%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET872+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n029.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 08:48:53 AM UTC 2026 % Result : Theorem 15.42s 15.68s % Output : Proof 15.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET872+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:16:17 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.42/15.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.42/15.68 --- Run --no-e-matching --full-saturate-quant at 6... % 15.42/15.68 % SZS status Theorem % 15.42/15.68 % SZS output start Proof % 15.42/15.68 ( % 15.42/15.68 (declare-sort $$unsorted 0) % 15.42/15.68 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.42/15.68 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 15.42/15.68 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 15.42/15.68 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.42/15.68 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.42/15.68 (define @t1 () (@var "A" $$unsorted)) % 15.42/15.68 (define @t2 () (@var "B" $$unsorted)) % 15.42/15.68 (define @t3 () (@list @t1 @t2)) % 15.42/15.68 (define @t4 () (tptp.unordered_pair @t1 @t2)) % 15.42/15.68 (define @t5 () (@var "C" $$unsorted)) % 15.42/15.68 (define @t6 () (tptp.in @t5 @t2)) % 15.42/15.68 (define @t7 () (= @t6 (= @t5 @t1))) % 15.42/15.68 (define @t8 () (@list @t5)) % 15.42/15.68 (define @t9 () (forall @t8 @t7)) % 15.42/15.68 (define @t10 () (tptp.singleton @t1)) % 15.42/15.68 (define @t11 () (= @t2 @t10)) % 15.42/15.68 (define @t12 () (= @t11 @t9)) % 15.42/15.68 (define @t13 () (forall @t3 @t12)) % 15.42/15.68 (define @t14 () (@var "D" $$unsorted)) % 15.42/15.69 (define @t15 () (or (= @t14 @t1) (= @t14 @t2))) % 15.42/15.69 (define @t16 () (tptp.in @t14 @t5)) % 15.42/15.69 (define @t17 () (= @t16 @t15)) % 15.42/15.69 (define @t18 () (@list @t14)) % 15.42/15.69 (define @t19 () (forall @t18 @t17)) % 15.42/15.69 (define @t20 () (= (= @t5 @t4) @t19)) % 15.42/15.69 (define @t21 () (@list @t1 @t2 @t5)) % 15.42/15.69 (define @t22 () (forall @t21 @t20)) % 15.42/15.69 (define @t23 () (tptp.in @t5 @t1)) % 15.42/15.69 (define @t24 () (forall @t8 (=> @t23 @t6))) % 15.42/15.69 (define @t25 () (tptp.subset @t1 @t2)) % 15.42/15.69 (define @t26 () (= @t25 @t24)) % 15.42/15.69 (define @t27 () (forall @t3 @t26)) % 15.42/15.69 (define @t28 () (tptp.empty @t1)) % 15.42/15.69 (define @t29 () (@list @t1)) % 15.42/15.69 (define @t30 () (forall @t3 (tptp.subset @t10 @t4))) % 15.42/15.69 (define @t31 () (@quantifiers_skolemize @t30 0)) % 15.42/15.69 (define @t32 () (tptp.singleton @t31)) % 15.42/15.69 (define @t33 () (tptp.in @t5 @t32)) % 15.42/15.69 (define @t34 () (forall @t8 (= (= @t5 @t31) @t33))) % 15.42/15.69 (define @t35 () (= @t31 @t5)) % 15.42/15.69 (define @t36 () (forall @t8 (= @t33 @t35))) % 15.42/15.69 (define @t37 () (= (= @t32 @t32) @t36)) % 15.42/15.69 (define @t38 () (forall @t3 (= @t11 (forall @t8 (= @t6 (= @t1 @t5)))))) % 15.42/15.69 (define @t39 () (@list false)) % 15.42/15.69 (define @t40 () (@quantifiers_skolemize @t30 1)) % 15.42/15.69 (define @t41 () (tptp.unordered_pair @t31 @t40)) % 15.42/15.69 (define @t42 () (forall @t8 (or (not @t33) (tptp.in @t5 @t41)))) % 15.42/15.69 (define @t43 () (tptp.subset @t32 @t41)) % 15.42/15.69 (define @t44 () (= @t43 @t42)) % 15.42/15.69 (define @t45 () (not @t42)) % 15.42/15.69 (define @t46 () (@list true false)) % 15.42/15.69 (define @t47 () (@quantifiers_skolemize @t42 0)) % 15.42/15.69 (define @t48 () (tptp.in @t47 @t41)) % 15.42/15.69 (define @t49 () (tptp.in @t47 @t32)) % 15.42/15.69 (define @t50 () (not @t49)) % 15.42/15.69 (define @t51 () (or @t50 @t48)) % 15.42/15.69 (define @t52 () (not @t48)) % 15.42/15.69 (define @t53 () (@list true)) % 15.42/15.69 (define @t54 () (@list @t51)) % 15.42/15.69 (define @t55 () (tptp.in @t14 @t41)) % 15.42/15.69 (define @t56 () (forall @t18 (= @t55 (or (= @t14 @t31) (= @t14 @t40))))) % 15.42/15.69 (define @t57 () (or (= @t31 @t14) (= @t40 @t14))) % 15.42/15.69 (define @t58 () (= @t55 @t57)) % 15.42/15.69 (define @t59 () (forall @t18 @t58)) % 15.42/15.69 (define @t60 () (= (= @t41 @t41) @t59)) % 15.42/15.69 (define @t61 () (forall @t21 (= (= @t4 @t5) (forall @t18 (= @t16 (or (= @t1 @t14) (= @t2 @t14))))))) % 15.42/15.69 (define @t62 () (tptp.in @t31 @t41)) % 15.42/15.69 (define @t63 () (= @t31 @t40)) % 15.42/15.69 (define @t64 () (or (= @t31 @t31) @t63)) % 15.42/15.69 (define @t65 () (= @t62 @t64)) % 15.42/15.69 (define @t66 () (= @t31 @t47)) % 15.42/15.69 (define @t67 () (not @t66)) % 15.42/15.69 (define @t68 () (not @t62)) % 15.42/15.69 (define @t69 () (and @t52 @t66 @t62)) % 15.42/15.69 (define @t70 () (@list false true)) % 15.42/15.69 (define @t71 () (= @t49 @t66)) % 15.42/15.69 (define @t72 () (not @t71)) % 15.42/15.69 (define @t73 () (= @t47 @t31)) % 15.42/15.69 (define @t74 () (= @t73 @t49)) % 15.42/15.69 (assume @p1 (forall @t3 (=> (tptp.in @t1 @t2) (not (tptp.in @t2 @t1))))) % 15.42/15.69 (assume @p2 (forall @t3 (= @t4 (tptp.unordered_pair @t2 @t1)))) % 15.42/15.69 (assume @p3 @t13) % 15.42/15.69 (assume @p4 @t22) % 15.42/15.69 (assume @p5 @t27) % 15.42/15.69 (assume @p6 (exists @t29 @t28)) % 15.42/15.69 (assume @p7 (exists @t29 (not @t28))) % 15.42/15.69 (assume @p8 (forall @t3 (tptp.subset @t1 @t1))) % 15.42/15.69 (assume @p9 (not @t30)) % 15.42/15.69 (assume @p10 true) % 15.42/15.69 (step @p11 :rule eq-symm :args (@t5 @t1)) % 15.42/15.69 (step @p12 :rule refl :args (@t6)) % 15.42/15.69 (step @p13 :rule cong :premises (@p12 @p11) :args (@t7)) % 15.42/15.69 (step @p14 :rule cong :premises (@p13) :args (@t9)) % 15.42/15.69 (step @p15 :rule refl :args (@t11)) % 15.42/15.69 (step @p16 :rule cong :premises (@p15 @p14) :args (@t12)) % 15.42/15.69 (step @p17 :rule cong :premises (@p16) :args (@t13)) % 15.42/15.69 (step @p18 :rule eq_resolve :premises (@p3 @p17)) % 15.42/15.69 (step @p19 :rule bool-eq-true :args (@t34)) % 15.42/15.69 (step @p20 :rule eq-symm :args (true @t34)) % 15.42/15.69 (step @p21 :rule trans :premises (@p20 @p19)) % 15.42/15.69 (step @p22 :rule refl :args (@t33)) % 15.42/15.69 (step @p23 :rule eq-symm :args (@t31 @t5)) % 15.42/15.69 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t35 @t33))) % 15.42/15.69 (step @p25 :rule eq-symm :args (@t33 @t35)) % 15.42/15.69 (step @p26 :rule trans :premises (@p25 @p24)) % 15.42/15.69 (step @p27 :rule cong :premises (@p26) :args (@t36)) % 15.42/15.69 (step @p28 :rule eq-refl :args (@t32)) % 15.42/15.69 (step @p29 :rule cong :premises (@p28 @p27) :args (@t37)) % 15.42/15.69 (step @p30 :rule trans :premises (@p29 @p21)) % 15.42/15.69 (step @p31 :rule refl :args (@t38)) % 15.42/15.69 (step @p32 :rule cong :premises (@p31 @p30) :args ((=> @t38 @t37))) % 15.42/15.69 (assume-push @p159 @t38) % 15.42/15.69 (step @p34 :rule instantiate :premises (@p18) :args ((@list @t31 @t32))) % 15.42/15.69 (step-pop @p160 :rule scope :premises (@p34)) % 15.42/15.69 (step @p35 :rule process_scope :premises (@p160) :args (@t37)) % 15.42/15.69 (step @p37 :rule eq_resolve :premises (@p35 @p32)) % 15.42/15.69 (step @p38 :rule implies_elim :premises (@p37)) % 15.42/15.69 (step @p39 :rule chain_m_resolution :premises (@p38 @p18) :args (@t34 @t39 (@list @t38))) % 15.42/15.69 (step @p40 :rule bool-impl-elim :args (@t23 @t6)) % 15.42/15.69 (step @p41 :rule cong :premises (@p40) :args (@t24)) % 15.42/15.69 (step @p42 :rule refl :args (@t25)) % 15.42/15.69 (step @p43 :rule cong :premises (@p42 @p41) :args (@t26)) % 15.42/15.69 (step @p44 :rule cong :premises (@p43) :args (@t27)) % 15.42/15.69 (step @p45 :rule eq_resolve :premises (@p5 @p44)) % 15.42/15.69 (step @p46 :rule instantiate :premises (@p45) :args ((@list @t32 @t41))) % 15.42/15.69 (step @p47 :rule skolemize :premises (@p9)) % 15.42/15.69 (step @p48 :rule cnf_equiv_pos2 :args (@t44)) % 15.42/15.69 (step @p49 :rule reordering :premises (@p48) :args ((or @t43 @t45 (not @t44)))) % 15.42/15.69 (step @p50 :rule chain_m_resolution :premises (@p49 @p47 @p46) :args (@t45 @t46 (@list @t43 @t44))) % 15.42/15.69 (step @p51 :rule skolemize :premises (@p50)) % 15.42/15.69 (step @p52 :rule cnf_or_neg :args (@t51 1)) % 15.42/15.69 (step @p53 :rule chain_m_resolution :premises (@p52 @p51) :args (@t52 @t53 @t54)) % 15.42/15.69 (step @p54 :rule eq-symm :args (@t14 @t2)) % 15.42/15.69 (step @p55 :rule eq-symm :args (@t14 @t1)) % 15.42/15.69 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t15)) % 15.42/15.69 (step @p57 :rule refl :args (@t16)) % 15.42/15.69 (step @p58 :rule cong :premises (@p57 @p56) :args (@t17)) % 15.42/15.69 (step @p59 :rule cong :premises (@p58) :args (@t19)) % 15.42/15.69 (step @p60 :rule eq-symm :args (@t5 @t4)) % 15.42/15.69 (step @p61 :rule cong :premises (@p60 @p59) :args (@t20)) % 15.42/15.69 (step @p62 :rule cong :premises (@p61) :args (@t22)) % 15.42/15.69 (step @p63 :rule eq_resolve :premises (@p4 @p62)) % 15.42/15.69 (step @p64 :rule bool-eq-true :args (@t56)) % 15.42/15.69 (step @p65 :rule eq-symm :args (true @t56)) % 15.42/15.69 (step @p66 :rule trans :premises (@p65 @p64)) % 15.42/15.69 (step @p67 :rule eq-symm :args (@t40 @t14)) % 15.42/15.69 (step @p68 :rule eq-symm :args (@t31 @t14)) % 15.42/15.69 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t57)) % 15.42/15.69 (step @p70 :rule refl :args (@t55)) % 15.42/15.69 (step @p71 :rule cong :premises (@p70 @p69) :args (@t58)) % 15.42/15.69 (step @p72 :rule cong :premises (@p71) :args (@t59)) % 15.42/15.69 (step @p73 :rule eq-refl :args (@t41)) % 15.42/15.69 (step @p74 :rule cong :premises (@p73 @p72) :args (@t60)) % 15.42/15.69 (step @p75 :rule trans :premises (@p74 @p66)) % 15.42/15.69 (step @p76 :rule refl :args (@t61)) % 15.42/15.69 (step @p77 :rule cong :premises (@p76 @p75) :args ((=> @t61 @t60))) % 15.42/15.69 (assume-push @p161 @t61) % 15.42/15.69 (step @p79 :rule instantiate :premises (@p63) :args ((@list @t31 @t40 @t41))) % 15.42/15.69 (step-pop @p162 :rule scope :premises (@p79)) % 15.42/15.69 (step @p80 :rule process_scope :premises (@p162) :args (@t60)) % 15.42/15.69 (step @p82 :rule eq_resolve :premises (@p80 @p77)) % 15.42/15.69 (step @p83 :rule implies_elim :premises (@p82)) % 15.42/15.69 (step @p84 :rule chain_m_resolution :premises (@p83 @p63) :args (@t56 @t39 (@list @t61))) % 15.42/15.69 (step @p85 :rule bool-eq-true :args (@t62)) % 15.42/15.69 (step @p86 :rule absorb :args ((= (or true @t63) true))) % 15.42/15.69 (step @p87 :rule refl :args (@t63)) % 15.42/15.69 (step @p88 :rule eq-refl :args (@t31)) % 15.42/15.69 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t64)) % 15.42/15.69 (step @p90 :rule trans :premises (@p89 @p86)) % 15.42/15.69 (step @p91 :rule refl :args (@t62)) % 15.42/15.69 (step @p92 :rule cong :premises (@p91 @p90) :args (@t65)) % 15.42/15.69 (step @p93 :rule trans :premises (@p92 @p85)) % 15.42/15.69 (step @p94 :rule refl :args (@t56)) % 15.42/15.69 (step @p95 :rule cong :premises (@p94 @p93) :args ((=> @t56 @t65))) % 15.42/15.69 (assume-push @p163 @t56) % 15.42/15.69 (step @p97 :rule instantiate :premises (@p84) :args ((@list @t31))) % 15.42/15.69 (step-pop @p164 :rule scope :premises (@p97)) % 15.42/15.69 (step @p98 :rule process_scope :premises (@p164) :args (@t65)) % 15.42/15.69 (step @p100 :rule eq_resolve :premises (@p98 @p95)) % 15.42/15.69 (step @p101 :rule implies_elim :premises (@p100)) % 15.42/15.69 (step @p102 :rule chain_m_resolution :premises (@p101 @p84) :args (@t62 @t39 (@list @t56))) % 15.42/15.69 (step @p103 :rule refl :args (@t67)) % 15.42/15.69 (step @p104 :rule bool-double-not-elim :args (@t48)) % 15.42/15.69 (step @p105 :rule refl :args (@t68)) % 15.42/15.69 (step @p106 :rule nary_cong :premises (@p105 @p104 @p103) :args ((or @t68 (not @t52) @t67))) % 15.42/15.69 (assume-push @p165 @t52) % 15.42/15.69 (assume-push @p166 @t66) % 15.42/15.69 (assume-push @p167 @t62) % 15.42/15.69 (step @p110 :rule evaluate :args ((= true false))) % 15.42/15.69 (step @p111 :rule false_intro :premises (@p53)) % 15.42/15.69 (step @p112 :rule refl :args (@t41)) % 15.42/15.69 (step @p113 :rule cong :premises (@p166 @p112) :args (@t62)) % 15.42/15.69 (step @p114 :rule true_intro :premises (@p102)) % 15.42/15.69 (step @p115 :rule symm :premises (@p114)) % 15.42/15.69 (step @p116 :rule trans :premises (@p115 @p113 @p111)) % 15.42/15.69 (step @p117 false :rule eq_resolve :premises (@p116 @p110)) % 15.42/15.69 (step-pop @p168 :rule scope :premises (@p117)) % 15.42/15.69 (step-pop @p169 :rule scope :premises (@p168)) % 15.42/15.69 (step-pop @p170 :rule scope :premises (@p169)) % 15.42/15.69 (step @p118 :rule process_scope :premises (@p170) :args (false)) % 15.42/15.69 (assume-push @p171 @t62) % 15.42/15.69 (assume-push @p172 @t52) % 15.42/15.69 (assume-push @p173 @t66) % 15.42/15.69 (step @p125 :rule and_intro :premises (@p53 @p173 @p102)) % 15.42/15.69 (step-pop @p174 :rule scope :premises (@p125)) % 15.42/15.69 (step-pop @p175 :rule scope :premises (@p174)) % 15.42/15.69 (step-pop @p176 :rule scope :premises (@p175)) % 15.42/15.69 (step @p126 :rule process_scope :premises (@p176) :args (@t69)) % 15.42/15.69 (step @p130 :rule implies_elim :premises (@p126)) % 15.42/15.69 (step @p131 :rule resolution :premises (@p130 @p118) :args (true @t69)) % 15.42/15.69 (step @p132 :rule not_and :premises (@p131)) % 15.42/15.69 (step @p133 :rule eq_resolve :premises (@p132 @p106)) % 15.42/15.69 (step @p134 :rule chain_m_resolution :premises (@p133 @p102 @p53) :args (@t67 @t70 (@list @t62 @t48))) % 15.42/15.69 (step @p135 :rule bool-double-not-elim :args (@t49)) % 15.42/15.69 (step @p136 :rule refl :args (@t51)) % 15.42/15.69 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or @t51 (not @t50)))) % 15.42/15.69 (step @p138 :rule cnf_or_neg :args (@t51 0)) % 15.42/15.69 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 15.42/15.69 (step @p140 :rule reordering :premises (@p139) :args ((or @t49 @t51))) % 15.42/15.69 (step @p141 :rule chain_m_resolution :premises (@p140 @p51) :args (@t49 @t53 @t54)) % 15.42/15.69 (step @p142 :rule cnf_equiv_pos1 :args (@t71)) % 15.42/15.69 (step @p143 :rule reordering :premises (@p142) :args ((or @t50 @t66 @t72))) % 15.42/15.69 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p134) :args (@t72 @t70 (@list @t49 @t66))) % 15.42/15.69 (step @p145 :rule eq-symm :args (@t47 @t31)) % 15.42/15.69 (step @p146 :rule refl :args (@t49)) % 15.42/15.69 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t49 @t73))) % 15.42/15.69 (step @p148 :rule eq-symm :args (@t73 @t49)) % 15.42/15.69 (step @p149 :rule trans :premises (@p148 @p147)) % 15.42/15.69 (step @p150 :rule refl :args (@t34)) % 15.42/15.69 (step @p151 :rule cong :premises (@p150 @p149) :args ((=> @t34 @t74))) % 15.42/15.69 (assume-push @p177 @t34) % 15.42/15.69 (step @p153 :rule instantiate :premises (@p39) :args ((@list @t47))) % 15.42/15.69 (step-pop @p178 :rule scope :premises (@p153)) % 15.42/15.69 (step @p154 :rule process_scope :premises (@p178) :args (@t74)) % 15.42/15.69 (step @p156 :rule eq_resolve :premises (@p154 @p151)) % 15.42/15.69 (step @p157 :rule implies_elim :premises (@p156)) % 15.42/15.69 (step @p158 false :rule chain_m_resolution :premises (@p157 @p144 @p39) :args (false @t46 (@list @t71 @t34))) % 15.42/15.69 ) % 15.42/15.69 % SZS output end Proof % 15.42/15.69 % cvc5 exiting %------------------------------------------------------------------------------