%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO267^5 : 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 : n023.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 0.84s 1.03s % Output : Proof 0.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO267^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n023.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 : Wed Jun 3 00:02:28 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.84/1.03 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.84/1.03 % SZS status Theorem % 0.84/1.03 % SZS output start Proof % 0.84/1.03 ( % 0.84/1.03 (declare-sort $$unsorted 0) % 0.84/1.03 (define @t1 () (@var "Y" $$unsorted)) % 0.84/1.03 (define @t2 () (@var "G" (-> $$unsorted $$unsorted))) % 0.84/1.03 (define @t3 () (_ @t2 @t1)) % 0.84/1.03 (define @t4 () (@var "P" (-> $$unsorted Bool))) % 0.84/1.03 (define @t5 () (_ @t4 @t3)) % 0.84/1.03 (define @t6 () (_ @t4 @t1)) % 0.84/1.03 (define @t7 () (@list @t1)) % 0.84/1.03 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.84/1.03 (define @t9 () (@var "Z" $$unsorted)) % 0.84/1.03 (define @t10 () (@var "H" (-> $$unsorted $$unsorted))) % 0.84/1.03 (define @t11 () (_ @t10 @t9)) % 0.84/1.03 (define @t12 () (_ @t2 @t11)) % 0.84/1.03 (define @t13 () (@list @t9)) % 0.84/1.03 (define @t14 () (lambda @t13 @t12)) % 0.84/1.03 (define @t15 () (@var "M" (-> (-> $$unsorted $$unsorted) Bool))) % 0.84/1.03 (define @t16 () (_ @t15 @t14)) % 0.84/1.03 (define @t17 () (and @t16 @t8)) % 0.84/1.03 (define @t18 () (_ @t15 @t10)) % 0.84/1.03 (define @t19 () (_ @t15 @t2)) % 0.84/1.03 (define @t20 () (and @t19 @t18)) % 0.84/1.03 (define @t21 () (=> @t20 @t17)) % 0.84/1.03 (define @t22 () (@list @t2 @t10)) % 0.84/1.03 (define @t23 () (forall @t22 @t21)) % 0.84/1.03 (define @t24 () (@list @t15)) % 0.84/1.03 (define @t25 () (exists @t24 @t23)) % 0.84/1.03 (define @t26 () (@list @t4)) % 0.84/1.03 (define @t27 () (forall @t26 @t25)) % 0.84/1.03 (define @t28 () (not @t27)) % 0.84/1.03 (define @t29 () (@var "BOUND_VARIABLE_7470" $$unsorted)) % 0.84/1.03 (define @t30 () (_ @t2 @t29)) % 0.84/1.03 (define @t31 () (or (not (_ @t4 @t29)) (_ @t4 @t30))) % 0.84/1.03 (define @t32 () (_ @t10 @t9)) % 0.84/1.03 (define @t33 () (_ @t2 @t32)) % 0.84/1.03 (define @t34 () (lambda @t13 @t33)) % 0.84/1.03 (define @t35 () (_ @t15 @t34)) % 0.84/1.03 (define @t36 () (and @t35 @t31)) % 0.84/1.03 (define @t37 () (_ @t15 @t10)) % 0.84/1.03 (define @t38 () (not @t37)) % 0.84/1.03 (define @t39 () (_ @t15 @t2)) % 0.84/1.03 (define @t40 () (not @t39)) % 0.84/1.03 (define @t41 () (or @t40 @t38 @t36)) % 0.84/1.03 (define @t42 () (@list @t2 @t10 @t29)) % 0.84/1.03 (define @t43 () (forall @t42 @t41)) % 0.84/1.03 (define @t44 () (not (forall @t24 (not @t43)))) % 0.84/1.03 (define @t45 () (@list @t29)) % 0.84/1.03 (define @t46 () (forall @t45 @t41)) % 0.84/1.03 (define @t47 () (forall @t45 @t31)) % 0.84/1.03 (define @t48 () (forall @t45 @t35)) % 0.84/1.03 (define @t49 () (and @t48 @t47)) % 0.84/1.03 (define @t50 () (forall @t45 @t36)) % 0.84/1.03 (define @t51 () (or @t40 @t38 @t50)) % 0.84/1.03 (define @t52 () (_ @t2 @t1)) % 0.84/1.03 (define @t53 () (_ @t4 @t52)) % 0.84/1.03 (define @t54 () (_ @t4 @t1)) % 0.84/1.03 (define @t55 () (forall @t7 (or (not @t54) @t53))) % 0.84/1.03 (define @t56 () (and @t16 @t55)) % 0.84/1.03 (define @t57 () (not @t18)) % 0.84/1.03 (define @t58 () (not @t19)) % 0.84/1.03 (define @t59 () (or @t58 @t57 @t56)) % 0.84/1.03 (define @t60 () (not @t6)) % 0.84/1.03 (define @t61 () (or @t60 @t5)) % 0.84/1.03 (define @t62 () (forall @t26 @t44)) % 0.84/1.03 (define @t63 () (@quantifiers_skolemize @t62 0)) % 0.84/1.03 (define @t64 () (or (not (_ @t63 @t29)) (_ @t63 @t30))) % 0.84/1.03 (define @t65 () (forall @t24 (not (forall @t42 (or @t40 @t38 (and @t35 @t64)))))) % 0.84/1.03 (define @t66 () (not @t62)) % 0.84/1.03 (define @t67 () (not (not @t65))) % 0.84/1.03 (define @t68 () (lambda (@list (@var "BOUND_VARIABLE_14635" (-> $$unsorted $$unsorted))) false)) % 0.84/1.03 (define @t69 () (_ @t68 @t34)) % 0.84/1.03 (define @t70 () (and @t69 @t64)) % 0.84/1.03 (define @t71 () (_ @t68 @t10)) % 0.84/1.03 (define @t72 () (not @t71)) % 0.84/1.03 (define @t73 () (_ @t68 @t2)) % 0.84/1.03 (define @t74 () (not @t73)) % 0.84/1.03 (define @t75 () (or @t74 @t72 @t70)) % 0.84/1.03 (define @t76 () (forall @t42 @t75)) % 0.84/1.03 (define @t77 () (not @t76)) % 0.84/1.03 (assume @p1 @t28) % 0.84/1.03 (assume @p2 true) % 0.84/1.03 (step @p3 :rule exists-elim :args ((= (exists @t24 @t43) @t44))) % 0.84/1.03 (step @p4 :rule quant-merge-prenex :args ((= (forall @t22 @t46) @t43))) % 0.84/1.03 (step @p5 :rule alpha_equiv :args (@t47 (@list @t29) (@list @t1))) % 0.84/1.03 (step @p6 :rule quant-unused-vars :args ((= @t48 @t35))) % 0.84/1.03 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t49)) % 0.84/1.03 (step @p8 :rule quant-miniscope-and :args ((= @t50 @t49))) % 0.84/1.03 (step @p9 :rule trans :premises (@p8 @p7)) % 0.84/1.03 (step @p10 :rule refl :args (@t38)) % 0.84/1.03 (step @p11 :rule refl :args (@t40)) % 0.84/1.03 (step @p12 :rule nary_cong :premises (@p11 @p10 @p9) :args (@t51)) % 0.84/1.03 (step @p13 :rule quant-miniscope-or :args ((= @t46 @t51))) % 0.84/1.03 (step @p14 :rule trans :premises (@p13 @p12)) % 0.84/1.03 (step @p15 :rule symm :premises (@p14)) % 0.84/1.03 (step @p16 :rule cong :premises (@p15) :args ((forall @t22 (or @t40 @t38 (and @t35 @t55))))) % 0.84/1.03 (step @p17 :rule trans :premises (@p16 @p4)) % 0.84/1.03 (step @p18 :rule refl :args (@t55)) % 0.84/1.03 (step @p19 :rule refl :args ((_ @t15 @t14))) % 0.84/1.03 (step @p20 :rule refl :args ((_ @t2 @t11))) % 0.84/1.03 (step @p21 :rule refl :args (@t32)) % 0.84/1.03 (step @p22 :rule cong :premises (@p21) :args (@t33)) % 0.84/1.03 (step @p23 :rule trans :premises (@p22 @p20)) % 0.84/1.03 (step @p24 :rule cong :premises (@p23) :args (@t34)) % 0.84/1.03 (step @p25 :rule cong :premises (@p24) :args (@t35)) % 0.84/1.03 (step @p26 :rule trans :premises (@p25 @p19)) % 0.84/1.03 (step @p27 :rule refl :args (@t15)) % 0.84/1.03 (step @p28 :rule ho_cong :premises (@p27 @p24)) % 0.84/1.03 (step @p29 :rule cong :premises (@p28 @p26) :args ((= (_ @t15 @t34) @t35))) % 0.84/1.03 (step @p30 :rule symm :premises (@p29)) % 0.84/1.03 (step @p31 :rule refl :args (@t16)) % 0.84/1.03 (step @p32 :rule eq_resolve :premises (@p31 @p30)) % 0.84/1.03 (step @p33 :rule refl :args (@t2)) % 0.84/1.03 (step @p34 :rule ho_cong :premises (@p33 @p21)) % 0.84/1.03 (step @p35 :rule cong :premises (@p34 @p23) :args ((= (_ @t2 @t32) @t33))) % 0.84/1.03 (step @p36 :rule symm :premises (@p35)) % 0.84/1.03 (step @p37 :rule refl :args (@t12)) % 0.84/1.03 (step @p38 :rule eq_resolve :premises (@p37 @p36)) % 0.84/1.03 (step @p39 :rule refl :args (@t11)) % 0.84/1.03 (step @p40 :rule cong :premises (@p39 @p21) :args ((= @t11 @t32))) % 0.84/1.03 (step @p41 :rule symm :premises (@p40)) % 0.84/1.03 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.84/1.03 (step @p43 :rule ho_cong :premises (@p33 @p42)) % 0.84/1.03 (step @p44 :rule trans :premises (@p43 @p38)) % 0.84/1.03 (step @p45 :rule cong :premises (@p44) :args (@t14)) % 0.84/1.03 (step @p46 :rule ho_cong :premises (@p27 @p45)) % 0.84/1.03 (step @p47 :rule trans :premises (@p46 @p32)) % 0.84/1.03 (step @p48 :rule nary_cong :premises (@p47 @p18) :args (@t56)) % 0.84/1.03 (step @p49 :rule refl :args (@t37)) % 0.84/1.03 (step @p50 :rule refl :args (@t18)) % 0.84/1.03 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t18 @t37))) % 0.84/1.03 (step @p52 :rule symm :premises (@p51)) % 0.84/1.03 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.84/1.03 (step @p54 :rule cong :premises (@p53) :args (@t57)) % 0.84/1.03 (step @p55 :rule refl :args (@t39)) % 0.84/1.03 (step @p56 :rule refl :args (@t19)) % 0.84/1.03 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t19 @t39))) % 0.84/1.03 (step @p58 :rule symm :premises (@p57)) % 0.84/1.03 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.84/1.03 (step @p60 :rule cong :premises (@p59) :args (@t58)) % 0.84/1.03 (step @p61 :rule nary_cong :premises (@p60 @p54 @p48) :args (@t59)) % 0.84/1.03 (step @p62 :rule cong :premises (@p61) :args ((forall @t22 @t59))) % 0.84/1.03 (step @p63 :rule trans :premises (@p62 @p17)) % 0.84/1.03 (step @p64 :rule aci_norm :args ((= (or (or @t58 @t57) @t56) @t59))) % 0.84/1.03 (step @p65 :rule refl :args (@t56)) % 0.84/1.03 (step @p66 :rule bool-and-de-morgan :args (@t19 @t18 true)) % 0.84/1.03 (step @p67 :rule nary_cong :premises (@p66 @p65) :args ((or (not @t20) @t56))) % 0.84/1.03 (step @p68 :rule trans :premises (@p67 @p64)) % 0.84/1.03 (step @p69 :rule bool-impl-elim :args (@t20 @t56)) % 0.84/1.03 (step @p70 :rule trans :premises (@p69 @p68)) % 0.84/1.03 (step @p71 :rule cong :premises (@p70) :args ((forall @t22 (=> @t20 @t56)))) % 0.84/1.03 (step @p72 :rule trans :premises (@p71 @p63)) % 0.84/1.03 (step @p73 :rule refl :args ((_ @t4 @t3))) % 0.84/1.03 (step @p74 :rule refl :args (@t52)) % 0.84/1.03 (step @p75 :rule cong :premises (@p74) :args (@t53)) % 0.84/1.03 (step @p76 :rule trans :premises (@p75 @p73)) % 0.84/1.03 (step @p77 :rule refl :args (@t4)) % 0.84/1.03 (step @p78 :rule ho_cong :premises (@p77 @p74)) % 0.84/1.03 (step @p79 :rule cong :premises (@p78 @p76) :args ((= (_ @t4 @t52) @t53))) % 0.84/1.03 (step @p80 :rule symm :premises (@p79)) % 0.84/1.03 (step @p81 :rule refl :args (@t5)) % 0.84/1.03 (step @p82 :rule eq_resolve :premises (@p81 @p80)) % 0.84/1.03 (step @p83 :rule refl :args (@t3)) % 0.84/1.03 (step @p84 :rule cong :premises (@p83 @p74) :args ((= @t3 @t52))) % 0.84/1.03 (step @p85 :rule symm :premises (@p84)) % 0.84/1.03 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.84/1.03 (step @p87 :rule ho_cong :premises (@p77 @p86)) % 0.84/1.03 (step @p88 :rule trans :premises (@p87 @p82)) % 0.84/1.03 (step @p89 :rule refl :args (@t54)) % 0.84/1.03 (step @p90 :rule refl :args (@t6)) % 0.84/1.03 (step @p91 :rule cong :premises (@p90 @p89) :args ((= @t6 @t54))) % 0.84/1.03 (step @p92 :rule symm :premises (@p91)) % 0.84/1.03 (step @p93 :rule eq_resolve :premises (@p90 @p92)) % 0.84/1.03 (step @p94 :rule cong :premises (@p93) :args (@t60)) % 0.84/1.03 (step @p95 :rule nary_cong :premises (@p94 @p88) :args (@t61)) % 0.84/1.03 (step @p96 :rule cong :premises (@p95) :args ((forall @t7 @t61))) % 0.84/1.03 (step @p97 :rule bool-impl-elim :args (@t6 @t5)) % 0.84/1.03 (step @p98 :rule cong :premises (@p97) :args (@t8)) % 0.84/1.03 (step @p99 :rule trans :premises (@p98 @p96)) % 0.84/1.03 (step @p100 :rule refl :args (@t16)) % 0.84/1.03 (step @p101 :rule nary_cong :premises (@p100 @p99) :args (@t17)) % 0.84/1.03 (step @p102 :rule refl :args (@t20)) % 0.84/1.03 (step @p103 :rule cong :premises (@p102 @p101) :args (@t21)) % 0.84/1.03 (step @p104 :rule cong :premises (@p103) :args (@t23)) % 0.84/1.03 (step @p105 :rule trans :premises (@p104 @p72)) % 0.84/1.03 (step @p106 :rule cong :premises (@p105) :args (@t25)) % 0.84/1.03 (step @p107 :rule trans :premises (@p106 @p3)) % 0.84/1.03 (step @p108 :rule cong :premises (@p107) :args (@t27)) % 0.84/1.03 (step @p109 :rule cong :premises (@p108) :args (@t28)) % 0.84/1.03 (step @p110 :rule eq_resolve :premises (@p1 @p109)) % 0.84/1.03 (step @p111 :rule refl :args (@t65)) % 0.84/1.03 (step @p112 :rule bool-double-not-elim :args (@t62)) % 0.84/1.03 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t66) @t65))) % 0.84/1.03 (step @p114 :rule bool-double-not-elim :args (@t65)) % 0.84/1.03 (step @p115 :rule refl :args (@t66)) % 0.84/1.03 (step @p116 :rule cong :premises (@p115 @p114) :args ((=> @t66 @t67))) % 0.84/1.03 (assume-push @p155 @t66) % 0.84/1.03 (step @p118 :rule skolemize :premises (@p110)) % 0.84/1.03 (step-pop @p156 :rule scope :premises (@p118)) % 0.84/1.03 (step @p119 :rule process_scope :premises (@p156) :args (@t67)) % 0.84/1.03 (step @p121 :rule eq_resolve :premises (@p119 @p116)) % 0.84/1.03 (step @p122 :rule implies_elim :premises (@p121)) % 0.84/1.03 (step @p123 :rule eq_resolve :premises (@p122 @p113)) % 0.84/1.03 (step @p124 :rule chain_m_resolution :premises (@p123 @p110) :args (@t65 (@list true) (@list @t62))) % 0.84/1.03 (step @p125 :rule bool-impl-false1 :args (@t65)) % 0.84/1.03 (step @p126 :rule evaluate :args ((not true))) % 0.84/1.03 (step @p127 :rule quant-unused-vars :args ((= (forall @t42 true) true))) % 0.84/1.03 (step @p128 :rule evaluate :args ((or true true false))) % 0.84/1.03 (step @p129 :rule absorb :args ((= (and false @t64) false))) % 0.84/1.03 (step @p130 :rule refl :args (@t64)) % 0.84/1.03 (step @p131 :rule beta-reduce :args ((= @t69 false))) % 0.84/1.03 (step @p132 :rule nary_cong :premises (@p131 @p130) :args (@t70)) % 0.84/1.03 (step @p133 :rule trans :premises (@p132 @p129)) % 0.84/1.03 (step @p134 :rule evaluate :args ((not false))) % 0.84/1.03 (step @p135 :rule beta-reduce :args ((= @t71 false))) % 0.84/1.03 (step @p136 :rule cong :premises (@p135) :args (@t72)) % 0.84/1.03 (step @p137 :rule trans :premises (@p136 @p134)) % 0.84/1.03 (step @p138 :rule beta-reduce :args ((= @t73 false))) % 0.84/1.03 (step @p139 :rule cong :premises (@p138) :args (@t74)) % 0.84/1.03 (step @p140 :rule trans :premises (@p139 @p134)) % 0.84/1.03 (step @p141 :rule nary_cong :premises (@p140 @p137 @p133) :args (@t75)) % 0.84/1.03 (step @p142 :rule trans :premises (@p141 @p128)) % 0.84/1.03 (step @p143 :rule cong :premises (@p142) :args (@t76)) % 0.84/1.03 (step @p144 :rule trans :premises (@p143 @p127)) % 0.84/1.03 (step @p145 :rule cong :premises (@p144) :args (@t77)) % 0.84/1.03 (step @p146 :rule trans :premises (@p145 @p126)) % 0.84/1.03 (step @p147 :rule cong :premises (@p111 @p146) :args ((=> @t65 @t77))) % 0.84/1.03 (step @p148 :rule trans :premises (@p147 @p125)) % 0.84/1.03 (assume-push @p157 @t65) % 0.84/1.03 (step @p150 :rule instantiate :premises (@p124) :args ((@list @t68))) % 0.84/1.03 (step-pop @p158 :rule scope :premises (@p150)) % 0.84/1.03 (step @p151 :rule process_scope :premises (@p158) :args (@t77)) % 0.84/1.03 (step @p153 :rule eq_resolve :premises (@p151 @p148)) % 0.84/1.03 (step @p154 false :rule chain_m_resolution :premises (@p153 @p124) :args (false (@list false) (@list @t65))) % 0.84/1.03 ) % 0.84/1.03 % SZS output end Proof % 0.84/1.03 % cvc5 exiting %------------------------------------------------------------------------------