%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO266^5 : TPTP v9.2.1. 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:12:20 AM UTC 2026 % Result : Theorem 0.62s 0.82s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO266^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n011.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Wed Jun 3 00:01:20 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.62/0.82 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.82 % SZS status Theorem % 0.62/0.82 % SZS output start Proof % 0.62/0.82 ( % 0.62/0.82 (declare-sort $$unsorted 0) % 0.62/0.82 (declare-const tptp.cP (-> $$unsorted Bool)) % 0.62/0.82 (declare-const tptp.cQ (-> $$unsorted Bool)) % 0.62/0.82 (define @t1 () (@var "Y" $$unsorted)) % 0.62/0.82 (define @t2 () (_ tptp.cQ @t1)) % 0.62/0.82 (define @t3 () (_ tptp.cP @t1)) % 0.62/0.82 (define @t4 () (or @t3 @t2)) % 0.62/0.82 (define @t5 () (@list @t1)) % 0.62/0.82 (define @t6 () (forall @t5 @t4)) % 0.62/0.82 (define @t7 () (@var "X" $$unsorted)) % 0.62/0.82 (define @t8 () (@var "S" (-> $$unsorted Bool))) % 0.62/0.82 (define @t9 () (_ @t8 @t7)) % 0.62/0.82 (define @t10 () (or (not @t9) (_ tptp.cQ @t7))) % 0.62/0.82 (define @t11 () (or @t9 (_ tptp.cP @t7))) % 0.62/0.82 (define @t12 () (@list @t7)) % 0.62/0.82 (define @t13 () (forall @t12 (and @t11 @t10))) % 0.62/0.82 (define @t14 () (@list @t8)) % 0.62/0.82 (define @t15 () (exists @t14 @t13)) % 0.62/0.82 (define @t16 () (= @t15 @t6)) % 0.62/0.82 (define @t17 () (not @t16)) % 0.62/0.82 (define @t18 () (tptp.cQ @t1)) % 0.62/0.82 (define @t19 () (tptp.cP @t1)) % 0.62/0.82 (define @t20 () (forall @t5 (or @t19 @t18))) % 0.62/0.82 (define @t21 () (not @t20)) % 0.62/0.82 (define @t22 () (@var "BOUND_VARIABLE_7437" $$unsorted)) % 0.62/0.82 (define @t23 () (tptp.cQ @t22)) % 0.62/0.82 (define @t24 () (_ @t8 @t22)) % 0.62/0.82 (define @t25 () (@list @t22)) % 0.62/0.82 (define @t26 () (forall @t25 (or (not @t24) @t23))) % 0.62/0.82 (define @t27 () (@var "BOUND_VARIABLE_7430" $$unsorted)) % 0.62/0.82 (define @t28 () (tptp.cP @t27)) % 0.62/0.82 (define @t29 () (_ @t8 @t27)) % 0.62/0.82 (define @t30 () (@list @t27)) % 0.62/0.82 (define @t31 () (forall @t30 (or @t29 @t28))) % 0.62/0.82 (define @t32 () (forall @t14 (or (not @t31) (not @t26)))) % 0.62/0.82 (define @t33 () (not @t32)) % 0.62/0.82 (define @t34 () (not @t33)) % 0.62/0.82 (define @t35 () (and @t31 @t26)) % 0.62/0.82 (define @t36 () (forall @t14 (not @t35))) % 0.62/0.82 (define @t37 () (not @t36)) % 0.62/0.82 (define @t38 () (_ tptp.cQ @t22)) % 0.62/0.82 (define @t39 () (_ @t8 @t22)) % 0.62/0.82 (define @t40 () (not @t39)) % 0.62/0.82 (define @t41 () (or @t40 @t38)) % 0.62/0.82 (define @t42 () (forall @t25 @t41)) % 0.62/0.82 (define @t43 () (_ tptp.cP @t27)) % 0.62/0.82 (define @t44 () (_ @t8 @t27)) % 0.62/0.82 (define @t45 () (or @t44 @t43)) % 0.62/0.82 (define @t46 () (forall @t30 @t45)) % 0.62/0.82 (define @t47 () (forall @t12 @t10)) % 0.62/0.82 (define @t48 () (@list @t7)) % 0.62/0.82 (define @t49 () (forall @t12 @t11)) % 0.62/0.82 (define @t50 () (@list @t27)) % 0.62/0.82 (define @t51 () (and @t49 @t47)) % 0.62/0.82 (define @t52 () (@quantifiers_skolemize @t32 0)) % 0.62/0.82 (define @t53 () (forall @t25 (or (not (_ @t52 @t22)) @t23))) % 0.62/0.82 (define @t54 () (not @t53)) % 0.62/0.82 (define @t55 () (forall @t30 (or (_ @t52 @t27) @t28))) % 0.62/0.82 (define @t56 () (not @t55)) % 0.62/0.82 (define @t57 () (or @t56 @t54)) % 0.62/0.82 (define @t58 () (not @t57)) % 0.62/0.82 (define @t59 () (@quantifiers_skolemize @t20 0)) % 0.62/0.82 (define @t60 () (tptp.cQ @t59)) % 0.62/0.82 (define @t61 () (tptp.cP @t59)) % 0.62/0.82 (define @t62 () (or @t61 @t60)) % 0.62/0.82 (define @t63 () (not @t62)) % 0.62/0.82 (define @t64 () (@list @t59)) % 0.62/0.82 (define @t65 () (_ @t52 @t59)) % 0.62/0.82 (define @t66 () (or @t65 @t61)) % 0.62/0.82 (define @t67 () (not @t65)) % 0.62/0.82 (define @t68 () (or @t67 @t60)) % 0.62/0.82 (define @t69 () (@list false)) % 0.62/0.82 (define @t70 () (tptp.cQ @t27)) % 0.62/0.82 (define @t71 () (or @t28 @t70)) % 0.62/0.82 (define @t72 () (or @t70 @t28)) % 0.62/0.82 (define @t73 () (forall @t30 @t72)) % 0.62/0.82 (define @t74 () (forall @t30 @t71)) % 0.62/0.82 (define @t75 () (not @t73)) % 0.62/0.82 (define @t76 () (@var "BOUND_VARIABLE_36021" $$unsorted)) % 0.62/0.82 (define @t77 () (lambda (@list @t76) (tptp.cQ @t76))) % 0.62/0.82 (define @t78 () (_ @t77 @t22)) % 0.62/0.82 (define @t79 () (not @t78)) % 0.62/0.82 (define @t80 () (or @t79 @t23)) % 0.62/0.82 (define @t81 () (forall @t25 @t80)) % 0.62/0.82 (define @t82 () (not @t81)) % 0.62/0.82 (define @t83 () (_ @t77 @t27)) % 0.62/0.82 (define @t84 () (or @t83 @t28)) % 0.62/0.82 (define @t85 () (forall @t30 @t84)) % 0.62/0.82 (define @t86 () (not @t85)) % 0.62/0.82 (define @t87 () (or @t86 @t82)) % 0.62/0.82 (assume @p1 @t17) % 0.62/0.82 (assume @p2 true) % 0.62/0.82 (step @p3 :rule refl :args (@t21)) % 0.62/0.82 (step @p4 :rule bool-double-not-elim :args (@t32)) % 0.62/0.82 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t34 @t21))) % 0.62/0.82 (step @p6 :rule refl :args (@t18)) % 0.62/0.82 (step @p7 :rule refl :args (@t2)) % 0.62/0.82 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t2 @t18))) % 0.62/0.82 (step @p9 :rule symm :premises (@p8)) % 0.62/0.82 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 0.62/0.82 (step @p11 :rule refl :args (@t19)) % 0.62/0.82 (step @p12 :rule refl :args (@t3)) % 0.62/0.82 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t3 @t19))) % 0.62/0.82 (step @p14 :rule symm :premises (@p13)) % 0.62/0.82 (step @p15 :rule eq_resolve :premises (@p12 @p14)) % 0.62/0.82 (step @p16 :rule nary_cong :premises (@p15 @p10) :args (@t4)) % 0.62/0.82 (step @p17 :rule cong :premises (@p16) :args (@t6)) % 0.62/0.82 (step @p18 :rule bool-and-de-morgan :args (@t31 @t26 true)) % 0.62/0.82 (step @p19 :rule cong :premises (@p18) :args (@t36)) % 0.62/0.82 (step @p20 :rule cong :premises (@p19) :args (@t37)) % 0.62/0.82 (step @p21 :rule exists-elim :args ((= (exists @t14 @t35) @t37))) % 0.62/0.82 (step @p22 :rule trans :premises (@p21 @p20)) % 0.62/0.82 (step @p23 :rule refl :args (@t23)) % 0.62/0.82 (step @p24 :rule refl :args (@t38)) % 0.62/0.82 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t38 @t23))) % 0.62/0.82 (step @p26 :rule symm :premises (@p25)) % 0.62/0.82 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.62/0.82 (step @p28 :rule refl :args (@t24)) % 0.62/0.82 (step @p29 :rule refl :args (@t39)) % 0.62/0.82 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t39 @t24))) % 0.62/0.82 (step @p31 :rule symm :premises (@p30)) % 0.62/0.82 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 0.62/0.82 (step @p33 :rule cong :premises (@p32) :args (@t40)) % 0.62/0.82 (step @p34 :rule nary_cong :premises (@p33 @p27) :args (@t41)) % 0.62/0.82 (step @p35 :rule cong :premises (@p34) :args (@t42)) % 0.62/0.82 (step @p36 :rule refl :args (@t28)) % 0.62/0.82 (step @p37 :rule refl :args (@t43)) % 0.62/0.82 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t43 @t28))) % 0.62/0.82 (step @p39 :rule symm :premises (@p38)) % 0.62/0.82 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.62/0.82 (step @p41 :rule refl :args (@t29)) % 0.62/0.82 (step @p42 :rule refl :args (@t44)) % 0.62/0.82 (step @p43 :rule cong :premises (@p42 @p41) :args ((= @t44 @t29))) % 0.62/0.82 (step @p44 :rule symm :premises (@p43)) % 0.62/0.82 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.62/0.82 (step @p46 :rule nary_cong :premises (@p45 @p40) :args (@t45)) % 0.62/0.82 (step @p47 :rule cong :premises (@p46) :args (@t46)) % 0.62/0.82 (step @p48 :rule nary_cong :premises (@p47 @p35) :args ((and @t46 @t42))) % 0.62/0.82 (step @p49 :rule alpha_equiv :args (@t47 @t48 (@list @t22))) % 0.62/0.82 (step @p50 :rule alpha_equiv :args (@t49 @t48 @t50)) % 0.62/0.82 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t51)) % 0.62/0.82 (step @p52 :rule quant-miniscope-and :args ((= @t13 @t51))) % 0.62/0.82 (step @p53 :rule trans :premises (@p52 @p51)) % 0.62/0.82 (step @p54 :rule trans :premises (@p53 @p48)) % 0.62/0.82 (step @p55 :rule cong :premises (@p54) :args (@t15)) % 0.62/0.82 (step @p56 :rule trans :premises (@p55 @p22)) % 0.62/0.82 (step @p57 :rule cong :premises (@p56 @p17) :args (@t16)) % 0.62/0.82 (step @p58 :rule cong :premises (@p57) :args (@t17)) % 0.62/0.82 (step @p59 :rule eq_resolve :premises (@p1 @p58)) % 0.62/0.82 (step @p60 :rule not_equiv_elim2 :premises (@p59)) % 0.62/0.82 (step @p61 :rule eq_resolve :premises (@p60 @p5)) % 0.62/0.82 (step @p62 :rule refl :args (@t58)) % 0.62/0.82 (step @p63 :rule nary_cong :premises (@p4 @p62) :args ((or @t34 @t58))) % 0.62/0.82 (assume-push @p152 @t33) % 0.62/0.82 (step @p65 :rule skolemize :premises (@p152)) % 0.62/0.82 (step-pop @p153 :rule scope :premises (@p65)) % 0.62/0.82 (step @p66 :rule process_scope :premises (@p153) :args (@t58)) % 0.62/0.82 (step @p68 :rule implies_elim :premises (@p66)) % 0.62/0.82 (step @p69 :rule eq_resolve :premises (@p68 @p63)) % 0.62/0.82 (step @p70 :rule refl :args (@t63)) % 0.62/0.82 (step @p71 :rule bool-double-not-elim :args (@t20)) % 0.62/0.82 (step @p72 :rule nary_cong :premises (@p71 @p70) :args ((or (not @t21) @t63))) % 0.62/0.82 (assume-push @p154 @t21) % 0.62/0.82 (step @p74 :rule skolemize :premises (@p154)) % 0.62/0.82 (step-pop @p155 :rule scope :premises (@p74)) % 0.62/0.82 (step @p75 :rule process_scope :premises (@p155) :args (@t63)) % 0.62/0.82 (step @p77 :rule implies_elim :premises (@p75)) % 0.62/0.82 (step @p78 :rule eq_resolve :premises (@p77 @p72)) % 0.62/0.82 (step @p79 :rule bool-double-not-elim :args (@t55)) % 0.62/0.82 (step @p80 :rule refl :args (@t57)) % 0.62/0.82 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t57 (not @t56)))) % 0.62/0.82 (step @p82 :rule cnf_or_neg :args (@t57 0)) % 0.62/0.82 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.62/0.82 (step @p84 :rule reordering :premises (@p83) :args ((or @t55 @t57))) % 0.62/0.82 (step @p85 :rule bool-double-not-elim :args (@t53)) % 0.62/0.82 (step @p86 :rule nary_cong :premises (@p80 @p85) :args ((or @t57 (not @t54)))) % 0.62/0.82 (step @p87 :rule cnf_or_neg :args (@t57 1)) % 0.62/0.82 (step @p88 :rule eq_resolve :premises (@p87 @p86)) % 0.62/0.82 (step @p89 :rule reordering :premises (@p88) :args ((or @t53 @t57))) % 0.62/0.82 (step @p90 :rule cnf_or_neg :args (@t62 0)) % 0.62/0.82 (step @p91 :rule cnf_or_neg :args (@t62 1)) % 0.62/0.82 (assume-push @p156 @t55) % 0.62/0.82 (step @p93 :rule instantiate :premises (@p156) :args (@t64)) % 0.62/0.82 (step-pop @p157 :rule scope :premises (@p93)) % 0.62/0.82 (step @p94 :rule process_scope :premises (@p157) :args (@t66)) % 0.62/0.82 (step @p96 :rule implies_elim :premises (@p94)) % 0.62/0.82 (assume-push @p158 @t53) % 0.62/0.82 (step @p98 :rule instantiate :premises (@p158) :args (@t64)) % 0.62/0.83 (step-pop @p159 :rule scope :premises (@p98)) % 0.62/0.83 (step @p99 :rule process_scope :premises (@p159) :args (@t68)) % 0.62/0.83 (step @p101 :rule implies_elim :premises (@p99)) % 0.62/0.83 (step @p102 :rule cnf_or_pos :args (@t66)) % 0.62/0.83 (step @p103 :rule reordering :premises (@p102) :args ((or @t61 @t65 (not @t66)))) % 0.62/0.83 (step @p104 :rule cnf_or_pos :args (@t68)) % 0.62/0.83 (step @p105 :rule reordering :premises (@p104) :args ((or @t60 @t67 (not @t68)))) % 0.62/0.83 (step @p106 :rule chain_m_resolution :premises (@p105 @p103 @p101 @p96 @p91 @p90 @p89 @p84 @p78 @p69 @p61) :args (@t32 (@list false false false true true false false true true true) (@list @t65 @t68 @t66 @t60 @t61 @t53 @t55 @t62 @t57 @t20))) % 0.62/0.83 (step @p107 :rule not_equiv_elim1 :premises (@p59)) % 0.62/0.83 (step @p108 :rule chain_m_resolution :premises (@p107 @p106) :args (@t20 @t69 (@list @t32))) % 0.62/0.83 (step @p109 :rule aci_norm :args ((= @t72 @t71))) % 0.62/0.83 (step @p110 :rule cong :premises (@p109) :args (@t73)) % 0.62/0.83 (step @p111 :rule symm :premises (@p110)) % 0.62/0.83 (step @p112 :rule true_intro :premises (@p111)) % 0.62/0.83 (step @p113 :rule eq-symm :args (@t73 @t74)) % 0.62/0.83 (step @p114 :rule trans :premises (@p113 @p112)) % 0.62/0.83 (step @p115 :rule cong :premises (@p111 @p110) :args ((= @t74 @t73))) % 0.62/0.83 (step @p116 :rule trans :premises (@p115 @p114)) % 0.62/0.83 (step @p117 :rule true_elim :premises (@p116)) % 0.62/0.83 (step @p118 :rule alpha_equiv :args (@t20 (@list @t1) @t50)) % 0.62/0.83 (step @p119 :rule trans :premises (@p118 @p117)) % 0.62/0.83 (step @p120 :rule equiv_elim1 :premises (@p119)) % 0.62/0.83 (step @p121 :rule chain_m_resolution :premises (@p120 @p108) :args (@t73 @t69 (@list @t20))) % 0.62/0.83 (step @p122 :rule aci_norm :args ((= (or @t75 false) @t75))) % 0.62/0.83 (step @p123 :rule evaluate :args ((not true))) % 0.62/0.83 (step @p124 :rule quant-unused-vars :args ((= (forall @t25 true) true))) % 0.62/0.83 (step @p125 :rule bool-or-taut2 :args (false @t23 false false)) % 0.62/0.83 (step @p126 :rule cong :premises (@p125) :args ((forall @t25 (or (not @t23) @t23)))) % 0.62/0.83 (step @p127 :rule trans :premises (@p126 @p124)) % 0.62/0.83 (step @p128 :rule refl :args (@t23)) % 0.62/0.83 (step @p129 :rule beta-reduce :args ((= @t78 @t23))) % 0.62/0.83 (step @p130 :rule cong :premises (@p129) :args (@t79)) % 0.62/0.83 (step @p131 :rule nary_cong :premises (@p130 @p128) :args (@t80)) % 0.62/0.83 (step @p132 :rule cong :premises (@p131) :args (@t81)) % 0.62/0.83 (step @p133 :rule trans :premises (@p132 @p127)) % 0.62/0.83 (step @p134 :rule cong :premises (@p133) :args (@t82)) % 0.62/0.83 (step @p135 :rule trans :premises (@p134 @p123)) % 0.62/0.83 (step @p136 :rule refl :args (@t28)) % 0.62/0.83 (step @p137 :rule beta-reduce :args ((= @t83 @t70))) % 0.62/0.83 (step @p138 :rule nary_cong :premises (@p137 @p136) :args (@t84)) % 0.62/0.83 (step @p139 :rule cong :premises (@p138) :args (@t85)) % 0.62/0.83 (step @p140 :rule cong :premises (@p139) :args (@t86)) % 0.62/0.83 (step @p141 :rule nary_cong :premises (@p140 @p135) :args (@t87)) % 0.62/0.83 (step @p142 :rule trans :premises (@p141 @p122)) % 0.62/0.83 (step @p143 :rule refl :args (@t32)) % 0.62/0.83 (step @p144 :rule cong :premises (@p143 @p142) :args ((=> @t32 @t87))) % 0.62/0.83 (assume-push @p160 @t32) % 0.62/0.83 (step @p146 :rule instantiate :premises (@p160) :args ((@list @t77))) % 0.62/0.83 (step-pop @p161 :rule scope :premises (@p146)) % 0.62/0.83 (step @p147 :rule process_scope :premises (@p161) :args (@t87)) % 0.62/0.83 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 0.62/0.83 (step @p150 :rule implies_elim :premises (@p149)) % 0.62/0.83 (step @p151 false :rule chain_m_resolution :premises (@p150 @p121 @p106) :args (false (@list false false) (@list @t73 @t32))) % 0.62/0.83 ) % 0.62/0.83 % SZS output end Proof % 0.62/0.83 % cvc5 exiting %------------------------------------------------------------------------------