%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN374^5 : 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 : n012.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 09:08:43 AM UTC 2026 % Result : Theorem 0.24s 0.43s % Output : Proof 0.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYN374^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 23:25:18 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.24/0.43 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.24/0.43 % SZS status Theorem % 0.24/0.43 % SZS output start Proof % 0.24/0.43 ( % 0.24/0.43 (declare-sort $$unsorted 0) % 0.24/0.43 (declare-const tptp.cP (-> $$unsorted Bool)) % 0.24/0.43 (define @t1 () (@var "Xy" $$unsorted)) % 0.24/0.43 (define @t2 () (_ tptp.cP @t1)) % 0.24/0.43 (define @t3 () (@list @t1)) % 0.24/0.43 (define @t4 () (forall @t3 @t2)) % 0.24/0.43 (define @t5 () (@var "Xx" $$unsorted)) % 0.24/0.43 (define @t6 () (_ tptp.cP @t5)) % 0.24/0.43 (define @t7 () (@list @t5)) % 0.24/0.43 (define @t8 () (exists @t7 @t6)) % 0.24/0.43 (define @t9 () (= @t8 @t4)) % 0.24/0.43 (define @t10 () (= @t6 @t2)) % 0.24/0.43 (define @t11 () (forall @t3 @t10)) % 0.24/0.43 (define @t12 () (exists @t7 @t11)) % 0.24/0.43 (define @t13 () (= @t12 @t9)) % 0.24/0.43 (define @t14 () (not @t13)) % 0.24/0.43 (define @t15 () (tptp.cP @t1)) % 0.24/0.43 (define @t16 () (forall @t3 @t15)) % 0.24/0.43 (define @t17 () (tptp.cP @t5)) % 0.24/0.43 (define @t18 () (forall @t7 (not @t17))) % 0.24/0.43 (define @t19 () (not @t18)) % 0.24/0.43 (define @t20 () (= @t19 @t16)) % 0.24/0.43 (define @t21 () (not @t20)) % 0.24/0.43 (define @t22 () (forall @t3 (= @t17 @t15))) % 0.24/0.43 (define @t23 () (forall @t7 (not @t22))) % 0.24/0.43 (define @t24 () (not @t23)) % 0.24/0.43 (define @t25 () (not @t24)) % 0.24/0.43 (define @t26 () (not @t6)) % 0.24/0.43 (define @t27 () (forall @t7 @t26)) % 0.24/0.43 (define @t28 () (not @t27)) % 0.24/0.43 (define @t29 () (tptp.cP (@quantifiers_skolemize @t23 0))) % 0.24/0.43 (define @t30 () (forall @t3 (= @t15 @t29))) % 0.24/0.43 (define @t31 () (forall @t3 (= @t29 @t15))) % 0.24/0.43 (define @t32 () (not (not @t31))) % 0.24/0.43 (define @t33 () (@quantifiers_skolemize @t18 0)) % 0.24/0.43 (define @t34 () (tptp.cP @t33)) % 0.24/0.43 (define @t35 () (= @t34 @t29)) % 0.24/0.43 (define @t36 () (@quantifiers_skolemize @t16 0)) % 0.24/0.43 (define @t37 () (tptp.cP @t36)) % 0.24/0.43 (define @t38 () (= @t37 @t29)) % 0.24/0.43 (define @t39 () (@list @t36)) % 0.24/0.43 (define @t40 () (not @t16)) % 0.24/0.43 (define @t41 () (not @t19)) % 0.24/0.43 (define @t42 () (not @t34)) % 0.24/0.43 (define @t43 () (not @t42)) % 0.24/0.43 (define @t44 () (not @t37)) % 0.24/0.43 (define @t45 () (= @t29 @t34)) % 0.24/0.43 (define @t46 () (not @t45)) % 0.24/0.43 (define @t47 () (= @t29 @t37)) % 0.24/0.43 (define @t48 () (not @t47)) % 0.24/0.43 (define @t49 () (@list false)) % 0.24/0.43 (define @t50 () (@list @t23)) % 0.24/0.43 (define @t51 () (@quantifiers_skolemize @t30 0)) % 0.24/0.43 (define @t52 () (@list @t51)) % 0.24/0.43 (define @t53 () (tptp.cP @t51)) % 0.24/0.43 (define @t54 () (forall @t3 (= @t53 @t15))) % 0.24/0.43 (define @t55 () (not @t54)) % 0.24/0.43 (define @t56 () (forall @t3 (= @t15 @t53))) % 0.24/0.43 (define @t57 () (not @t56)) % 0.24/0.43 (define @t58 () (@quantifiers_skolemize @t56 0)) % 0.24/0.43 (define @t59 () (tptp.cP @t58)) % 0.24/0.43 (define @t60 () (= @t53 @t59)) % 0.24/0.43 (define @t61 () (not @t60)) % 0.24/0.43 (define @t62 () (not (= @t59 @t53))) % 0.24/0.43 (define @t63 () (not @t59)) % 0.24/0.43 (define @t64 () (not @t53)) % 0.24/0.43 (define @t65 () (@list @t58)) % 0.24/0.43 (assume @p1 @t14) % 0.24/0.43 (assume @p2 true) % 0.24/0.43 (step @p3 :rule refl :args (@t21)) % 0.24/0.43 (step @p4 :rule bool-double-not-elim :args (@t23)) % 0.24/0.43 (step @p5 :rule nary_cong :premises (@p4 @p3) :args ((or @t25 @t21))) % 0.24/0.43 (step @p6 :rule refl :args (@t15)) % 0.24/0.43 (step @p7 :rule refl :args (@t2)) % 0.24/0.43 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t2 @t15))) % 0.24/0.43 (step @p9 :rule symm :premises (@p8)) % 0.24/0.43 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 0.24/0.43 (step @p11 :rule cong :premises (@p10) :args (@t4)) % 0.24/0.43 (step @p12 :rule refl :args (@t17)) % 0.24/0.43 (step @p13 :rule refl :args (@t6)) % 0.24/0.43 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t6 @t17))) % 0.24/0.43 (step @p15 :rule symm :premises (@p14)) % 0.24/0.43 (step @p16 :rule eq_resolve :premises (@p13 @p15)) % 0.24/0.43 (step @p17 :rule cong :premises (@p16) :args (@t26)) % 0.24/0.43 (step @p18 :rule cong :premises (@p17) :args (@t27)) % 0.24/0.43 (step @p19 :rule cong :premises (@p18) :args (@t28)) % 0.24/0.43 (step @p20 :rule exists-elim :args ((= @t8 @t28))) % 0.24/0.43 (step @p21 :rule trans :premises (@p20 @p19)) % 0.24/0.43 (step @p22 :rule cong :premises (@p21 @p11) :args (@t9)) % 0.24/0.43 (step @p23 :rule exists-elim :args ((= (exists @t7 @t22) @t24))) % 0.24/0.43 (step @p24 :rule cong :premises (@p16 @p10) :args (@t10)) % 0.24/0.43 (step @p25 :rule cong :premises (@p24) :args (@t11)) % 0.24/0.43 (step @p26 :rule cong :premises (@p25) :args (@t12)) % 0.24/0.43 (step @p27 :rule trans :premises (@p26 @p23)) % 0.24/0.43 (step @p28 :rule cong :premises (@p27 @p22) :args (@t13)) % 0.24/0.43 (step @p29 :rule cong :premises (@p28) :args (@t14)) % 0.24/0.43 (step @p30 :rule eq_resolve :premises (@p1 @p29)) % 0.24/0.43 (step @p31 :rule not_equiv_elim2 :premises (@p30)) % 0.24/0.43 (step @p32 :rule eq_resolve :premises (@p31 @p5)) % 0.24/0.43 (step @p33 :rule refl :args (@t30)) % 0.24/0.43 (step @p34 :rule nary_cong :premises (@p4 @p33) :args ((or @t25 @t30))) % 0.24/0.43 (step @p35 :rule eq-symm :args (@t29 @t15)) % 0.24/0.43 (step @p36 :rule cong :premises (@p35) :args (@t31)) % 0.24/0.43 (step @p37 :rule bool-double-not-elim :args (@t31)) % 0.24/0.43 (step @p38 :rule trans :premises (@p37 @p36)) % 0.24/0.43 (step @p39 :rule refl :args (@t24)) % 0.24/0.43 (step @p40 :rule cong :premises (@p39 @p38) :args ((=> @t24 @t32))) % 0.24/0.43 (assume-push @p173 @t24) % 0.24/0.43 (step @p42 :rule skolemize :premises (@p173)) % 0.24/0.43 (step-pop @p174 :rule scope :premises (@p42)) % 0.24/0.43 (step @p43 :rule process_scope :premises (@p174) :args (@t32)) % 0.24/0.43 (step @p45 :rule eq_resolve :premises (@p43 @p40)) % 0.24/0.43 (step @p46 :rule implies_elim :premises (@p45)) % 0.24/0.43 (step @p47 :rule eq_resolve :premises (@p46 @p34)) % 0.24/0.43 (step @p48 :rule eq-symm :args (@t34 @t29)) % 0.24/0.43 (step @p49 :rule cong :premises (@p33 @p48) :args ((=> @t30 @t35))) % 0.24/0.43 (assume-push @p175 @t30) % 0.24/0.43 (step @p51 :rule instantiate :premises (@p175) :args ((@list @t33))) % 0.24/0.43 (step-pop @p176 :rule scope :premises (@p51)) % 0.24/0.43 (step @p52 :rule process_scope :premises (@p176) :args (@t35)) % 0.24/0.43 (step @p54 :rule eq_resolve :premises (@p52 @p49)) % 0.24/0.43 (step @p55 :rule implies_elim :premises (@p54)) % 0.24/0.43 (step @p56 :rule eq-symm :args (@t37 @t29)) % 0.24/0.43 (step @p57 :rule cong :premises (@p33 @p56) :args ((=> @t30 @t38))) % 0.24/0.43 (assume-push @p177 @t30) % 0.24/0.43 (step @p59 :rule instantiate :premises (@p177) :args (@t39)) % 0.24/0.43 (step-pop @p178 :rule scope :premises (@p59)) % 0.24/0.43 (step @p60 :rule process_scope :premises (@p178) :args (@t38)) % 0.24/0.43 (step @p62 :rule eq_resolve :premises (@p60 @p57)) % 0.24/0.43 (step @p63 :rule implies_elim :premises (@p62)) % 0.24/0.43 (step @p64 :rule refl :args (@t40)) % 0.24/0.43 (step @p65 :rule bool-double-not-elim :args (@t18)) % 0.24/0.43 (step @p66 :rule refl :args (@t20)) % 0.24/0.43 (step @p67 :rule nary_cong :premises (@p66 @p65 @p64) :args ((or @t20 @t41 @t40))) % 0.24/0.43 (step @p68 :rule cnf_equiv_neg2 :args (@t20)) % 0.24/0.43 (step @p69 :rule eq_resolve :premises (@p68 @p67)) % 0.24/0.43 (step @p70 :rule reordering :premises (@p69) :args ((or @t18 @t20 @t40))) % 0.24/0.43 (step @p71 :rule refl :args (@t34)) % 0.24/0.43 (step @p72 :rule nary_cong :premises (@p65 @p71) :args ((or @t41 @t34))) % 0.24/0.43 (step @p73 :rule bool-double-not-elim :args (@t34)) % 0.24/0.43 (step @p74 :rule refl :args (@t19)) % 0.24/0.43 (step @p75 :rule cong :premises (@p74 @p73) :args ((=> @t19 @t43))) % 0.24/0.43 (assume-push @p179 @t19) % 0.24/0.43 (step @p77 :rule skolemize :premises (@p179)) % 0.24/0.43 (step-pop @p180 :rule scope :premises (@p77)) % 0.24/0.43 (step @p78 :rule process_scope :premises (@p180) :args (@t43)) % 0.24/0.43 (step @p80 :rule eq_resolve :premises (@p78 @p75)) % 0.24/0.43 (step @p81 :rule implies_elim :premises (@p80)) % 0.24/0.43 (step @p82 :rule eq_resolve :premises (@p81 @p72)) % 0.24/0.43 (step @p83 :rule refl :args (@t44)) % 0.24/0.43 (step @p84 :rule bool-double-not-elim :args (@t16)) % 0.24/0.43 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or (not @t40) @t44))) % 0.24/0.43 (assume-push @p181 @t40) % 0.24/0.43 (step @p87 :rule skolemize :premises (@p181)) % 0.24/0.43 (step-pop @p182 :rule scope :premises (@p87)) % 0.24/0.43 (step @p88 :rule process_scope :premises (@p182) :args (@t44)) % 0.24/0.43 (step @p90 :rule implies_elim :premises (@p88)) % 0.24/0.43 (step @p91 :rule eq_resolve :premises (@p90 @p85)) % 0.24/0.43 (step @p92 :rule cnf_equiv_pos2 :args (@t45)) % 0.24/0.43 (step @p93 :rule reordering :premises (@p92) :args ((or @t29 @t42 @t46))) % 0.24/0.43 (step @p94 :rule cnf_equiv_pos1 :args (@t47)) % 0.24/0.43 (step @p95 :rule reordering :premises (@p94) :args ((or @t37 (not @t29) @t48))) % 0.24/0.43 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p91 @p82 @p70) :args ((or @t18 @t20 @t46 @t48) (@list false true false true) (@list @t29 @t37 @t34 @t16))) % 0.24/0.43 (step @p97 :rule cnf_equiv_neg1 :args (@t20)) % 0.24/0.43 (step @p98 :rule reordering :premises (@p97) :args ((or @t19 @t16 @t20))) % 0.24/0.43 (assume-push @p183 @t18) % 0.24/0.43 (step @p100 :rule instantiate :premises (@p183) :args (@t39)) % 0.24/0.43 (step-pop @p184 :rule scope :premises (@p100)) % 0.24/0.43 (step @p101 :rule process_scope :premises (@p184) :args (@t44)) % 0.24/0.43 (step @p103 :rule implies_elim :premises (@p101)) % 0.24/0.43 (assume-push @p185 @t16) % 0.24/0.43 (step @p105 :rule instantiate :premises (@p185) :args (@t39)) % 0.24/0.43 (step-pop @p186 :rule scope :premises (@p105)) % 0.24/0.43 (step @p106 :rule process_scope :premises (@p186) :args (@t37)) % 0.24/0.43 (step @p108 :rule implies_elim :premises (@p106)) % 0.24/0.43 (step @p109 :rule chain_m_resolution :premises (@p108 @p103 @p98 @p96 @p63 @p55 @p47 @p32) :args (@t23 (@list true false false false false false true) (@list @t37 @t16 @t18 @t47 @t45 @t30 @t20))) % 0.24/0.43 (step @p110 :rule not_equiv_elim1 :premises (@p30)) % 0.24/0.43 (step @p111 :rule chain_m_resolution :premises (@p110 @p109) :args (@t20 @t49 @t50)) % 0.24/0.43 (assume-push @p187 @t16) % 0.24/0.43 (step @p113 :rule instantiate :premises (@p187) :args (@t52)) % 0.24/0.43 (step-pop @p188 :rule scope :premises (@p113)) % 0.24/0.43 (step @p114 :rule process_scope :premises (@p188) :args (@t53)) % 0.24/0.43 (step @p116 :rule implies_elim :premises (@p114)) % 0.24/0.43 (step @p117 :rule eq-symm :args (@t53 @t15)) % 0.24/0.43 (step @p118 :rule cong :premises (@p117) :args (@t54)) % 0.24/0.43 (step @p119 :rule cong :premises (@p118) :args (@t55)) % 0.24/0.43 (step @p120 :rule refl :args (@t23)) % 0.24/0.43 (step @p121 :rule cong :premises (@p120 @p119) :args ((=> @t23 @t55))) % 0.24/0.43 (assume-push @p189 @t23) % 0.24/0.43 (step @p123 :rule instantiate :premises (@p189) :args (@t52)) % 0.24/0.43 (step-pop @p190 :rule scope :premises (@p123)) % 0.24/0.43 (step @p124 :rule process_scope :premises (@p190) :args (@t55)) % 0.24/0.43 (step @p126 :rule eq_resolve :premises (@p124 @p121)) % 0.24/0.43 (step @p127 :rule implies_elim :premises (@p126)) % 0.24/0.43 (step @p128 :rule chain_m_resolution :premises (@p127 @p109) :args (@t57 @t49 @t50)) % 0.24/0.43 (step @p129 :rule refl :args (@t61)) % 0.24/0.43 (step @p130 :rule bool-double-not-elim :args (@t56)) % 0.24/0.43 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or (not @t57) @t61))) % 0.24/0.43 (step @p132 :rule eq-symm :args (@t59 @t53)) % 0.24/0.43 (step @p133 :rule cong :premises (@p132) :args (@t62)) % 0.24/0.43 (step @p134 :rule refl :args (@t57)) % 0.24/0.43 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t57 @t62))) % 0.24/0.43 (assume-push @p191 @t57) % 0.24/0.43 (step @p137 :rule skolemize :premises (@p191)) % 0.24/0.43 (step-pop @p192 :rule scope :premises (@p137)) % 0.24/0.43 (step @p138 :rule process_scope :premises (@p192) :args (@t62)) % 0.24/0.43 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 0.24/0.43 (step @p141 :rule implies_elim :premises (@p140)) % 0.24/0.43 (step @p142 :rule eq_resolve :premises (@p141 @p131)) % 0.24/0.43 (step @p143 :rule chain_m_resolution :premises (@p142 @p128) :args (@t61 (@list true) (@list @t56))) % 0.24/0.43 (step @p144 :rule cnf_equiv_neg2 :args (@t60)) % 0.24/0.43 (step @p145 :rule reordering :premises (@p144) :args ((or @t64 @t60 @t63))) % 0.24/0.43 (assume-push @p193 @t16) % 0.24/0.43 (step @p147 :rule instantiate :premises (@p193) :args (@t65)) % 0.24/0.43 (step-pop @p194 :rule scope :premises (@p147)) % 0.24/0.43 (step @p148 :rule process_scope :premises (@p194) :args (@t59)) % 0.24/0.43 (step @p150 :rule implies_elim :premises (@p148)) % 0.24/0.43 (step @p151 :rule chain_m_resolution :premises (@p150 @p145 @p143 @p116) :args (@t40 (@list true true false) (@list @t59 @t60 @t53))) % 0.24/0.43 (step @p152 :rule refl :args (@t16)) % 0.24/0.43 (step @p153 :rule nary_cong :premises (@p3 @p65 @p152) :args ((or @t21 @t41 @t16))) % 0.24/0.43 (step @p154 :rule cnf_equiv_pos1 :args (@t20)) % 0.24/0.43 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.24/0.43 (step @p156 :rule reordering :premises (@p155) :args ((or @t18 @t16 @t21))) % 0.24/0.43 (step @p157 :rule chain_m_resolution :premises (@p156 @p151 @p111) :args (@t18 (@list true false) (@list @t16 @t20))) % 0.24/0.43 (assume-push @p195 @t18) % 0.24/0.43 (step @p159 :rule instantiate :premises (@p195) :args (@t52)) % 0.24/0.43 (step-pop @p196 :rule scope :premises (@p159)) % 0.24/0.43 (step @p160 :rule process_scope :premises (@p196) :args (@t64)) % 0.24/0.43 (step @p162 :rule implies_elim :premises (@p160)) % 0.24/0.43 (step @p163 :rule chain_m_resolution :premises (@p162 @p157) :args (@t64 @t49 (@list @t18))) % 0.24/0.43 (step @p164 :rule cnf_equiv_neg1 :args (@t60)) % 0.24/0.43 (step @p165 :rule reordering :premises (@p164) :args ((or @t53 @t59 @t60))) % 0.24/0.43 (step @p166 :rule chain_m_resolution :premises (@p165 @p163 @p143) :args (@t59 (@list true true) (@list @t53 @t60))) % 0.24/0.43 (assume-push @p197 @t18) % 0.24/0.43 (step @p168 :rule instantiate :premises (@p197) :args (@t65)) % 0.24/0.43 (step-pop @p198 :rule scope :premises (@p168)) % 0.24/0.43 (step @p169 :rule process_scope :premises (@p198) :args (@t63)) % 0.24/0.43 (step @p171 :rule implies_elim :premises (@p169)) % 0.24/0.43 (step @p172 false :rule chain_m_resolution :premises (@p171 @p166 @p157) :args (false (@list false false) (@list @t59 @t18))) % 0.24/0.43 ) % 0.24/0.43 % SZS output end Proof % 0.24/0.43 % cvc5 exiting %------------------------------------------------------------------------------