%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN984^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n002.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 09:10:11 AM UTC 2026 % Result : Theorem 0.39s 0.56s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN984^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n002.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 23:50:48 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.39/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.56 % SZS status Theorem % 0.39/0.56 % SZS output start Proof % 0.39/0.56 ( % 0.39/0.56 (declare-sort $$unsorted 0) % 0.39/0.56 (declare-const tptp.p (-> (-> $$unsorted Bool) Bool)) % 0.39/0.56 (declare-const tptp.a Bool) % 0.39/0.56 (declare-const tptp.b Bool) % 0.39/0.56 (define @t1 () (and tptp.a tptp.b)) % 0.39/0.56 (define @t2 () (@list (@var "X" $$unsorted))) % 0.39/0.56 (define @t3 () (lambda @t2 @t1)) % 0.39/0.56 (define @t4 () (lambda @t2 tptp.b)) % 0.39/0.56 (define @t5 () (lambda @t2 tptp.a)) % 0.39/0.56 (define @t6 () (and (_ tptp.p @t5) (_ tptp.p @t4))) % 0.39/0.56 (define @t7 () (=> @t6 (_ tptp.p @t3))) % 0.39/0.56 (define @t8 () (not @t7)) % 0.39/0.56 (define @t9 () (@purify @t3)) % 0.39/0.56 (define @t10 () (tptp.p @t9)) % 0.39/0.56 (define @t11 () (_ tptp.p @t9)) % 0.39/0.56 (define @t12 () (@purify @t4)) % 0.39/0.56 (define @t13 () (tptp.p @t12)) % 0.39/0.56 (define @t14 () (_ tptp.p @t12)) % 0.39/0.56 (define @t15 () (@purify @t5)) % 0.39/0.56 (define @t16 () (tptp.p @t15)) % 0.39/0.56 (define @t17 () (_ tptp.p @t15)) % 0.39/0.56 (define @t18 () (= @t9 @t15)) % 0.39/0.56 (define @t19 () (not @t18)) % 0.39/0.56 (define @t20 () (not @t16)) % 0.39/0.56 (define @t21 () (not @t10)) % 0.39/0.56 (define @t22 () (not @t21)) % 0.39/0.56 (define @t23 () (= true false)) % 0.39/0.56 (define @t24 () (and @t21 @t18 @t16)) % 0.39/0.56 (define @t25 () (@list true false)) % 0.39/0.56 (define @t26 () (@const 0 $$unsorted)) % 0.39/0.56 (define @t27 () (_ @t5 @t26)) % 0.39/0.56 (define @t28 () (_ @t15 @t26)) % 0.39/0.56 (define @t29 () (_ @t3 @t26)) % 0.39/0.56 (define @t30 () (_ @t9 @t26)) % 0.39/0.56 (define @t31 () (= @t30 @t28)) % 0.39/0.56 (define @t32 () (not @t31)) % 0.39/0.56 (define @t33 () (or @t18 @t32)) % 0.39/0.56 (define @t34 () (= tptp.a @t1)) % 0.39/0.56 (define @t35 () (@list true)) % 0.39/0.56 (define @t36 () (= @t9 @t12)) % 0.39/0.56 (define @t37 () (not @t36)) % 0.39/0.56 (define @t38 () (not @t13)) % 0.39/0.56 (define @t39 () (and @t21 @t36 @t13)) % 0.39/0.56 (define @t40 () (@const 1 $$unsorted)) % 0.39/0.56 (define @t41 () (_ @t4 @t40)) % 0.39/0.56 (define @t42 () (_ @t12 @t40)) % 0.39/0.56 (define @t43 () (_ @t3 @t40)) % 0.39/0.56 (define @t44 () (_ @t9 @t40)) % 0.39/0.56 (define @t45 () (= @t44 @t42)) % 0.39/0.56 (define @t46 () (not @t45)) % 0.39/0.56 (define @t47 () (or @t36 @t46)) % 0.39/0.56 (define @t48 () (= tptp.b @t1)) % 0.39/0.56 (define @t49 () (not @t1)) % 0.39/0.56 (assume @p1 @t8) % 0.39/0.56 (assume @p2 true) % 0.39/0.56 (step @p3 :rule refl :args (@t10)) % 0.39/0.56 (step @p4 :rule refl :args (@t11)) % 0.39/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t11 @t10))) % 0.39/0.56 (step @p6 :rule symm :premises (@p5)) % 0.39/0.56 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.39/0.56 (step @p8 :rule eq-refl :args (@t3)) % 0.39/0.56 (step @p9 :rule skolem_intro :args (@t9)) % 0.39/0.56 (step @p10 :rule refl :args (@t3)) % 0.39/0.56 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t3 @t9))) % 0.39/0.56 (step @p12 :rule trans :premises (@p11 @p8)) % 0.39/0.56 (step @p13 :rule true_elim :premises (@p12)) % 0.39/0.56 (step @p14 :rule refl :args (tptp.p)) % 0.39/0.56 (step @p15 :rule ho_cong :premises (@p14 @p13)) % 0.39/0.56 (step @p16 :rule trans :premises (@p15 @p7)) % 0.39/0.56 (step @p17 :rule refl :args (@t13)) % 0.39/0.56 (step @p18 :rule refl :args (@t14)) % 0.39/0.56 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t14 @t13))) % 0.39/0.56 (step @p20 :rule symm :premises (@p19)) % 0.39/0.56 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.39/0.56 (step @p22 :rule eq-refl :args (@t4)) % 0.39/0.56 (step @p23 :rule skolem_intro :args (@t12)) % 0.39/0.56 (step @p24 :rule refl :args (@t4)) % 0.39/0.56 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t4 @t12))) % 0.39/0.56 (step @p26 :rule trans :premises (@p25 @p22)) % 0.39/0.56 (step @p27 :rule true_elim :premises (@p26)) % 0.39/0.56 (step @p28 :rule ho_cong :premises (@p14 @p27)) % 0.39/0.56 (step @p29 :rule trans :premises (@p28 @p21)) % 0.39/0.56 (step @p30 :rule refl :args (@t16)) % 0.39/0.56 (step @p31 :rule refl :args (@t17)) % 0.39/0.56 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t17 @t16))) % 0.39/0.56 (step @p33 :rule symm :premises (@p32)) % 0.39/0.56 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.39/0.56 (step @p35 :rule eq-refl :args (@t5)) % 0.39/0.56 (step @p36 :rule skolem_intro :args (@t15)) % 0.39/0.56 (step @p37 :rule refl :args (@t5)) % 0.39/0.56 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t5 @t15))) % 0.39/0.56 (step @p39 :rule trans :premises (@p38 @p35)) % 0.39/0.56 (step @p40 :rule true_elim :premises (@p39)) % 0.39/0.56 (step @p41 :rule ho_cong :premises (@p14 @p40)) % 0.39/0.56 (step @p42 :rule trans :premises (@p41 @p34)) % 0.39/0.56 (step @p43 :rule nary_cong :premises (@p42 @p29) :args (@t6)) % 0.39/0.56 (step @p44 :rule cong :premises (@p43 @p16) :args (@t7)) % 0.39/0.56 (step @p45 :rule cong :premises (@p44) :args (@t8)) % 0.39/0.56 (step @p46 :rule eq_resolve :premises (@p1 @p45)) % 0.39/0.56 (step @p47 :rule not_implies_elim1 :premises (@p46)) % 0.39/0.56 (step @p48 :rule and_elim :premises (@p47) :args (0)) % 0.39/0.56 (step @p49 :rule not_implies_elim2 :premises (@p46)) % 0.39/0.56 (step @p50 :rule refl :args (@t19)) % 0.39/0.56 (step @p51 :rule bool-double-not-elim :args (@t10)) % 0.39/0.56 (step @p52 :rule refl :args (@t20)) % 0.39/0.56 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50) :args ((or @t20 @t22 @t19))) % 0.39/0.56 (assume-push @p183 @t21) % 0.39/0.56 (assume-push @p184 @t18) % 0.39/0.56 (assume-push @p185 @t16) % 0.39/0.56 (step @p57 :rule evaluate :args (@t23)) % 0.39/0.56 (step @p58 :rule false_intro :premises (@p49)) % 0.39/0.56 (step @p59 :rule symm :premises (@p184)) % 0.39/0.56 (step @p60 :rule cong :premises (@p59) :args (@t16)) % 0.39/0.56 (step @p61 :rule true_intro :premises (@p48)) % 0.39/0.56 (step @p62 :rule symm :premises (@p61)) % 0.39/0.56 (step @p63 :rule trans :premises (@p62 @p60 @p58)) % 0.39/0.56 (step @p64 false :rule eq_resolve :premises (@p63 @p57)) % 0.39/0.56 (step-pop @p186 :rule scope :premises (@p64)) % 0.39/0.56 (step-pop @p187 :rule scope :premises (@p186)) % 0.39/0.56 (step-pop @p188 :rule scope :premises (@p187)) % 0.39/0.56 (step @p65 :rule process_scope :premises (@p188) :args (false)) % 0.39/0.56 (assume-push @p189 @t16) % 0.39/0.56 (assume-push @p190 @t21) % 0.39/0.56 (assume-push @p191 @t18) % 0.39/0.56 (step @p72 :rule and_intro :premises (@p49 @p191 @p48)) % 0.39/0.56 (step-pop @p192 :rule scope :premises (@p72)) % 0.39/0.56 (step-pop @p193 :rule scope :premises (@p192)) % 0.39/0.56 (step-pop @p194 :rule scope :premises (@p193)) % 0.39/0.56 (step @p73 :rule process_scope :premises (@p194) :args (@t24)) % 0.39/0.56 (step @p77 :rule implies_elim :premises (@p73)) % 0.39/0.56 (step @p78 :rule resolution :premises (@p77 @p65) :args (true @t24)) % 0.39/0.56 (step @p79 :rule not_and :premises (@p78)) % 0.39/0.56 (step @p80 :rule eq_resolve :premises (@p79 @p53)) % 0.39/0.56 (step @p81 :rule reordering :premises (@p80) :args ((or @t10 @t20 @t19))) % 0.39/0.56 (step @p82 :rule chain_m_resolution :premises (@p81 @p49 @p48) :args (@t19 @t25 (@list @t10 @t16))) % 0.39/0.56 (step @p83 :rule eq-symm :args (@t1 tptp.a)) % 0.39/0.56 (step @p84 :rule eq-refl :args (tptp.a)) % 0.39/0.56 (step @p85 :rule beta-reduce :args ((= @t27 tptp.a))) % 0.39/0.56 (step @p86 :rule refl :args (tptp.a)) % 0.39/0.56 (step @p87 :rule cong :premises (@p86 @p85) :args ((= tptp.a @t27))) % 0.39/0.56 (step @p88 :rule trans :premises (@p87 @p84)) % 0.39/0.56 (step @p89 :rule refl :args (@t26)) % 0.39/0.56 (step @p90 :rule ho_cong :premises (@p36 @p89)) % 0.39/0.56 (step @p91 :rule cong :premises (@p86 @p90) :args ((= tptp.a @t28))) % 0.39/0.57 (step @p92 :rule eq-symm :args (@t28 tptp.a)) % 0.39/0.57 (step @p93 :rule trans :premises (@p92 @p91 @p88)) % 0.39/0.57 (step @p94 :rule true_elim :premises (@p93)) % 0.39/0.57 (step @p95 :rule eq-refl :args (@t1)) % 0.39/0.57 (step @p96 :rule beta-reduce :args ((= @t29 @t1))) % 0.39/0.57 (step @p97 :rule refl :args (@t1)) % 0.39/0.57 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t1 @t29))) % 0.39/0.57 (step @p99 :rule trans :premises (@p98 @p95)) % 0.39/0.57 (step @p100 :rule ho_cong :premises (@p9 @p89)) % 0.39/0.57 (step @p101 :rule cong :premises (@p97 @p100) :args ((= @t1 @t30))) % 0.39/0.57 (step @p102 :rule eq-symm :args (@t30 @t1)) % 0.39/0.57 (step @p103 :rule trans :premises (@p102 @p101 @p99)) % 0.39/0.57 (step @p104 :rule true_elim :premises (@p103)) % 0.39/0.57 (step @p105 :rule cong :premises (@p104 @p94) :args (@t31)) % 0.39/0.57 (step @p106 :rule trans :premises (@p105 @p83)) % 0.39/0.57 (step @p107 :rule cong :premises (@p106) :args (@t32)) % 0.39/0.57 (step @p108 :rule refl :args (@t18)) % 0.39/0.57 (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t33)) % 0.39/0.57 ; WARNING: add trust step for TRUST % 0.39/0.57 ; trust TRUST THEORY_LEMMA % 0.39/0.57 (step @p110 :rule trust :premises () :args (@t33)) % 0.39/0.57 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.39/0.57 (step @p112 :rule chain_m_resolution :premises (@p111 @p82) :args ((not @t34) @t35 (@list @t18))) % 0.39/0.57 (step @p113 :rule cnf_equiv_neg2 :args (@t34)) % 0.39/0.57 (step @p114 :rule and_elim :premises (@p47) :args (1)) % 0.39/0.57 (step @p115 :rule refl :args (@t37)) % 0.39/0.57 (step @p116 :rule refl :args (@t38)) % 0.39/0.57 (step @p117 :rule nary_cong :premises (@p116 @p51 @p115) :args ((or @t38 @t22 @t37))) % 0.39/0.57 (assume-push @p195 @t21) % 0.39/0.57 (assume-push @p196 @t36) % 0.39/0.57 (assume-push @p197 @t13) % 0.39/0.57 (step @p57 :rule evaluate :args (@t23)) % 0.39/0.57 (step @p58 :rule false_intro :premises (@p49)) % 0.39/0.57 (step @p121 :rule symm :premises (@p196)) % 0.39/0.57 (step @p122 :rule cong :premises (@p121) :args (@t13)) % 0.39/0.57 (step @p123 :rule true_intro :premises (@p114)) % 0.39/0.57 (step @p124 :rule symm :premises (@p123)) % 0.39/0.57 (step @p125 :rule trans :premises (@p124 @p122 @p58)) % 0.39/0.57 (step @p126 false :rule eq_resolve :premises (@p125 @p57)) % 0.39/0.57 (step-pop @p198 :rule scope :premises (@p126)) % 0.39/0.57 (step-pop @p199 :rule scope :premises (@p198)) % 0.39/0.57 (step-pop @p200 :rule scope :premises (@p199)) % 0.39/0.57 (step @p127 :rule process_scope :premises (@p200) :args (false)) % 0.39/0.57 (assume-push @p201 @t13) % 0.39/0.57 (assume-push @p202 @t21) % 0.39/0.57 (assume-push @p203 @t36) % 0.39/0.57 (step @p134 :rule and_intro :premises (@p49 @p203 @p114)) % 0.39/0.57 (step-pop @p204 :rule scope :premises (@p134)) % 0.39/0.57 (step-pop @p205 :rule scope :premises (@p204)) % 0.39/0.57 (step-pop @p206 :rule scope :premises (@p205)) % 0.39/0.57 (step @p135 :rule process_scope :premises (@p206) :args (@t39)) % 0.39/0.57 (step @p139 :rule implies_elim :premises (@p135)) % 0.39/0.57 (step @p140 :rule resolution :premises (@p139 @p127) :args (true @t39)) % 0.39/0.57 (step @p141 :rule not_and :premises (@p140)) % 0.39/0.57 (step @p142 :rule eq_resolve :premises (@p141 @p117)) % 0.39/0.57 (step @p143 :rule reordering :premises (@p142) :args ((or @t10 @t38 @t37))) % 0.39/0.57 (step @p144 :rule chain_m_resolution :premises (@p143 @p49 @p114) :args (@t37 @t25 (@list @t10 @t13))) % 0.39/0.57 (step @p145 :rule eq-symm :args (@t1 tptp.b)) % 0.39/0.57 (step @p146 :rule eq-refl :args (tptp.b)) % 0.39/0.57 (step @p147 :rule beta-reduce :args ((= @t41 tptp.b))) % 0.39/0.57 (step @p148 :rule refl :args (tptp.b)) % 0.39/0.57 (step @p149 :rule cong :premises (@p148 @p147) :args ((= tptp.b @t41))) % 0.39/0.57 (step @p150 :rule trans :premises (@p149 @p146)) % 0.39/0.57 (step @p151 :rule refl :args (@t40)) % 0.39/0.57 (step @p152 :rule ho_cong :premises (@p23 @p151)) % 0.39/0.57 (step @p153 :rule cong :premises (@p148 @p152) :args ((= tptp.b @t42))) % 0.39/0.57 (step @p154 :rule eq-symm :args (@t42 tptp.b)) % 0.39/0.57 (step @p155 :rule trans :premises (@p154 @p153 @p150)) % 0.39/0.57 (step @p156 :rule true_elim :premises (@p155)) % 0.39/0.57 (step @p157 :rule beta-reduce :args ((= @t43 @t1))) % 0.39/0.57 (step @p158 :rule cong :premises (@p97 @p157) :args ((= @t1 @t43))) % 0.39/0.57 (step @p159 :rule trans :premises (@p158 @p95)) % 0.39/0.57 (step @p160 :rule ho_cong :premises (@p9 @p151)) % 0.39/0.57 (step @p161 :rule cong :premises (@p97 @p160) :args ((= @t1 @t44))) % 0.39/0.57 (step @p162 :rule eq-symm :args (@t44 @t1)) % 0.39/0.57 (step @p163 :rule trans :premises (@p162 @p161 @p159)) % 0.39/0.57 (step @p164 :rule true_elim :premises (@p163)) % 0.39/0.57 (step @p165 :rule cong :premises (@p164 @p156) :args (@t45)) % 0.39/0.57 (step @p166 :rule trans :premises (@p165 @p145)) % 0.39/0.57 (step @p167 :rule cong :premises (@p166) :args (@t46)) % 0.39/0.57 (step @p168 :rule refl :args (@t36)) % 0.39/0.57 (step @p169 :rule nary_cong :premises (@p168 @p167) :args (@t47)) % 0.39/0.57 ; trust TRUST THEORY_LEMMA % 0.39/0.57 (step @p170 :rule trust :premises () :args (@t47)) % 0.39/0.57 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 0.39/0.57 (step @p172 :rule chain_m_resolution :premises (@p171 @p144) :args ((not @t48) @t35 (@list @t36))) % 0.39/0.57 (step @p173 :rule cnf_equiv_neg1 :args (@t48)) % 0.39/0.57 (step @p174 :rule reordering :premises (@p173) :args ((or tptp.b @t1 @t48))) % 0.39/0.57 (step @p175 :rule cnf_and_neg :args (@t1)) % 0.39/0.57 (step @p176 :rule chain_m_resolution :premises (@p175 @p174 @p172 @p113 @p112) :args ((not tptp.a) (@list false true true true) (@list tptp.b @t48 @t1 @t34))) % 0.39/0.57 (step @p177 :rule cnf_and_pos :args (@t1 0)) % 0.39/0.57 (step @p178 :rule reordering :premises (@p177) :args ((or tptp.a @t49))) % 0.39/0.57 (step @p179 :rule chain_m_resolution :premises (@p178 @p176) :args (@t49 @t35 (@list tptp.a))) % 0.39/0.57 (step @p180 :rule cnf_equiv_neg1 :args (@t34)) % 0.39/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or tptp.a @t1 @t34))) % 0.39/0.57 (step @p182 false :rule chain_m_resolution :premises (@p181 @p179 @p176 @p112) :args (false (@list true true true) (@list @t1 tptp.a @t34))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------