%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET914+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 : n010.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 08:48:58 AM UTC 2026 % Result : Theorem 15.44s 15.66s % Output : Proof 15.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET914+1 : TPTP v9.2.1. Released v3.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.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 16:17:10 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.44/15.66 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.44/15.66 --- Run --no-e-matching --full-saturate-quant at 6... % 15.44/15.66 % SZS status Theorem % 15.44/15.66 % SZS output start Proof % 15.44/15.66 ( % 15.44/15.66 (declare-sort $$unsorted 0) % 15.44/15.66 (declare-const tptp.disjoint (-> $$unsorted $$unsorted Bool)) % 15.44/15.66 (declare-const tptp.empty_set $$unsorted) % 15.44/15.66 (declare-const tptp.empty (-> $$unsorted Bool)) % 15.44/15.66 (declare-const tptp.set_intersection2 (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.66 (declare-const tptp.unordered_pair (-> $$unsorted $$unsorted $$unsorted)) % 15.44/15.66 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 15.44/15.66 (define @t1 () (@var "A" $$unsorted)) % 15.44/15.66 (define @t2 () (@var "B" $$unsorted)) % 15.44/15.66 (define @t3 () (not (tptp.in @t2 @t1))) % 15.44/15.66 (define @t4 () (@list @t1 @t2)) % 15.44/15.66 (define @t5 () (tptp.unordered_pair @t1 @t2)) % 15.44/15.66 (define @t6 () (tptp.set_intersection2 @t1 @t2)) % 15.44/15.66 (define @t7 () (@list @t2)) % 15.44/15.66 (define @t8 () (@list @t1)) % 15.44/15.66 (define @t9 () (forall @t8 (= (= @t1 tptp.empty_set) (forall @t7 @t3)))) % 15.44/15.66 (define @t10 () (@var "D" $$unsorted)) % 15.44/15.66 (define @t11 () (or (= @t10 @t1) (= @t10 @t2))) % 15.44/15.66 (define @t12 () (@var "C" $$unsorted)) % 15.44/15.66 (define @t13 () (tptp.in @t10 @t12)) % 15.44/15.66 (define @t14 () (= @t13 @t11)) % 15.44/15.66 (define @t15 () (@list @t10)) % 15.44/15.66 (define @t16 () (forall @t15 @t14)) % 15.44/15.66 (define @t17 () (= (= @t12 @t5) @t16)) % 15.44/15.66 (define @t18 () (@list @t1 @t2 @t12)) % 15.44/15.66 (define @t19 () (forall @t18 @t17)) % 15.44/15.66 (define @t20 () (forall @t15 (= @t13 (and (tptp.in @t10 @t1) (tptp.in @t10 @t2))))) % 15.44/15.66 (define @t21 () (= (= @t12 @t6) @t20)) % 15.44/15.66 (define @t22 () (forall @t18 @t21)) % 15.44/15.66 (define @t23 () (tptp.disjoint @t1 @t2)) % 15.44/15.66 (define @t24 () (forall @t4 (= @t23 (= @t6 tptp.empty_set)))) % 15.44/15.66 (define @t25 () (tptp.empty @t1)) % 15.44/15.66 (define @t26 () (tptp.in @t1 @t12)) % 15.44/15.66 (define @t27 () (tptp.disjoint @t5 @t12)) % 15.44/15.66 (define @t28 () (forall @t18 (not (and @t27 @t26)))) % 15.44/15.66 (define @t29 () (not @t28)) % 15.44/15.66 (define @t30 () (forall @t7 (not (tptp.in @t2 tptp.empty_set)))) % 15.44/15.66 (define @t31 () (= (= tptp.empty_set tptp.empty_set) @t30)) % 15.44/15.66 (define @t32 () (@list false)) % 15.44/15.66 (define @t33 () (forall @t18 (or (not @t27) (not @t26)))) % 15.44/15.66 (define @t34 () (@quantifiers_skolemize @t33 0)) % 15.44/15.66 (define @t35 () (@list @t34)) % 15.44/15.66 (define @t36 () (@quantifiers_skolemize @t33 1)) % 15.44/15.66 (define @t37 () (tptp.unordered_pair @t34 @t36)) % 15.44/15.66 (define @t38 () (tptp.in @t10 @t37)) % 15.44/15.66 (define @t39 () (forall @t15 (= @t38 (or (= @t10 @t34) (= @t10 @t36))))) % 15.44/15.66 (define @t40 () (or (= @t34 @t10) (= @t36 @t10))) % 15.44/15.66 (define @t41 () (= @t38 @t40)) % 15.44/15.66 (define @t42 () (forall @t15 @t41)) % 15.44/15.66 (define @t43 () (= (= @t37 @t37) @t42)) % 15.44/15.66 (define @t44 () (forall @t18 (= (= @t5 @t12) (forall @t15 (= @t13 (or (= @t1 @t10) (= @t2 @t10))))))) % 15.44/15.66 (define @t45 () (tptp.in @t34 @t37)) % 15.44/15.66 (define @t46 () (= @t34 @t36)) % 15.44/15.66 (define @t47 () (or (= @t34 @t34) @t46)) % 15.44/15.66 (define @t48 () (= @t45 @t47)) % 15.44/15.66 (define @t49 () (@quantifiers_skolemize @t33 2)) % 15.44/15.66 (define @t50 () (tptp.in @t34 @t49)) % 15.44/15.66 (define @t51 () (not @t50)) % 15.44/15.66 (define @t52 () (tptp.disjoint @t37 @t49)) % 15.44/15.66 (define @t53 () (not @t52)) % 15.44/15.66 (define @t54 () (or @t53 @t51)) % 15.44/15.66 (define @t55 () (@list true)) % 15.44/15.66 (define @t56 () (@list @t54)) % 15.44/15.66 (define @t57 () (and @t50 @t45)) % 15.44/15.66 (define @t58 () (@list false false)) % 15.44/15.66 (define @t59 () (= @t6 @t12)) % 15.44/15.66 (define @t60 () (forall @t15 (= (tptp.in @t10 tptp.empty_set) (and (tptp.in @t10 @t49) @t38)))) % 15.44/15.66 (define @t61 () (tptp.set_intersection2 @t49 @t37)) % 15.44/15.66 (define @t62 () (= @t61 tptp.empty_set)) % 15.44/15.66 (define @t63 () (forall @t18 (= @t20 @t59))) % 15.44/15.66 (define @t64 () (= @t60 @t62)) % 15.44/15.66 (define @t65 () (= tptp.empty_set @t61)) % 15.44/15.66 (define @t66 () (= @t65 @t60)) % 15.44/15.66 (define @t67 () (tptp.set_intersection2 @t37 @t49)) % 15.44/15.66 (define @t68 () (= @t52 (= @t67 tptp.empty_set))) % 15.44/15.66 (define @t69 () (= tptp.empty_set @t67)) % 15.44/15.66 (define @t70 () (= @t52 @t69)) % 15.44/15.66 (define @t71 () (tptp.in @t34 tptp.empty_set)) % 15.44/15.66 (define @t72 () (= @t71 @t57)) % 15.44/15.66 (assume @p1 (forall @t4 (=> (tptp.in @t1 @t2) @t3))) % 15.44/15.66 (assume @p2 (forall @t4 (= @t5 (tptp.unordered_pair @t2 @t1)))) % 15.44/15.66 (assume @p3 (forall @t4 (= @t6 (tptp.set_intersection2 @t2 @t1)))) % 15.44/15.66 (assume @p4 @t9) % 15.44/15.66 (assume @p5 @t19) % 15.44/15.66 (assume @p6 @t22) % 15.44/15.66 (assume @p7 @t24) % 15.44/15.66 (assume @p8 (tptp.empty tptp.empty_set)) % 15.44/15.66 (assume @p9 (forall @t4 (= (tptp.set_intersection2 @t1 @t1) @t1))) % 15.44/15.66 (assume @p10 (exists @t8 @t25)) % 15.44/15.66 (assume @p11 (exists @t8 (not @t25))) % 15.44/15.66 (assume @p12 (forall @t4 (=> @t23 (tptp.disjoint @t2 @t1)))) % 15.44/15.66 (assume @p13 @t29) % 15.44/15.66 (assume @p14 true) % 15.44/15.66 (step @p15 :rule bool-eq-true :args (@t30)) % 15.44/15.66 (step @p16 :rule eq-symm :args (true @t30)) % 15.44/15.66 (step @p17 :rule trans :premises (@p16 @p15)) % 15.44/15.66 (step @p18 :rule refl :args (@t30)) % 15.44/15.66 (step @p19 :rule eq-refl :args (tptp.empty_set)) % 15.44/15.66 (step @p20 :rule cong :premises (@p19 @p18) :args (@t31)) % 15.44/15.66 (step @p21 :rule trans :premises (@p20 @p17)) % 15.44/15.66 (step @p22 :rule refl :args (@t9)) % 15.44/15.66 (step @p23 :rule cong :premises (@p22 @p21) :args ((=> @t9 @t31))) % 15.44/15.66 (assume-push @p148 @t9) % 15.44/15.66 (step @p25 :rule instantiate :premises (@p4) :args ((@list tptp.empty_set))) % 15.44/15.66 (step-pop @p149 :rule scope :premises (@p25)) % 15.44/15.66 (step @p26 :rule process_scope :premises (@p149) :args (@t31)) % 15.44/15.66 (step @p28 :rule eq_resolve :premises (@p26 @p23)) % 15.44/15.66 (step @p29 :rule implies_elim :premises (@p28)) % 15.44/15.66 (step @p30 :rule chain_m_resolution :premises (@p29 @p4) :args (@t30 @t32 (@list @t9))) % 15.44/15.66 (step @p31 :rule instantiate :premises (@p30) :args (@t35)) % 15.44/15.66 (step @p32 :rule eq-symm :args (@t10 @t2)) % 15.44/15.66 (step @p33 :rule eq-symm :args (@t10 @t1)) % 15.44/15.66 (step @p34 :rule nary_cong :premises (@p33 @p32) :args (@t11)) % 15.44/15.66 (step @p35 :rule refl :args (@t13)) % 15.44/15.66 (step @p36 :rule cong :premises (@p35 @p34) :args (@t14)) % 15.44/15.66 (step @p37 :rule cong :premises (@p36) :args (@t16)) % 15.44/15.66 (step @p38 :rule eq-symm :args (@t12 @t5)) % 15.44/15.66 (step @p39 :rule cong :premises (@p38 @p37) :args (@t17)) % 15.44/15.66 (step @p40 :rule cong :premises (@p39) :args (@t19)) % 15.44/15.66 (step @p41 :rule eq_resolve :premises (@p5 @p40)) % 15.44/15.66 (step @p42 :rule bool-eq-true :args (@t39)) % 15.44/15.66 (step @p43 :rule eq-symm :args (true @t39)) % 15.44/15.66 (step @p44 :rule trans :premises (@p43 @p42)) % 15.44/15.66 (step @p45 :rule eq-symm :args (@t36 @t10)) % 15.44/15.66 (step @p46 :rule eq-symm :args (@t34 @t10)) % 15.44/15.66 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t40)) % 15.44/15.66 (step @p48 :rule refl :args (@t38)) % 15.44/15.66 (step @p49 :rule cong :premises (@p48 @p47) :args (@t41)) % 15.44/15.66 (step @p50 :rule cong :premises (@p49) :args (@t42)) % 15.44/15.66 (step @p51 :rule eq-refl :args (@t37)) % 15.44/15.66 (step @p52 :rule cong :premises (@p51 @p50) :args (@t43)) % 15.44/15.66 (step @p53 :rule trans :premises (@p52 @p44)) % 15.44/15.66 (step @p54 :rule refl :args (@t44)) % 15.44/15.66 (step @p55 :rule cong :premises (@p54 @p53) :args ((=> @t44 @t43))) % 15.44/15.66 (assume-push @p150 @t44) % 15.44/15.66 (step @p57 :rule instantiate :premises (@p41) :args ((@list @t34 @t36 @t37))) % 15.44/15.66 (step-pop @p151 :rule scope :premises (@p57)) % 15.44/15.66 (step @p58 :rule process_scope :premises (@p151) :args (@t43)) % 15.44/15.66 (step @p60 :rule eq_resolve :premises (@p58 @p55)) % 15.44/15.66 (step @p61 :rule implies_elim :premises (@p60)) % 15.44/15.66 (step @p62 :rule chain_m_resolution :premises (@p61 @p41) :args (@t39 @t32 (@list @t44))) % 15.44/15.66 (step @p63 :rule bool-eq-true :args (@t45)) % 15.44/15.66 (step @p64 :rule absorb :args ((= (or true @t46) true))) % 15.44/15.66 (step @p65 :rule refl :args (@t46)) % 15.44/15.66 (step @p66 :rule eq-refl :args (@t34)) % 15.44/15.66 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t47)) % 15.44/15.66 (step @p68 :rule trans :premises (@p67 @p64)) % 15.44/15.66 (step @p69 :rule refl :args (@t45)) % 15.44/15.66 (step @p70 :rule cong :premises (@p69 @p68) :args (@t48)) % 15.44/15.66 (step @p71 :rule trans :premises (@p70 @p63)) % 15.44/15.66 (step @p72 :rule refl :args (@t39)) % 15.44/15.66 (step @p73 :rule cong :premises (@p72 @p71) :args ((=> @t39 @t48))) % 15.44/15.66 (assume-push @p152 @t39) % 15.44/15.66 (step @p75 :rule instantiate :premises (@p62) :args (@t35)) % 15.44/15.66 (step-pop @p153 :rule scope :premises (@p75)) % 15.44/15.66 (step @p76 :rule process_scope :premises (@p153) :args (@t48)) % 15.44/15.66 (step @p78 :rule eq_resolve :premises (@p76 @p73)) % 15.44/15.66 (step @p79 :rule implies_elim :premises (@p78)) % 15.44/15.66 (step @p80 :rule chain_m_resolution :premises (@p79 @p62) :args (@t45 @t32 (@list @t39))) % 15.44/15.66 (step @p81 :rule bool-and-de-morgan :args (@t27 @t26 true)) % 15.44/15.66 (step @p82 :rule cong :premises (@p81) :args (@t28)) % 15.44/15.66 (step @p83 :rule cong :premises (@p82) :args (@t29)) % 15.44/15.66 (step @p84 :rule eq_resolve :premises (@p13 @p83)) % 15.44/15.66 (step @p85 :rule skolemize :premises (@p84)) % 15.44/15.66 (step @p86 :rule bool-double-not-elim :args (@t50)) % 15.44/15.66 (step @p87 :rule refl :args (@t54)) % 15.44/15.66 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t54 (not @t51)))) % 15.44/15.66 (step @p89 :rule cnf_or_neg :args (@t54 1)) % 15.44/15.66 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 15.44/15.66 (step @p91 :rule reordering :premises (@p90) :args ((or @t50 @t54))) % 15.44/15.66 (step @p92 :rule chain_m_resolution :premises (@p91 @p85) :args (@t50 @t55 @t56)) % 15.44/15.66 (step @p93 :rule cnf_and_neg :args (@t57)) % 15.44/15.66 (step @p94 :rule reordering :premises (@p93) :args ((or @t51 (not @t45) @t57))) % 15.44/15.66 (step @p95 :rule chain_m_resolution :premises (@p94 @p92 @p80) :args (@t57 @t58 (@list @t50 @t45))) % 15.44/15.66 (step @p96 :rule eq-symm :args (@t59 @t20)) % 15.44/15.66 (step @p97 :rule refl :args (@t20)) % 15.44/15.66 (step @p98 :rule eq-symm :args (@t12 @t6)) % 15.44/15.66 (step @p99 :rule cong :premises (@p98 @p97) :args (@t21)) % 15.44/15.66 (step @p100 :rule trans :premises (@p99 @p96)) % 15.44/15.66 (step @p101 :rule cong :premises (@p100) :args (@t22)) % 15.44/15.66 (step @p102 :rule eq_resolve :premises (@p6 @p101)) % 15.44/15.66 (step @p103 :rule refl :args (@t60)) % 15.44/15.66 (step @p104 :rule eq-symm :args (@t61 tptp.empty_set)) % 15.44/15.66 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t62 @t60))) % 15.44/15.66 (step @p106 :rule eq-symm :args (@t60 @t62)) % 15.44/15.66 (step @p107 :rule trans :premises (@p106 @p105)) % 15.44/15.66 (step @p108 :rule refl :args (@t63)) % 15.44/15.66 (step @p109 :rule cong :premises (@p108 @p107) :args ((=> @t63 @t64))) % 15.44/15.66 (assume-push @p154 @t63) % 15.44/15.66 (step @p111 :rule instantiate :premises (@p102) :args ((@list @t49 @t37 tptp.empty_set))) % 15.44/15.66 (step-pop @p155 :rule scope :premises (@p111)) % 15.44/15.66 (step @p112 :rule process_scope :premises (@p155) :args (@t64)) % 15.44/15.66 (step @p114 :rule eq_resolve :premises (@p112 @p109)) % 15.44/15.66 (step @p115 :rule implies_elim :premises (@p114)) % 15.44/15.66 (step @p116 :rule chain_m_resolution :premises (@p115 @p102) :args (@t66 @t32 (@list @t63))) % 15.44/15.66 (step @p117 :rule instantiate :premises (@p3) :args ((@list @t49 @t37))) % 15.44/15.66 (step @p118 :rule symm :premises (@p117)) % 15.44/15.66 (step @p119 :rule eq-symm :args (@t67 tptp.empty_set)) % 15.44/15.66 (step @p120 :rule refl :args (@t52)) % 15.44/15.66 (step @p121 :rule cong :premises (@p120 @p119) :args (@t68)) % 15.44/15.66 (step @p122 :rule refl :args (@t24)) % 15.44/15.66 (step @p123 :rule cong :premises (@p122 @p121) :args ((=> @t24 @t68))) % 15.44/15.66 (assume-push @p156 @t24) % 15.44/15.66 (step @p125 :rule instantiate :premises (@p7) :args ((@list @t37 @t49))) % 15.44/15.66 (step-pop @p157 :rule scope :premises (@p125)) % 15.44/15.66 (step @p126 :rule process_scope :premises (@p157) :args (@t68)) % 15.44/15.66 (step @p128 :rule eq_resolve :premises (@p126 @p123)) % 15.44/15.66 (step @p129 :rule implies_elim :premises (@p128)) % 15.44/15.66 (step @p130 :rule chain_m_resolution :premises (@p129 @p7) :args (@t70 @t32 (@list @t24))) % 15.44/15.66 (step @p131 :rule bool-double-not-elim :args (@t52)) % 15.44/15.66 (step @p132 :rule nary_cong :premises (@p87 @p131) :args ((or @t54 (not @t53)))) % 15.44/15.66 (step @p133 :rule cnf_or_neg :args (@t54 0)) % 15.44/15.66 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 15.44/15.66 (step @p135 :rule reordering :premises (@p134) :args ((or @t52 @t54))) % 15.44/15.66 (step @p136 :rule chain_m_resolution :premises (@p135 @p85) :args (@t52 @t55 @t56)) % 15.44/15.66 (step @p137 :rule cnf_equiv_pos1 :args (@t70)) % 15.44/15.66 (step @p138 :rule reordering :premises (@p137) :args ((or @t53 @t69 (not @t70)))) % 15.44/15.66 (step @p139 :rule chain_m_resolution :premises (@p138 @p136 @p130) :args (@t69 @t58 (@list @t52 @t70))) % 15.44/15.66 (step @p140 :rule trans :premises (@p139 @p118)) % 15.44/15.66 (step @p141 :rule cnf_equiv_pos1 :args (@t66)) % 15.44/15.66 (step @p142 :rule reordering :premises (@p141) :args ((or @t60 (not @t65) (not @t66)))) % 15.44/15.66 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p116) :args (@t60 @t58 (@list @t65 @t66))) % 15.44/15.66 (step @p144 :rule instantiate :premises (@p143) :args (@t35)) % 15.44/15.66 (step @p145 :rule cnf_equiv_pos2 :args (@t72)) % 15.44/15.66 (step @p146 :rule reordering :premises (@p145) :args ((or @t71 (not @t57) (not @t72)))) % 15.44/15.66 (step @p147 false :rule chain_m_resolution :premises (@p146 @p144 @p95 @p31) :args (false (@list false false true) (@list @t72 @t57 @t71))) % 15.44/15.66 ) % 15.44/15.66 % SZS output end Proof % 15.44/15.66 % cvc5 exiting %------------------------------------------------------------------------------