%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET909+1 : TPTP v9.2.1. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:48:57 AM UTC 2026 % Result : Theorem 0.61s 0.86s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET909+1 : TPTP v9.2.1. Released v3.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n025.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 16:17:31 EDT 2026 % 0.15/0.34 % CPUTime : % 0.27/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.61/0.86 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.61/0.86 % SZS status Theorem % 0.61/0.86 % SZS output start Proof % 0.61/0.86 ( % 0.61/0.86 (declare-sort $$unsorted 0) % 0.61/0.86 (declare-const tptp.empty_set $$unsorted) % 0.61/0.86 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.61/0.86 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.61/0.86 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 0.61/0.86 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.61/0.86 (define @t1 () (@var "A" $$unsorted)) % 0.61/0.86 (define @t2 () (@var "B" $$unsorted)) % 0.61/0.86 (define @t3 () (not (tptp.in @t2 @t1))) % 0.61/0.86 (define @t4 () (@list @t1 @t2)) % 0.61/0.86 (define @t5 () (tptp.unordered_pair @t1 @t2)) % 0.61/0.86 (define @t6 () (tptp.set_union2 @t2 @t1)) % 0.61/0.86 (define @t7 () (tptp.set_union2 @t1 @t2)) % 0.61/0.86 (define @t8 () (@list @t2)) % 0.61/0.86 (define @t9 () (@list @t1)) % 0.61/0.86 (define @t10 () (forall @t9 (= (= @t1 tptp.empty_set) (forall @t8 @t3)))) % 0.61/0.86 (define @t11 () (@var "D" $$unsorted)) % 0.61/0.86 (define @t12 () (or (= @t11 @t1) (= @t11 @t2))) % 0.61/0.86 (define @t13 () (@var "C" $$unsorted)) % 0.61/0.86 (define @t14 () (tptp.in @t11 @t13)) % 0.61/0.86 (define @t15 () (= @t14 @t12)) % 0.61/0.86 (define @t16 () (@list @t11)) % 0.61/0.86 (define @t17 () (forall @t16 @t15)) % 0.61/0.86 (define @t18 () (= (= @t13 @t5) @t17)) % 0.61/0.86 (define @t19 () (@list @t1 @t2 @t13)) % 0.61/0.86 (define @t20 () (forall @t19 @t18)) % 0.61/0.86 (define @t21 () (forall @t16 (= @t14 (or (tptp.in @t11 @t1) (tptp.in @t11 @t2))))) % 0.61/0.86 (define @t22 () (= (= @t13 @t7) @t21)) % 0.61/0.86 (define @t23 () (forall @t19 @t22)) % 0.61/0.86 (define @t24 () (tptp.empty @t1)) % 0.61/0.86 (define @t25 () (not @t24)) % 0.61/0.86 (define @t26 () (tptp.set_union2 @t5 @t13)) % 0.61/0.86 (define @t27 () (not (= @t26 tptp.empty_set))) % 0.61/0.86 (define @t28 () (forall @t19 @t27)) % 0.61/0.86 (define @t29 () (not @t28)) % 0.61/0.86 (define @t30 () (forall @t8 (not (tptp.in @t2 tptp.empty_set)))) % 0.61/0.86 (define @t31 () (= (= tptp.empty_set tptp.empty_set) @t30)) % 0.61/0.86 (define @t32 () (@list false)) % 0.61/0.86 (define @t33 () (@list @t10)) % 0.61/0.86 (define @t34 () (forall @t19 (not (= tptp.empty_set @t26)))) % 0.61/0.86 (define @t35 () (@quantifiers_skolemize @t34 1)) % 0.61/0.86 (define @t36 () (@list @t35)) % 0.61/0.86 (define @t37 () (@quantifiers_skolemize @t34 0)) % 0.61/0.86 (define @t38 () (or (= @t37 @t11) (= @t35 @t11))) % 0.61/0.86 (define @t39 () (tptp.in @t11 tptp.empty_set)) % 0.61/0.86 (define @t40 () (= @t39 @t38)) % 0.61/0.86 (define @t41 () (forall @t16 @t40)) % 0.61/0.86 (define @t42 () (tptp.unordered_pair @t37 @t35)) % 0.61/0.86 (define @t43 () (= @t42 tptp.empty_set)) % 0.61/0.86 (define @t44 () (= @t43 @t41)) % 0.61/0.86 (define @t45 () (forall @t19 (= (= @t5 @t13) (forall @t16 (= @t14 (or (= @t1 @t11) (= @t2 @t11))))))) % 0.61/0.86 (define @t46 () (forall @t16 (= @t39 (or (= @t11 @t37) (= @t11 @t35))))) % 0.61/0.86 (define @t47 () (= tptp.empty_set @t42)) % 0.61/0.86 (define @t48 () (= @t47 @t46)) % 0.61/0.86 (define @t49 () (forall @t8 (not (tptp.in @t2 @t42)))) % 0.61/0.86 (define @t50 () (= @t43 @t49)) % 0.61/0.86 (define @t51 () (= @t49 @t47)) % 0.61/0.86 (define @t52 () (= @t7 @t13)) % 0.61/0.86 (define @t53 () (@quantifiers_skolemize @t34 2)) % 0.61/0.86 (define @t54 () (tptp.set_union2 @t53 @t42)) % 0.61/0.86 (define @t55 () (= tptp.empty_set @t54)) % 0.61/0.86 (define @t56 () (forall @t16 (= @t39 (or (tptp.in @t11 @t53) (tptp.in @t11 @t42))))) % 0.61/0.86 (define @t57 () (= @t54 tptp.empty_set)) % 0.61/0.86 (define @t58 () (forall @t19 (= @t21 @t52))) % 0.61/0.86 (define @t59 () (= @t56 @t57)) % 0.61/0.86 (define @t60 () (= @t56 @t55)) % 0.61/0.86 (define @t61 () (= tptp.empty_set (tptp.set_union2 @t42 @t53))) % 0.61/0.86 (define @t62 () (not @t34)) % 0.61/0.86 (define @t63 () (not (not @t61))) % 0.61/0.86 (define @t64 () (@list true)) % 0.61/0.86 (define @t65 () (@list false false)) % 0.61/0.86 (define @t66 () (@quantifiers_skolemize @t49 0)) % 0.61/0.86 (define @t67 () (@list @t66)) % 0.61/0.86 (define @t68 () (tptp.in @t66 @t42)) % 0.61/0.86 (define @t69 () (or (tptp.in @t66 @t53) @t68)) % 0.61/0.86 (define @t70 () (tptp.in @t66 tptp.empty_set)) % 0.61/0.86 (define @t71 () (= @t70 @t69)) % 0.61/0.86 (define @t72 () (not @t69)) % 0.61/0.86 (define @t73 () (not @t68)) % 0.61/0.86 (define @t74 () (not @t49)) % 0.61/0.86 (define @t75 () (not @t73)) % 0.61/0.86 (define @t76 () (tptp.in @t35 tptp.empty_set)) % 0.61/0.86 (define @t77 () (or (= @t35 @t37) (= @t35 @t35))) % 0.61/0.86 (define @t78 () (= @t76 @t77)) % 0.61/0.86 (assume @p1 (forall @t4 (=> (tptp.in @t1 @t2) @t3))) % 0.61/0.86 (assume @p2 (forall @t4 (= @t5 (tptp.unordered_pair @t2 @t1)))) % 0.61/0.86 (assume @p3 (forall @t4 (= @t7 @t6))) % 0.61/0.86 (assume @p4 @t10) % 0.61/0.86 (assume @p5 @t20) % 0.61/0.86 (assume @p6 @t23) % 0.61/0.86 (assume @p7 (tptp.empty tptp.empty_set)) % 0.61/0.86 (assume @p8 (forall @t4 (=> @t25 (not (tptp.empty @t7))))) % 0.61/0.86 (assume @p9 (forall @t4 (=> @t25 (not (tptp.empty @t6))))) % 0.61/0.86 (assume @p10 (forall @t4 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.61/0.86 (assume @p11 (exists @t9 @t24)) % 0.61/0.86 (assume @p12 (exists @t9 @t25)) % 0.61/0.86 (assume @p13 @t29) % 0.61/0.86 (assume @p14 true) % 0.61/0.86 (step @p15 :rule bool-eq-true :args (@t30)) % 0.61/0.86 (step @p16 :rule eq-symm :args (true @t30)) % 0.61/0.86 (step @p17 :rule trans :premises (@p16 @p15)) % 0.61/0.86 (step @p18 :rule refl :args (@t30)) % 0.61/0.86 (step @p19 :rule eq-refl :args (tptp.empty_set)) % 0.61/0.86 (step @p20 :rule cong :premises (@p19 @p18) :args (@t31)) % 0.61/0.86 (step @p21 :rule trans :premises (@p20 @p17)) % 0.61/0.86 (step @p22 :rule refl :args (@t10)) % 0.61/0.86 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t10 @t31))) % 0.61/0.86 (assume-push @p165 @t10) % 0.61/0.86 (step @p25 :rule instantiate :premises (@p4) :args ((@list tptp.empty_set))) % 0.61/0.86 (step-pop @p166 :rule scope :premises (@p25)) % 0.61/0.86 (step @p26 :rule process_scope :premises (@p166) :args (@t31)) % 0.61/0.86 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 0.61/0.86 (step @p29 :rule implies_elim :premises (@p28)) % 0.61/0.86 (step @p30 :rule chain_m_resolution :premises (@p29 @p4) :args (@t30 @t32 @t33)) % 0.61/0.86 (step @p31 :rule instantiate :premises (@p30) :args (@t36)) % 0.61/0.86 (step @p32 :rule eq-symm :args (@t11 @t2)) % 0.61/0.86 (step @p33 :rule eq-symm :args (@t11 @t1)) % 0.61/0.86 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t12)) % 0.61/0.86 (step @p35 :rule refl :args (@t14)) % 0.61/0.86 (step @p36 :rule cong :premises (@p35 @p34) :args (@t15)) % 0.61/0.86 (step @p37 :rule cong :premises (@p36) :args (@t17)) % 0.61/0.86 (step @p38 :rule eq-symm :args (@t13 @t5)) % 0.61/0.86 (step @p39 :rule cong :premises (@p38 @p37) :args (@t18)) % 0.61/0.86 (step @p40 :rule cong :premises (@p39) :args (@t20)) % 0.61/0.86 (step @p41 :rule eq_resolve :premises (@p5 @p40)) % 0.61/0.86 (step @p42 :rule eq-symm :args (@t35 @t11)) % 0.61/0.86 (step @p43 :rule eq-symm :args (@t37 @t11)) % 0.61/0.86 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t38)) % 0.61/0.86 (step @p45 :rule refl :args (@t39)) % 0.61/0.86 (step @p46 :rule cong :premises (@p45 @p44) :args (@t40)) % 0.61/0.86 (step @p47 :rule cong :premises (@p46) :args (@t41)) % 0.61/0.86 (step @p48 :rule eq-symm :args (@t42 tptp.empty_set)) % 0.61/0.86 (step @p49 :rule cong :premises (@p48 @p47) :args (@t44)) % 0.61/0.86 (step @p50 :rule refl :args (@t45)) % 0.61/0.86 (step @p51 :rule cong :premises (@p50 @p49) :args ((=> @t45 @t44))) % 0.61/0.86 (assume-push @p167 @t45) % 0.61/0.86 (step @p53 :rule instantiate :premises (@p41) :args ((@list @t37 @t35 tptp.empty_set))) % 0.61/0.86 (step-pop @p168 :rule scope :premises (@p53)) % 0.61/0.86 (step @p54 :rule process_scope :premises (@p168) :args (@t44)) % 0.61/0.86 (step @p56 :rule eq_resolve :premises (@p54 @p51)) % 0.61/0.86 (step @p57 :rule implies_elim :premises (@p56)) % 0.61/0.86 (step @p58 :rule chain_m_resolution :premises (@p57 @p41) :args (@t48 @t32 (@list @t45))) % 0.61/0.86 (step @p59 :rule eq-symm :args (@t47 @t49)) % 0.61/0.86 (step @p60 :rule refl :args (@t49)) % 0.61/0.86 (step @p61 :rule cong :premises (@p48 @p60) :args (@t50)) % 0.61/0.86 (step @p62 :rule trans :premises (@p61 @p59)) % 0.61/0.86 (step @p63 :rule cong :premises (@p22 @p62) :args ((=> @t10 @t50))) % 0.61/0.86 (assume-push @p169 @t10) % 0.61/0.86 (step @p65 :rule instantiate :premises (@p4) :args ((@list @t42))) % 0.61/0.86 (step-pop @p170 :rule scope :premises (@p65)) % 0.61/0.86 (step @p66 :rule process_scope :premises (@p170) :args (@t50)) % 0.61/0.86 (step @p68 :rule eq_resolve :premises (@p66 @p63)) % 0.61/0.86 (step @p69 :rule implies_elim :premises (@p68)) % 0.61/0.86 (step @p70 :rule chain_m_resolution :premises (@p69 @p4) :args (@t51 @t32 @t33)) % 0.61/0.86 (step @p71 :rule eq-symm :args (@t52 @t21)) % 0.61/0.86 (step @p72 :rule refl :args (@t21)) % 0.61/0.86 (step @p73 :rule eq-symm :args (@t13 @t7)) % 0.61/0.86 (step @p74 :rule cong :premises (@p73 @p72) :args (@t22)) % 0.61/0.86 (step @p75 :rule trans :premises (@p74 @p71)) % 0.61/0.86 (step @p76 :rule cong :premises (@p75) :args (@t23)) % 0.61/0.86 (step @p77 :rule eq_resolve :premises (@p6 @p76)) % 0.61/0.86 (step @p78 :rule eq-symm :args (@t55 @t56)) % 0.61/0.86 (step @p79 :rule refl :args (@t56)) % 0.61/0.86 (step @p80 :rule eq-symm :args (@t54 tptp.empty_set)) % 0.61/0.86 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t57 @t56))) % 0.61/0.86 (step @p82 :rule trans :premises (@p81 @p78)) % 0.61/0.86 (step @p83 :rule eq-symm :args (@t56 @t57)) % 0.61/0.86 (step @p84 :rule trans :premises (@p83 @p82)) % 0.61/0.86 (step @p85 :rule refl :args (@t58)) % 0.61/0.86 (step @p86 :rule cong :premises (@p85 @p84) :args ((=> @t58 @t59))) % 0.61/0.86 (assume-push @p171 @t58) % 0.61/0.86 (step @p88 :rule instantiate :premises (@p77) :args ((@list @t53 @t42 tptp.empty_set))) % 0.61/0.86 (step-pop @p172 :rule scope :premises (@p88)) % 0.61/0.86 (step @p89 :rule process_scope :premises (@p172) :args (@t59)) % 0.61/0.86 (step @p91 :rule eq_resolve :premises (@p89 @p86)) % 0.61/0.86 (step @p92 :rule implies_elim :premises (@p91)) % 0.61/0.86 (step @p93 :rule chain_m_resolution :premises (@p92 @p77) :args (@t60 @t32 (@list @t58))) % 0.61/0.86 (step @p94 :rule instantiate :premises (@p3) :args ((@list @t42 @t53))) % 0.61/0.86 (step @p95 :rule eq-symm :args (@t26 tptp.empty_set)) % 0.61/0.86 (step @p96 :rule cong :premises (@p95) :args (@t27)) % 0.61/0.86 (step @p97 :rule cong :premises (@p96) :args (@t28)) % 0.61/0.86 (step @p98 :rule cong :premises (@p97) :args (@t29)) % 0.61/0.86 (step @p99 :rule eq_resolve :premises (@p13 @p98)) % 0.61/0.86 (step @p100 :rule refl :args (@t61)) % 0.61/0.86 (step @p101 :rule bool-double-not-elim :args (@t34)) % 0.61/0.86 (step @p102 :rule nary_cong :premises (@p101 @p100) :args ((or (not @t62) @t61))) % 0.61/0.86 (step @p103 :rule bool-double-not-elim :args (@t61)) % 0.61/0.86 (step @p104 :rule refl :args (@t62)) % 0.61/0.86 (step @p105 :rule cong :premises (@p104 @p103) :args ((=> @t62 @t63))) % 0.61/0.86 (assume-push @p173 @t62) % 0.61/0.86 (step @p107 :rule skolemize :premises (@p99)) % 0.61/0.86 (step-pop @p174 :rule scope :premises (@p107)) % 0.61/0.86 (step @p108 :rule process_scope :premises (@p174) :args (@t63)) % 0.61/0.86 (step @p110 :rule eq_resolve :premises (@p108 @p105)) % 0.61/0.86 (step @p111 :rule implies_elim :premises (@p110)) % 0.61/0.86 (step @p112 :rule eq_resolve :premises (@p111 @p102)) % 0.61/0.86 (step @p113 :rule chain_m_resolution :premises (@p112 @p99) :args (@t61 @t64 (@list @t34))) % 0.61/0.86 (step @p114 :rule trans :premises (@p113 @p94)) % 0.61/0.86 (step @p115 :rule cnf_equiv_pos2 :args (@t60)) % 0.61/0.86 (step @p116 :rule reordering :premises (@p115) :args ((or @t56 (not @t55) (not @t60)))) % 0.61/0.86 (step @p117 :rule chain_m_resolution :premises (@p116 @p114 @p93) :args (@t56 @t65 (@list @t55 @t60))) % 0.61/0.86 (step @p118 :rule instantiate :premises (@p117) :args (@t67)) % 0.61/0.86 (step @p119 :rule instantiate :premises (@p30) :args (@t67)) % 0.61/0.86 (step @p120 :rule cnf_equiv_pos2 :args (@t71)) % 0.61/0.86 (step @p121 :rule reordering :premises (@p120) :args ((or @t70 @t72 (not @t71)))) % 0.61/0.86 (step @p122 :rule chain_m_resolution :premises (@p121 @p119 @p118) :args (@t72 (@list true false) (@list @t70 @t71))) % 0.61/0.86 (step @p123 :rule cnf_or_neg :args (@t69 1)) % 0.61/0.86 (step @p124 :rule reordering :premises (@p123) :args ((or @t73 @t69))) % 0.61/0.86 (step @p125 :rule chain_m_resolution :premises (@p124 @p122) :args (@t73 @t64 (@list @t69))) % 0.61/0.86 (step @p126 :rule refl :args (@t68)) % 0.61/0.86 (step @p127 :rule bool-double-not-elim :args (@t49)) % 0.61/0.86 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or (not @t74) @t68))) % 0.61/0.86 (step @p129 :rule bool-double-not-elim :args (@t68)) % 0.61/0.86 (step @p130 :rule refl :args (@t74)) % 0.61/0.86 (step @p131 :rule cong :premises (@p130 @p129) :args ((=> @t74 @t75))) % 0.61/0.86 (assume-push @p175 @t74) % 0.61/0.86 (step @p133 :rule skolemize :premises (@p175)) % 0.61/0.86 (step-pop @p176 :rule scope :premises (@p133)) % 0.61/0.86 (step @p134 :rule process_scope :premises (@p176) :args (@t75)) % 0.61/0.86 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 0.61/0.86 (step @p137 :rule implies_elim :premises (@p136)) % 0.61/0.86 (step @p138 :rule eq_resolve :premises (@p137 @p128)) % 0.61/0.86 (step @p139 :rule chain_m_resolution :premises (@p138 @p125) :args (@t49 @t64 (@list @t68))) % 0.61/0.86 (step @p140 :rule cnf_equiv_pos1 :args (@t51)) % 0.61/0.86 (step @p141 :rule reordering :premises (@p140) :args ((or @t47 @t74 (not @t51)))) % 0.61/0.86 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p70) :args (@t47 @t65 (@list @t49 @t51))) % 0.61/0.86 (step @p143 :rule cnf_equiv_pos1 :args (@t48)) % 0.61/0.86 (step @p144 :rule reordering :premises (@p143) :args ((or (not @t47) @t46 (not @t48)))) % 0.61/0.86 (step @p145 :rule chain_m_resolution :premises (@p144 @p142 @p58) :args (@t46 @t65 (@list @t47 @t48))) % 0.61/0.86 (step @p146 :rule bool-eq-true :args (@t76)) % 0.61/0.86 (step @p147 :rule absorb :args ((= (or (= @t37 @t35) true) true))) % 0.61/0.86 (step @p148 :rule eq-refl :args (@t35)) % 0.61/0.86 (step @p149 :rule eq-symm :args (@t35 @t37)) % 0.61/0.86 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t77)) % 0.61/0.86 (step @p151 :rule trans :premises (@p150 @p147)) % 0.61/0.86 (step @p152 :rule refl :args (@t76)) % 0.61/0.86 (step @p153 :rule cong :premises (@p152 @p151) :args (@t78)) % 0.61/0.86 (step @p154 :rule trans :premises (@p153 @p146)) % 0.61/0.86 (step @p155 :rule refl :args (@t46)) % 0.61/0.86 (step @p156 :rule cong :premises (@p155 @p154) :args ((=> @t46 @t78))) % 0.61/0.86 (assume-push @p177 @t46) % 0.61/0.86 (step @p158 :rule instantiate :premises (@p177) :args (@t36)) % 0.61/0.86 (step-pop @p178 :rule scope :premises (@p158)) % 0.61/0.86 (step @p159 :rule process_scope :premises (@p178) :args (@t78)) % 0.61/0.86 (step @p161 :rule eq_resolve :premises (@p159 @p156)) % 0.61/0.86 (step @p162 :rule implies_elim :premises (@p161)) % 0.61/0.86 (step @p163 :rule reordering :premises (@p162) :args ((or @t76 (not @t46)))) % 0.61/0.86 (step @p164 false :rule chain_m_resolution :premises (@p163 @p145 @p31) :args (false (@list false true) (@list @t46 @t76))) % 0.61/0.86 ) % 0.61/0.86 % SZS output end Proof % 0.61/0.86 % cvc5 exiting %------------------------------------------------------------------------------