37/0.56 (step @p96 :rule skolemize :premises (@p67)) % 0.37/0.56 (step-pop @p164 :rule scope :premises (@p96)) % 0.37/0.56 (step @p97 :rule process_scope :premises (@p164) :args (@t67)) % 0.37/0.56 (step @p99 :rule eq_resolve :premises (@p97 @p94)) % 0.37/0.56 (step @p100 :rule implies_elim :premises (@p99)) % 0.37/0.56 (step @p101 :rule eq_resolve :premises (@p100 @p70)) % 0.37/0.56 (step @p102 :rule chain_m_resolution :premises (@p101 @p67) :args (@t61 @t68 (@list @t46))) % 0.37/0.56 (step @p103 :rule bool-double-not-elim :args (@t53)) % 0.37/0.56 (step @p104 :rule refl :args (@t60)) % 0.37/0.56 (step @p105 :rule nary_cong :premises (@p104 @p103) :args ((or @t60 (not @t54)))) % 0.37/0.56 (step @p106 :rule cnf_or_neg :args (@t60 2)) % 0.37/0.56 (step @p107 :rule eq_resolve :premises (@p106 @p105)) % 0.37/0.56 (step @p108 :rule reordering :premises (@p107) :args ((or @t53 @t60))) % 0.37/0.56 (step @p109 :rule chain_m_resolution :premises (@p108 @p102) :args (@t53 @t68 @t69)) % 0.37/0.56 (step @p110 :rule bool-double-not-elim :args (@t56)) % 0.37/0.56 (step @p111 :rule nary_cong :premises (@p104 @p110) :args ((or @t60 (not @t57)))) % 0.37/0.56 (step @p112 :rule cnf_or_neg :args (@t60 1)) % 0.37/0.56 (step @p113 :rule eq_resolve :premises (@p112 @p111)) % 0.37/0.56 (step @p114 :rule reordering :premises (@p113) :args ((or @t56 @t60))) % 0.37/0.56 (step @p115 :rule chain_m_resolution :premises (@p114 @p102) :args (@t56 @t68 @t69)) % 0.37/0.56 (step @p116 :rule instantiate :premises (@p115) :args (@t71)) % 0.37/0.56 (step @p117 :rule cnf_or_neg :args (@t60 3)) % 0.37/0.56 (step @p118 :rule chain_m_resolution :premises (@p117 @p102) :args ((not @t48) @t68 @t69)) % 0.37/0.56 (step @p119 :rule bool-double-not-elim :args (@t72)) % 0.37/0.56 (step @p120 :rule bool-eq-false :args (@t72)) % 0.37/0.56 (step @p121 :rule evaluate :args ((not false))) % 0.37/0.56 (step @p122 :rule beta-reduce :args ((= @t73 false))) % 0.37/0.56 (step @p123 :rule cong :premises (@p122) :args ((not @t73))) % 0.37/0.56 (step @p124 :rule trans :premises (@p123 @p121)) % 0.37/0.56 (step @p125 :rule refl :args (@t70)) % 0.37/0.56 (step @p126 :rule ho_cong :premises (@p77 @p125)) % 0.37/0.56 (step @p127 :rule cong :premises (@p126) :args ((not @t74))) % 0.37/0.56 (step @p128 :rule bool-eq-false :args (@t74)) % 0.37/0.56 (step @p129 :rule trans :premises (@p128 @p127 @p124)) % 0.37/0.56 (step @p130 :rule true_elim :premises (@p129)) % 0.37/0.56 (step @p131 :rule refl :args (@t72)) % 0.37/0.56 (step @p132 :rule cong :premises (@p131 @p130) :args (@t75)) % 0.37/0.56 (step @p133 :rule trans :premises (@p132 @p120)) % 0.37/0.56 (step @p134 :rule cong :premises (@p133) :args (@t76)) % 0.37/0.56 (step @p135 :rule trans :premises (@p134 @p119)) % 0.37/0.56 (step @p136 :rule refl :args (@t48)) % 0.37/0.56 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t77)) % 0.37/0.56 ; WARNING: add trust step for TRUST % 0.37/0.56 ; trust TRUST THEORY_LEMMA % 0.37/0.56 (step @p138 :rule trust :premises () :args (@t77)) % 0.37/0.56 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.37/0.56 (step @p140 :rule chain_m_resolution :premises (@p139 @p118) :args (@t72 @t68 (@list @t48))) % 0.37/0.56 (step @p141 :rule cnf_or_pos :args (@t80)) % 0.37/0.56 (step @p142 :rule reordering :premises (@p141) :args ((or @t79 @t78 (not @t80)))) % 0.37/0.56 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p116) :args (@t78 @t81 (@list @t72 @t80))) % 0.37/0.56 (step @p144 :rule bool-double-not-elim :args (@t58)) % 0.37/0.56 (step @p145 :rule nary_cong :premises (@p104 @p144) :args ((or @t60 (not @t59)))) % 0.37/0.56 (step @p146 :rule cnf_or_neg :args (@t60 0)) % 0.37/0.56 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 0.37/0.56 (step @p148 :rule reordering :premises (@p147) :args ((or @t58 @t60))) % 0.37/0.56 (step @p149 :rule chain_m_resolution :premises (@p148 @p102) :args (@t58 @t68 @t69)) % 0.37/0.57 (step @p150 :rule instantiate :premises (@p149) :args (@t71)) % 0.37/0.57 (step @p151 :rule cnf_or_pos :args (@t83)) % 0.37/0.57 (step @p152 :rule reordering :premises (@p151) :args ((or @t79 @t82 (not @t83)))) % 0.37/0.57 (step @p153 :rule chain_m_resolution :premises (@p152 @p140 @p150) :args (@t82 @t81 (@list @t72 @t83))) % 0.37/0.57 (step @p154 :rule cnf_or_pos :args (@t86)) % 0.37/0.57 (step @p155 :rule reordering :premises (@p154) :args ((or @t85 @t84 @t87))) % 0.37/0.57 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p143) :args (@t87 @t81 (@list @t82 @t78))) % 0.37/0.57 (assume-push @p165 @t53) % 0.37/0.57 (step @p158 :rule instantiate :premises (@p109) :args (@t71)) % 0.37/0.57 (step-pop @p166 :rule scope :premises (@p158)) % 0.37/0.57 (step @p159 :rule process_scope :premises (@p166) :args (@t86)) % 0.37/0.57 (step @p161 :rule implies_elim :premises (@p159)) % 0.37/0.57 (step @p162 false :rule chain_m_resolution :premises (@p161 @p156 @p109) :args (false (@list true false) (@list @t86 @t53))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------