%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET908+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 : n017.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 0.62s 0.80s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET908+1 : TPTP v9.2.1. Released v3.2.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.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 16:15:46 EDT 2026 % 0.17/0.35 % CPUTime : % 0.30/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.62/0.80 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.62/0.80 % SZS status Theorem % 0.62/0.80 % SZS output start Proof % 0.62/0.80 ( % 0.62/0.80 (declare-sort $$unsorted 0) % 0.62/0.80 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.62/0.80 (declare-const tptp.empty_set $$unsorted) % 0.62/0.80 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.62/0.80 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.80 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.62/0.80 (define @t1 () (@var "A" $$unsorted)) % 0.62/0.80 (define @t2 () (@var "B" $$unsorted)) % 0.62/0.80 (define @t3 () (not (tptp.in @t2 @t1))) % 0.62/0.80 (define @t4 () (@list @t1 @t2)) % 0.62/0.80 (define @t5 () (tptp.set_union2 @t2 @t1)) % 0.62/0.80 (define @t6 () (tptp.set_union2 @t1 @t2)) % 0.62/0.80 (define @t7 () (@var "C" $$unsorted)) % 0.62/0.80 (define @t8 () (tptp.in @t7 @t2)) % 0.62/0.80 (define @t9 () (= @t8 (= @t7 @t1))) % 0.62/0.80 (define @t10 () (@list @t7)) % 0.62/0.80 (define @t11 () (forall @t10 @t9)) % 0.62/0.80 (define @t12 () (tptp.singleton @t1)) % 0.62/0.80 (define @t13 () (= @t2 @t12)) % 0.62/0.80 (define @t14 () (= @t13 @t11)) % 0.62/0.80 (define @t15 () (forall @t4 @t14)) % 0.62/0.80 (define @t16 () (@list @t2)) % 0.62/0.80 (define @t17 () (@list @t1)) % 0.62/0.80 (define @t18 () (forall @t17 (= (= @t1 tptp.empty_set) (forall @t16 @t3)))) % 0.62/0.80 (define @t19 () (@var "D" $$unsorted)) % 0.62/0.80 (define @t20 () (@list @t19)) % 0.62/0.80 (define @t21 () (forall @t20 (= (tptp.in @t19 @t7) (or (tptp.in @t19 @t1) (tptp.in @t19 @t2))))) % 0.62/0.80 (define @t22 () (= (= @t7 @t6) @t21)) % 0.62/0.80 (define @t23 () (@list @t1 @t2 @t7)) % 0.62/0.80 (define @t24 () (forall @t23 @t22)) % 0.62/0.80 (define @t25 () (tptp.empty @t1)) % 0.62/0.80 (define @t26 () (not @t25)) % 0.62/0.80 (define @t27 () (tptp.set_union2 @t12 @t2)) % 0.62/0.80 (define @t28 () (not (= @t27 tptp.empty_set))) % 0.62/0.80 (define @t29 () (forall @t4 @t28)) % 0.62/0.80 (define @t30 () (not @t29)) % 0.62/0.80 (define @t31 () (forall @t4 (not (= tptp.empty_set @t27)))) % 0.62/0.80 (define @t32 () (@quantifiers_skolemize @t31 0)) % 0.62/0.80 (define @t33 () (tptp.in @t7 tptp.empty_set)) % 0.62/0.80 (define @t34 () (= @t33 (= @t32 @t7))) % 0.62/0.80 (define @t35 () (forall @t10 @t34)) % 0.62/0.80 (define @t36 () (tptp.singleton @t32)) % 0.62/0.80 (define @t37 () (= tptp.empty_set @t36)) % 0.62/0.80 (define @t38 () (= @t37 @t35)) % 0.62/0.80 (define @t39 () (forall @t4 (= @t13 (forall @t10 (= @t8 (= @t1 @t7)))))) % 0.62/0.80 (define @t40 () (forall @t10 (= @t33 (= @t7 @t32)))) % 0.62/0.80 (define @t41 () (= @t37 @t40)) % 0.62/0.80 (define @t42 () (@list false)) % 0.62/0.80 (define @t43 () (forall @t16 (not (tptp.in @t2 @t36)))) % 0.62/0.80 (define @t44 () (= (= @t36 tptp.empty_set) @t43)) % 0.62/0.80 (define @t45 () (= @t37 @t43)) % 0.62/0.80 (define @t46 () (@list @t18)) % 0.62/0.80 (define @t47 () (= @t6 @t7)) % 0.62/0.80 (define @t48 () (@quantifiers_skolemize @t31 1)) % 0.62/0.80 (define @t49 () (tptp.set_union2 @t48 @t36)) % 0.62/0.80 (define @t50 () (= tptp.empty_set @t49)) % 0.62/0.80 (define @t51 () (forall @t20 (= (tptp.in @t19 tptp.empty_set) (or (tptp.in @t19 @t48) (tptp.in @t19 @t36))))) % 0.62/0.80 (define @t52 () (= @t49 tptp.empty_set)) % 0.62/0.80 (define @t53 () (forall @t23 (= @t21 @t47))) % 0.62/0.80 (define @t54 () (= @t51 @t52)) % 0.62/0.80 (define @t55 () (= @t51 @t50)) % 0.62/0.80 (define @t56 () (= tptp.empty_set (tptp.set_union2 @t36 @t48))) % 0.62/0.80 (define @t57 () (not @t31)) % 0.62/0.80 (define @t58 () (not (not @t56))) % 0.62/0.80 (define @t59 () (@list true)) % 0.62/0.80 (define @t60 () (@list false false)) % 0.62/0.80 (define @t61 () (@quantifiers_skolemize @t43 0)) % 0.62/0.80 (define @t62 () (@list @t61)) % 0.62/0.80 (define @t63 () (forall @t16 (not (tptp.in @t2 tptp.empty_set)))) % 0.62/0.80 (define @t64 () (= (= tptp.empty_set tptp.empty_set) @t63)) % 0.62/0.80 (define @t65 () (tptp.in @t61 @t36)) % 0.62/0.80 (define @t66 () (or (tptp.in @t61 @t48) @t65)) % 0.62/0.80 (define @t67 () (tptp.in @t61 tptp.empty_set)) % 0.62/0.80 (define @t68 () (= @t67 @t66)) % 0.62/0.80 (define @t69 () (not @t66)) % 0.62/0.80 (define @t70 () (@list true false)) % 0.62/0.80 (define @t71 () (not @t65)) % 0.62/0.80 (define @t72 () (not @t43)) % 0.62/0.80 (define @t73 () (not @t71)) % 0.62/0.80 (define @t74 () (@list @t32)) % 0.62/0.80 (define @t75 () (tptp.in @t32 tptp.empty_set)) % 0.62/0.80 (define @t76 () (= @t75 (= @t32 @t32))) % 0.62/0.80 (assume @p1 (forall @t4 (=> (tptp.in @t1 @t2) @t3))) % 0.62/0.80 (assume @p2 (forall @t4 (= @t6 @t5))) % 0.62/0.80 (assume @p3 @t15) % 0.62/0.80 (assume @p4 @t18) % 0.62/0.80 (assume @p5 @t24) % 0.62/0.80 (assume @p6 (tptp.empty tptp.empty_set)) % 0.62/0.80 (assume @p7 (forall @t4 (=> @t26 (not (tptp.empty @t6))))) % 0.62/0.80 (assume @p8 (forall @t4 (=> @t26 (not (tptp.empty @t5))))) % 0.62/0.80 (assume @p9 (forall @t4 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.62/0.80 (assume @p10 (exists @t17 @t25)) % 0.62/0.80 (assume @p11 (exists @t17 @t26)) % 0.62/0.80 (assume @p12 @t30) % 0.62/0.80 (assume @p13 true) % 0.62/0.80 (step @p14 :rule eq-symm :args (@t7 @t1)) % 0.62/0.80 (step @p15 :rule refl :args (@t8)) % 0.62/0.80 (step @p16 :rule cong :premises (@p15 @p14) :args (@t9)) % 0.62/0.80 (step @p17 :rule cong :premises (@p16) :args (@t11)) % 0.62/0.80 (step @p18 :rule refl :args (@t13)) % 0.62/0.80 (step @p19 :rule cong :premises (@p18 @p17) :args (@t14)) % 0.62/0.80 (step @p20 :rule cong :premises (@p19) :args (@t15)) % 0.62/0.80 (step @p21 :rule eq_resolve :premises (@p3 @p20)) % 0.62/0.80 (step @p22 :rule eq-symm :args (@t32 @t7)) % 0.62/0.80 (step @p23 :rule refl :args (@t33)) % 0.62/0.80 (step @p24 :rule cong :premises (@p23 @p22) :args (@t34)) % 0.62/0.80 (step @p25 :rule cong :premises (@p24) :args (@t35)) % 0.62/0.80 (step @p26 :rule refl :args (@t37)) % 0.62/0.80 (step @p27 :rule cong :premises (@p26 @p25) :args (@t38)) % 0.62/0.80 (step @p28 :rule refl :args (@t39)) % 0.62/0.80 (step @p29 :rule cong :premises (@p28 @p27) :args ((=> @t39 @t38))) % 0.62/0.80 (assume-push @p154 @t39) % 0.62/0.80 (step @p31 :rule instantiate :premises (@p21) :args ((@list @t32 tptp.empty_set))) % 0.62/0.80 (step-pop @p155 :rule scope :premises (@p31)) % 0.62/0.80 (step @p32 :rule process_scope :premises (@p155) :args (@t38)) % 0.62/0.80 (step @p34 :rule eq_resolve :premises (@p32 @p29)) % 0.62/0.80 (step @p35 :rule implies_elim :premises (@p34)) % 0.62/0.80 (step @p36 :rule chain_m_resolution :premises (@p35 @p21) :args (@t41 @t42 (@list @t39))) % 0.62/0.80 (step @p37 :rule refl :args (@t43)) % 0.62/0.80 (step @p38 :rule eq-symm :args (@t36 tptp.empty_set)) % 0.62/0.80 (step @p39 :rule cong :premises (@p38 @p37) :args (@t44)) % 0.62/0.80 (step @p40 :rule refl :args (@t18)) % 0.62/0.80 (step @p41 :rule cong :premises (@p40 @p39) :args ((=> @t18 @t44))) % 0.62/0.80 (assume-push @p156 @t18) % 0.62/0.80 (step @p43 :rule instantiate :premises (@p4) :args ((@list @t36))) % 0.62/0.80 (step-pop @p157 :rule scope :premises (@p43)) % 0.62/0.80 (step @p44 :rule process_scope :premises (@p157) :args (@t44)) % 0.62/0.80 (step @p46 :rule eq_resolve :premises (@p44 @p41)) % 0.62/0.80 (step @p47 :rule implies_elim :premises (@p46)) % 0.62/0.80 (step @p48 :rule chain_m_resolution :premises (@p47 @p4) :args (@t45 @t42 @t46)) % 0.62/0.80 (step @p49 :rule eq-symm :args (@t47 @t21)) % 0.62/0.80 (step @p50 :rule refl :args (@t21)) % 0.62/0.80 (step @p51 :rule eq-symm :args (@t7 @t6)) % 0.62/0.80 (step @p52 :rule cong :premises (@p51 @p50) :args (@t22)) % 0.62/0.80 (step @p53 :rule trans :premises (@p52 @p49)) % 0.62/0.80 (step @p54 :rule cong :premises (@p53) :args (@t24)) % 0.62/0.80 (step @p55 :rule eq_resolve :premises (@p5 @p54)) % 0.62/0.80 (step @p56 :rule eq-symm :args (@t50 @t51)) % 0.62/0.80 (step @p57 :rule refl :args (@t51)) % 0.62/0.80 (step @p58 :rule eq-symm :args (@t49 tptp.empty_set)) % 0.62/0.80 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t52 @t51))) % 0.62/0.80 (step @p60 :rule trans :premises (@p59 @p56)) % 0.62/0.80 (step @p61 :rule eq-symm :args (@t51 @t52)) % 0.62/0.80 (step @p62 :rule trans :premises (@p61 @p60)) % 0.62/0.80 (step @p63 :rule refl :args (@t53)) % 0.62/0.80 (step @p64 :rule cong :premises (@p63 @p62) :args ((=> @t53 @t54))) % 0.62/0.80 (assume-push @p158 @t53) % 0.62/0.80 (step @p66 :rule instantiate :premises (@p55) :args ((@list @t48 @t36 tptp.empty_set))) % 0.62/0.80 (step-pop @p159 :rule scope :premises (@p66)) % 0.62/0.80 (step @p67 :rule process_scope :premises (@p159) :args (@t54)) % 0.62/0.80 (step @p69 :rule eq_resolve :premises (@p67 @p64)) % 0.62/0.80 (step @p70 :rule implies_elim :premises (@p69)) % 0.62/0.80 (step @p71 :rule chain_m_resolution :premises (@p70 @p55) :args (@t55 @t42 (@list @t53))) % 0.62/0.80 (step @p72 :rule instantiate :premises (@p2) :args ((@list @t36 @t48))) % 0.62/0.80 (step @p73 :rule eq-symm :args (@t27 tptp.empty_set)) % 0.62/0.80 (step @p74 :rule cong :premises (@p73) :args (@t28)) % 0.62/0.80 (step @p75 :rule cong :premises (@p74) :args (@t29)) % 0.62/0.80 (step @p76 :rule cong :premises (@p75) :args (@t30)) % 0.62/0.80 (step @p77 :rule eq_resolve :premises (@p12 @p76)) % 0.62/0.80 (step @p78 :rule refl :args (@t56)) % 0.62/0.80 (step @p79 :rule bool-double-not-elim :args (@t31)) % 0.62/0.80 (step @p80 :rule nary_cong :premises (@p79 @p78) :args ((or (not @t57) @t56))) % 0.62/0.80 (step @p81 :rule bool-double-not-elim :args (@t56)) % 0.62/0.80 (step @p82 :rule refl :args (@t57)) % 0.62/0.80 (step @p83 :rule cong :premises (@p82 @p81) :args ((=> @t57 @t58))) % 0.62/0.80 (assume-push @p160 @t57) % 0.62/0.80 (step @p85 :rule skolemize :premises (@p77)) % 0.62/0.80 (step-pop @p161 :rule scope :premises (@p85)) % 0.62/0.80 (step @p86 :rule process_scope :premises (@p161) :args (@t58)) % 0.62/0.80 (step @p88 :rule eq_resolve :premises (@p86 @p83)) % 0.62/0.80 (step @p89 :rule implies_elim :premises (@p88)) % 0.62/0.80 (step @p90 :rule eq_resolve :premises (@p89 @p80)) % 0.62/0.80 (step @p91 :rule chain_m_resolution :premises (@p90 @p77) :args (@t56 @t59 (@list @t31))) % 0.62/0.80 (step @p92 :rule trans :premises (@p91 @p72)) % 0.62/0.80 (step @p93 :rule cnf_equiv_pos2 :args (@t55)) % 0.62/0.81 (step @p94 :rule reordering :premises (@p93) :args ((or @t51 (not @t50) (not @t55)))) % 0.62/0.81 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p71) :args (@t51 @t60 (@list @t50 @t55))) % 0.62/0.81 (step @p96 :rule instantiate :premises (@p95) :args (@t62)) % 0.62/0.81 (step @p97 :rule bool-eq-true :args (@t63)) % 0.62/0.81 (step @p98 :rule eq-symm :args (true @t63)) % 0.62/0.81 (step @p99 :rule trans :premises (@p98 @p97)) % 0.62/0.81 (step @p100 :rule refl :args (@t63)) % 0.62/0.81 (step @p101 :rule eq-refl :args (tptp.empty_set)) % 0.62/0.81 (step @p102 :rule cong :premises (@p101 @p100) :args (@t64)) % 0.62/0.81 (step @p103 :rule trans :premises (@p102 @p99)) % 0.62/0.81 (step @p104 :rule cong :premises (@p40 @p103) :args ((=> @t18 @t64))) % 0.62/0.81 (assume-push @p162 @t18) % 0.62/0.81 (step @p106 :rule instantiate :premises (@p4) :args ((@list tptp.empty_set))) % 0.62/0.81 (step-pop @p163 :rule scope :premises (@p106)) % 0.62/0.81 (step @p107 :rule process_scope :premises (@p163) :args (@t64)) % 0.62/0.81 (step @p109 :rule eq_resolve :premises (@p107 @p104)) % 0.62/0.81 (step @p110 :rule implies_elim :premises (@p109)) % 0.62/0.81 (step @p111 :rule chain_m_resolution :premises (@p110 @p4) :args (@t63 @t42 @t46)) % 0.62/0.81 (step @p112 :rule instantiate :premises (@p111) :args (@t62)) % 0.62/0.81 (step @p113 :rule cnf_equiv_pos2 :args (@t68)) % 0.62/0.81 (step @p114 :rule reordering :premises (@p113) :args ((or @t67 @t69 (not @t68)))) % 0.62/0.81 (step @p115 :rule chain_m_resolution :premises (@p114 @p112 @p96) :args (@t69 @t70 (@list @t67 @t68))) % 0.62/0.81 (step @p116 :rule cnf_or_neg :args (@t66 1)) % 0.62/0.81 (step @p117 :rule reordering :premises (@p116) :args ((or @t71 @t66))) % 0.62/0.81 (step @p118 :rule chain_m_resolution :premises (@p117 @p115) :args (@t71 @t59 (@list @t66))) % 0.62/0.81 (step @p119 :rule refl :args (@t65)) % 0.62/0.81 (step @p120 :rule bool-double-not-elim :args (@t43)) % 0.62/0.81 (step @p121 :rule nary_cong :premises (@p120 @p119) :args ((or (not @t72) @t65))) % 0.62/0.81 (step @p122 :rule bool-double-not-elim :args (@t65)) % 0.62/0.81 (step @p123 :rule refl :args (@t72)) % 0.62/0.81 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t72 @t73))) % 0.62/0.81 (assume-push @p164 @t72) % 0.62/0.81 (step @p126 :rule skolemize :premises (@p164)) % 0.62/0.81 (step-pop @p165 :rule scope :premises (@p126)) % 0.62/0.81 (step @p127 :rule process_scope :premises (@p165) :args (@t73)) % 0.62/0.81 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 0.62/0.81 (step @p130 :rule implies_elim :premises (@p129)) % 0.62/0.81 (step @p131 :rule eq_resolve :premises (@p130 @p121)) % 0.62/0.81 (step @p132 :rule chain_m_resolution :premises (@p131 @p118) :args (@t43 @t59 (@list @t65))) % 0.62/0.81 (step @p133 :rule cnf_equiv_pos2 :args (@t45)) % 0.62/0.81 (step @p134 :rule reordering :premises (@p133) :args ((or @t37 @t72 (not @t45)))) % 0.62/0.81 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p48) :args (@t37 @t60 (@list @t43 @t45))) % 0.62/0.81 (step @p136 :rule cnf_equiv_pos1 :args (@t41)) % 0.62/0.81 (step @p137 :rule reordering :premises (@p136) :args ((or @t40 (not @t37) (not @t41)))) % 0.62/0.81 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p36) :args (@t40 @t60 (@list @t37 @t41))) % 0.62/0.81 (step @p139 :rule instantiate :premises (@p111) :args (@t74)) % 0.62/0.81 (step @p140 :rule bool-eq-true :args (@t75)) % 0.62/0.81 (step @p141 :rule eq-refl :args (@t32)) % 0.62/0.81 (step @p142 :rule refl :args (@t75)) % 0.62/0.81 (step @p143 :rule cong :premises (@p142 @p141) :args (@t76)) % 0.62/0.81 (step @p144 :rule trans :premises (@p143 @p140)) % 0.62/0.81 (step @p145 :rule refl :args (@t40)) % 0.62/0.81 (step @p146 :rule cong :premises (@p145 @p144) :args ((=> @t40 @t76))) % 0.62/0.81 (assume-push @p166 @t40) % 0.62/0.81 (step @p148 :rule instantiate :premises (@p166) :args (@t74)) % 0.62/0.81 (step-pop @p167 :rule scope :premises (@p148)) % 0.62/0.81 (step @p149 :rule process_scope :premises (@p167) :args (@t76)) % 0.62/0.81 (step @p151 :rule eq_resolve :premises (@p149 @p146)) % 0.62/0.81 (step @p152 :rule implies_elim :premises (@p151)) % 0.62/0.81 (step @p153 false :rule chain_m_resolution :premises (@p152 @p139 @p138) :args (false @t70 (@list @t75 @t40))) % 0.62/0.81 ) % 0.62/0.81 % SZS output end Proof % 0.62/0.81 % cvc5 exiting %------------------------------------------------------------------------------