%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET903+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 : n009.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 08:48:56 AM UTC 2026 % Result : Theorem 0.34s 0.57s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET903+1 : TPTP v9.2.1. Released v3.2.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n009.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:17:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.34/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.34/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.34/0.57 % SZS status Theorem % 0.34/0.57 % SZS output start Proof % 0.34/0.57 ( % 0.34/0.57 (declare-sort $$unsorted 0) % 0.34/0.57 (declare-const tptp.singleton (-> $$unsorted $$unsorted)) % 0.34/0.57 (declare-const tptp.empty (-> $$unsorted Bool)) % 0.34/0.57 (declare-const tptp.empty_set $$unsorted) % 0.34/0.57 (declare-const tptp.set_union2 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.34/0.57 (define @t2 () (@var "B" $$unsorted)) % 0.34/0.57 (define @t3 () (tptp.set_union2 @t2 @t1)) % 0.34/0.57 (define @t4 () (tptp.set_union2 @t1 @t2)) % 0.34/0.57 (define @t5 () (@list @t1 @t2)) % 0.34/0.57 (define @t6 () (tptp.empty @t1)) % 0.34/0.57 (define @t7 () (not @t6)) % 0.34/0.57 (define @t8 () (@list @t1)) % 0.34/0.57 (define @t9 () (@var "C" $$unsorted)) % 0.34/0.57 (define @t10 () (= @t9 tptp.empty_set)) % 0.34/0.57 (define @t11 () (tptp.singleton @t1)) % 0.34/0.57 (define @t12 () (= @t2 @t11)) % 0.34/0.57 (define @t13 () (and @t12 @t10)) % 0.34/0.57 (define @t14 () (not @t13)) % 0.34/0.57 (define @t15 () (= @t9 @t11)) % 0.34/0.57 (define @t16 () (= @t2 tptp.empty_set)) % 0.34/0.57 (define @t17 () (and @t16 @t15)) % 0.34/0.57 (define @t18 () (not @t17)) % 0.34/0.57 (define @t19 () (and @t12 @t15)) % 0.34/0.57 (define @t20 () (not @t19)) % 0.34/0.57 (define @t21 () (= @t11 (tptp.set_union2 @t2 @t9))) % 0.34/0.57 (define @t22 () (and @t21 @t20 @t18 @t14)) % 0.34/0.57 (define @t23 () (not @t22)) % 0.34/0.57 (define @t24 () (@list @t1 @t2 @t9)) % 0.34/0.57 (define @t25 () (forall @t24 @t23)) % 0.34/0.57 (define @t26 () (not @t10)) % 0.34/0.57 (define @t27 () (not @t16)) % 0.34/0.57 (define @t28 () (= @t2 @t9)) % 0.34/0.57 (define @t29 () (not @t28)) % 0.34/0.57 (define @t30 () (and @t21 @t29 @t27 @t26)) % 0.34/0.57 (define @t31 () (not @t30)) % 0.34/0.57 (define @t32 () (forall @t24 @t31)) % 0.34/0.57 (define @t33 () (not @t32)) % 0.34/0.57 (define @t34 () (= tptp.empty_set @t9)) % 0.34/0.57 (define @t35 () (not @t21)) % 0.34/0.57 (define @t36 () (not @t34)) % 0.34/0.57 (define @t37 () (not @t36)) % 0.34/0.57 (define @t38 () (not @t27)) % 0.34/0.57 (define @t39 () (not @t29)) % 0.34/0.57 (define @t40 () (or @t35 @t39 @t38 @t37)) % 0.34/0.57 (define @t41 () (forall @t24 (or @t35 @t28 @t16 @t34))) % 0.34/0.57 (define @t42 () (@quantifiers_skolemize @t41 2)) % 0.34/0.57 (define @t43 () (= tptp.empty_set @t42)) % 0.34/0.57 (define @t44 () (@quantifiers_skolemize @t41 1)) % 0.34/0.57 (define @t45 () (= tptp.empty_set @t44)) % 0.34/0.57 (define @t46 () (= @t44 @t42)) % 0.34/0.57 (define @t47 () (@quantifiers_skolemize @t41 0)) % 0.34/0.57 (define @t48 () (tptp.singleton @t47)) % 0.34/0.57 (define @t49 () (= @t48 (tptp.set_union2 @t44 @t42))) % 0.34/0.57 (define @t50 () (not @t49)) % 0.34/0.57 (define @t51 () (or @t50 @t46 @t45 @t43)) % 0.34/0.57 (define @t52 () (not @t51)) % 0.34/0.57 (define @t53 () (not @t41)) % 0.34/0.57 (define @t54 () (= @t44 tptp.empty_set)) % 0.34/0.57 (define @t55 () (or @t50 @t46 @t54 @t43)) % 0.34/0.57 (define @t56 () (not @t55)) % 0.34/0.57 (define @t57 () (@list true)) % 0.34/0.57 (define @t58 () (@list @t51)) % 0.34/0.57 (define @t59 () (and @t12 @t34)) % 0.34/0.57 (define @t60 () (not @t59)) % 0.34/0.57 (define @t61 () (not @t60)) % 0.34/0.57 (define @t62 () (not @t18)) % 0.34/0.57 (define @t63 () (not @t20)) % 0.34/0.57 (define @t64 () (or @t35 @t63 @t62 @t61)) % 0.34/0.57 (define @t65 () (= @t44 @t48)) % 0.34/0.57 (define @t66 () (and @t65 @t43)) % 0.34/0.57 (define @t67 () (= @t42 @t48)) % 0.34/0.57 (define @t68 () (and @t54 @t67)) % 0.34/0.57 (define @t69 () (and @t65 @t67)) % 0.34/0.57 (define @t70 () (or @t50 @t69 @t68 @t66)) % 0.34/0.57 (define @t71 () (forall @t24 (or @t35 @t19 @t17 @t59))) % 0.34/0.57 (define @t72 () (and @t45 @t67)) % 0.34/0.57 (define @t73 () (or @t50 @t69 @t72 @t66)) % 0.34/0.57 (define @t74 () (@list false)) % 0.34/0.57 (define @t75 () (not @t72)) % 0.34/0.57 (define @t76 () (not @t66)) % 0.34/0.57 (define @t77 () (not @t69)) % 0.34/0.57 (define @t78 () (@list @t69)) % 0.34/0.57 (assume @p1 (forall @t5 (= @t4 @t3))) % 0.34/0.57 (assume @p2 (tptp.empty tptp.empty_set)) % 0.34/0.57 (assume @p3 (forall @t5 (=> @t7 (not (tptp.empty @t4))))) % 0.34/0.57 (assume @p4 (forall @t5 (=> @t7 (not (tptp.empty @t3))))) % 0.34/0.57 (assume @p5 (forall @t5 (= (tptp.set_union2 @t1 @t1) @t1))) % 0.34/0.57 (assume @p6 (exists @t8 @t6)) % 0.34/0.57 (assume @p7 (exists @t8 @t7)) % 0.34/0.57 (assume @p8 @t25) % 0.34/0.57 (assume @p9 @t33) % 0.34/0.57 (assume @p10 true) % 0.34/0.57 (step @p11 :rule evaluate :args ((= false true))) % 0.34/0.57 (step @p12 :rule bool-double-not-elim :args (@t34)) % 0.34/0.57 (step @p13 :rule bool-double-not-elim :args (@t16)) % 0.34/0.57 (step @p14 :rule bool-double-not-elim :args (@t28)) % 0.34/0.57 (step @p15 :rule refl :args (@t35)) % 0.34/0.57 (step @p16 :rule nary_cong :premises (@p15 @p14 @p13 @p12) :args (@t40)) % 0.34/0.57 (step @p17 :rule aci_norm :args ((= (or @t35 (or @t39 (or @t38 @t37))) @t40))) % 0.34/0.57 (step @p18 :rule trans :premises (@p17 @p16)) % 0.34/0.57 (step @p19 :rule bool-and-de-morgan :args (@t27 @t36 true)) % 0.34/0.57 (step @p20 :rule refl :args (@t39)) % 0.34/0.57 (step @p21 :rule nary_cong :premises (@p20 @p19) :args ((or @t39 (not (and @t27 @t36))))) % 0.34/0.57 (step @p22 :rule bool-and-de-morgan :args (@t29 @t27 (and @t36))) % 0.34/0.57 (step @p23 :rule trans :premises (@p22 @p21)) % 0.34/0.57 (step @p24 :rule nary_cong :premises (@p15 @p23) :args ((or @t35 (not (and @t29 @t27 @t36))))) % 0.34/0.57 (step @p25 :rule bool-and-de-morgan :args (@t21 @t29 (and @t27 @t36))) % 0.34/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.34/0.57 (step @p27 :rule trans :premises (@p26 @p18)) % 0.34/0.57 (step @p28 :rule cong :premises (@p27) :args ((forall @t24 (not (and @t21 @t29 @t27 @t36))))) % 0.34/0.57 (step @p29 :rule eq-symm :args (@t9 tptp.empty_set)) % 0.34/0.57 (step @p30 :rule cong :premises (@p29) :args (@t26)) % 0.34/0.57 (step @p31 :rule refl :args (@t27)) % 0.34/0.57 (step @p32 :rule refl :args (@t29)) % 0.34/0.57 (step @p33 :rule refl :args (@t21)) % 0.34/0.57 (step @p34 :rule nary_cong :premises (@p33 @p32 @p31 @p30) :args (@t30)) % 0.34/0.57 (step @p35 :rule cong :premises (@p34) :args (@t31)) % 0.34/0.57 (step @p36 :rule cong :premises (@p35) :args (@t32)) % 0.34/0.57 (step @p37 :rule trans :premises (@p36 @p28)) % 0.34/0.57 (step @p38 :rule cong :premises (@p37) :args (@t33)) % 0.34/0.57 (step @p39 :rule eq_resolve :premises (@p9 @p38)) % 0.34/0.57 (step @p40 :rule refl :args (@t52)) % 0.34/0.57 (step @p41 :rule bool-double-not-elim :args (@t41)) % 0.34/0.57 (step @p42 :rule nary_cong :premises (@p41 @p40) :args ((or (not @t53) @t52))) % 0.34/0.57 (step @p43 :rule refl :args (@t43)) % 0.34/0.57 (step @p44 :rule eq-symm :args (@t44 tptp.empty_set)) % 0.34/0.57 (step @p45 :rule refl :args (@t46)) % 0.34/0.57 (step @p46 :rule refl :args (@t50)) % 0.34/0.57 (step @p47 :rule nary_cong :premises (@p46 @p45 @p44 @p43) :args (@t55)) % 0.34/0.57 (step @p48 :rule cong :premises (@p47) :args (@t56)) % 0.34/0.57 (step @p49 :rule refl :args (@t53)) % 0.34/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args ((=> @t53 @t56))) % 0.34/0.57 (assume-push @p135 @t53) % 0.34/0.57 (step @p52 :rule skolemize :premises (@p39)) % 0.34/0.57 (step-pop @p136 :rule scope :premises (@p52)) % 0.34/0.57 (step @p53 :rule process_scope :premises (@p136) :args (@t56)) % 0.34/0.57 (step @p55 :rule eq_resolve :premises (@p53 @p50)) % 0.34/0.57 (step @p56 :rule implies_elim :premises (@p55)) % 0.34/0.57 (step @p57 :rule eq_resolve :premises (@p56 @p42)) % 0.34/0.57 (step @p58 :rule chain_m_resolution :premises (@p57 @p39) :args (@t52 @t57 (@list @t41))) % 0.34/0.57 (step @p59 :rule bool-double-not-elim :args (@t49)) % 0.34/0.57 (step @p60 :rule refl :args (@t51)) % 0.34/0.57 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t51 (not @t50)))) % 0.34/0.57 (step @p62 :rule cnf_or_neg :args (@t51 0)) % 0.34/0.57 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.34/0.57 (step @p64 :rule reordering :premises (@p63) :args ((or @t49 @t51))) % 0.34/0.57 (step @p65 :rule chain_m_resolution :premises (@p64 @p58) :args (@t49 @t57 @t58)) % 0.34/0.57 (step @p66 :rule bool-double-not-elim :args (@t59)) % 0.34/0.57 (step @p67 :rule bool-double-not-elim :args (@t17)) % 0.34/0.57 (step @p68 :rule bool-double-not-elim :args (@t19)) % 0.34/0.57 (step @p69 :rule nary_cong :premises (@p15 @p68 @p67 @p66) :args (@t64)) % 0.34/0.57 (step @p70 :rule aci_norm :args ((= (or @t35 (or @t63 (or @t62 @t61))) @t64))) % 0.34/0.57 (step @p71 :rule trans :premises (@p70 @p69)) % 0.34/0.57 (step @p72 :rule bool-and-de-morgan :args (@t18 @t60 true)) % 0.34/0.57 (step @p73 :rule refl :args (@t63)) % 0.34/0.57 (step @p74 :rule nary_cong :premises (@p73 @p72) :args ((or @t63 (not (and @t18 @t60))))) % 0.34/0.57 (step @p75 :rule bool-and-de-morgan :args (@t20 @t18 (and @t60))) % 0.34/0.57 (step @p76 :rule trans :premises (@p75 @p74)) % 0.34/0.57 (step @p77 :rule nary_cong :premises (@p15 @p76) :args ((or @t35 (not (and @t20 @t18 @t60))))) % 0.34/0.57 (step @p78 :rule bool-and-de-morgan :args (@t21 @t20 (and @t18 @t60))) % 0.34/0.57 (step @p79 :rule trans :premises (@p78 @p77)) % 0.34/0.57 (step @p80 :rule trans :premises (@p79 @p71)) % 0.34/0.57 (step @p81 :rule cong :premises (@p80) :args ((forall @t24 (not (and @t21 @t20 @t18 @t60))))) % 0.34/0.57 (step @p82 :rule refl :args (@t12)) % 0.34/0.57 (step @p83 :rule nary_cong :premises (@p82 @p29) :args (@t13)) % 0.34/0.57 (step @p84 :rule cong :premises (@p83) :args (@t14)) % 0.34/0.57 (step @p85 :rule refl :args (@t18)) % 0.34/0.57 (step @p86 :rule refl :args (@t20)) % 0.34/0.57 (step @p87 :rule nary_cong :premises (@p33 @p86 @p85 @p84) :args (@t22)) % 0.34/0.57 (step @p88 :rule cong :premises (@p87) :args (@t23)) % 0.34/0.57 (step @p89 :rule cong :premises (@p88) :args (@t25)) % 0.34/0.57 (step @p90 :rule trans :premises (@p89 @p81)) % 0.34/0.57 (step @p91 :rule eq_resolve :premises (@p8 @p90)) % 0.34/0.57 (step @p92 :rule refl :args (@t66)) % 0.34/0.57 (step @p93 :rule refl :args (@t67)) % 0.34/0.57 (step @p94 :rule nary_cong :premises (@p44 @p93) :args (@t68)) % 0.34/0.57 (step @p95 :rule refl :args (@t69)) % 0.34/0.57 (step @p96 :rule nary_cong :premises (@p46 @p95 @p94 @p92) :args (@t70)) % 0.34/0.57 (step @p97 :rule refl :args (@t71)) % 0.34/0.57 (step @p98 :rule cong :premises (@p97 @p96) :args ((=> @t71 @t70))) % 0.34/0.57 (assume-push @p137 @t71) % 0.34/0.57 (step @p100 :rule instantiate :premises (@p91) :args ((@list @t47 @t44 @t42))) % 0.34/0.57 (step-pop @p138 :rule scope :premises (@p100)) % 0.34/0.57 (step @p101 :rule process_scope :premises (@p138) :args (@t70)) % 0.34/0.57 (step @p103 :rule eq_resolve :premises (@p101 @p98)) % 0.34/0.57 (step @p104 :rule implies_elim :premises (@p103)) % 0.34/0.57 (step @p105 :rule chain_m_resolution :premises (@p104 @p91) :args (@t73 @t74 (@list @t71))) % 0.34/0.57 (step @p106 :rule cnf_or_neg :args (@t51 2)) % 0.34/0.57 (step @p107 :rule chain_m_resolution :premises (@p106 @p58) :args ((not @t45) @t57 @t58)) % 0.34/0.57 (step @p108 :rule cnf_and_pos :args (@t72 0)) % 0.34/0.57 (step @p109 :rule reordering :premises (@p108) :args ((or @t45 @t75))) % 0.34/0.57 (step @p110 :rule chain_m_resolution :premises (@p109 @p107) :args (@t75 @t57 (@list @t45))) % 0.34/0.57 (step @p111 :rule cnf_or_neg :args (@t51 3)) % 0.34/0.57 (step @p112 :rule chain_m_resolution :premises (@p111 @p58) :args ((not @t43) @t57 @t58)) % 0.34/0.57 (step @p113 :rule cnf_and_pos :args (@t66 1)) % 0.34/0.57 (step @p114 :rule reordering :premises (@p113) :args ((or @t43 @t76))) % 0.34/0.57 (step @p115 :rule chain_m_resolution :premises (@p114 @p112) :args (@t76 @t57 (@list @t43))) % 0.34/0.57 (step @p116 :rule cnf_or_pos :args (@t73)) % 0.34/0.57 (step @p117 :rule reordering :premises (@p116) :args ((or @t50 @t69 @t66 @t72 (not @t73)))) % 0.34/0.57 (step @p118 :rule chain_m_resolution :premises (@p117 @p65 @p115 @p110 @p105) :args (@t69 (@list false true true false) (@list @t49 @t66 @t72 @t73))) % 0.34/0.57 (step @p119 :rule cnf_and_pos :args (@t69 1)) % 0.34/0.57 (step @p120 :rule reordering :premises (@p119) :args ((or @t67 @t77))) % 0.34/0.57 (step @p121 :rule chain_m_resolution :premises (@p120 @p118) :args (@t67 @t74 @t78)) % 0.34/0.57 (step @p122 :rule trans :premises (@p121 @p65)) % 0.34/0.57 (step @p123 :rule symm :premises (@p122)) % 0.34/0.57 (step @p124 :rule cnf_and_pos :args (@t69 0)) % 0.34/0.57 (step @p125 :rule reordering :premises (@p124) :args ((or @t65 @t77))) % 0.34/0.57 (step @p126 :rule chain_m_resolution :premises (@p125 @p118) :args (@t65 @t74 @t78)) % 0.34/0.57 (step @p127 :rule trans :premises (@p126 @p65 @p123)) % 0.34/0.57 (step @p128 :rule true_intro :premises (@p127)) % 0.34/0.57 (step @p129 :rule cnf_or_neg :args (@t51 1)) % 0.34/0.57 (step @p130 :rule chain_m_resolution :premises (@p129 @p58) :args ((not @t46) @t57 @t58)) % 0.34/0.57 (step @p131 :rule false_intro :premises (@p130)) % 0.34/0.57 (step @p132 :rule symm :premises (@p131)) % 0.34/0.57 (step @p133 :rule trans :premises (@p132 @p128)) % 0.34/0.57 (step @p134 false :rule eq_resolve :premises (@p133 @p11)) % 0.34/0.57 ) % 0.34/0.57 % SZS output end Proof % 0.34/0.57 % cvc5 exiting %------------------------------------------------------------------------------