%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU582^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n016.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 08:52:17 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU582^2 : TPTP v9.2.1. Released v3.7.0. % 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 : n016.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 17:42:54 EDT 2026 % 0.17/0.34 % CPUTime : % 0.32/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (declare-const tptp.emptyset $$unsorted) % 0.37/0.56 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.setunionI Bool) % 0.37/0.56 (declare-const tptp.setadjoinIL Bool) % 0.37/0.56 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (define tptp.binunion () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (lambda (@list _let_2 _let_1) (_ tptp.setunion (_ (_ tptp.setadjoin _let_2) (_ (_ tptp.setadjoin _let_1) tptp.emptyset))))))) % 0.37/0.56 (define @t1 () (@var "Xy" $$unsorted)) % 0.37/0.56 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.56 (define @t3 () (_ tptp.setadjoin @t2)) % 0.37/0.56 (define @t4 () (_ @t3 @t1)) % 0.37/0.56 (define @t5 () (_ tptp.in @t2)) % 0.37/0.56 (define @t6 () (_ @t5 @t4)) % 0.37/0.56 (define @t7 () (@list @t2 @t1)) % 0.37/0.56 (define @t8 () (forall @t7 @t6)) % 0.37/0.56 (define @t9 () (= tptp.setadjoinIL @t8)) % 0.37/0.56 (define @t10 () (@var "A" $$unsorted)) % 0.37/0.56 (define @t11 () (_ tptp.setunion @t10)) % 0.37/0.56 (define @t12 () (_ @t5 @t11)) % 0.37/0.56 (define @t13 () (@var "B" $$unsorted)) % 0.37/0.56 (define @t14 () (_ (_ tptp.in @t13) @t10)) % 0.37/0.56 (define @t15 () (=> @t14 @t12)) % 0.37/0.56 (define @t16 () (_ @t5 @t13)) % 0.37/0.56 (define @t17 () (@list @t10 @t2 @t13)) % 0.37/0.56 (define @t18 () (forall @t17 (=> @t16 @t15))) % 0.37/0.56 (define @t19 () (= tptp.setunionI @t18)) % 0.37/0.56 (define @t20 () (_ @t5 @t10)) % 0.37/0.56 (define @t21 () (=> @t20 (_ @t5 (_ (_ tptp.binunion @t10) @t13)))) % 0.37/0.56 (define @t22 () (@list @t10 @t13 @t2)) % 0.37/0.56 (define @t23 () (forall @t22 @t21)) % 0.37/0.56 (define @t24 () (=> tptp.setunionI @t23)) % 0.37/0.56 (define @t25 () (=> tptp.setadjoinIL @t24)) % 0.37/0.56 (define @t26 () (not @t25)) % 0.37/0.56 (define @t27 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.37/0.56 (define @t28 () (lambda @t7 (_ tptp.setunion (_ @t3 @t27)))) % 0.37/0.56 (define @t29 () (tptp.setadjoin @t13 tptp.emptyset)) % 0.37/0.56 (define @t30 () (tptp.setadjoin @t10 @t29)) % 0.37/0.56 (define @t31 () (tptp.setunion @t30)) % 0.37/0.56 (define @t32 () (tptp.in @t2 @t31)) % 0.37/0.56 (define @t33 () (tptp.in @t2 @t10)) % 0.37/0.56 (define @t34 () (forall @t22 (or (not @t33) @t32))) % 0.37/0.56 (define @t35 () (tptp.setunion @t10)) % 0.37/0.56 (define @t36 () (tptp.in @t2 @t35)) % 0.37/0.56 (define @t37 () (tptp.in @t13 @t10)) % 0.37/0.56 (define @t38 () (not @t14)) % 0.37/0.56 (define @t39 () (tptp.in @t2 @t13)) % 0.37/0.56 (define @t40 () (not @t16)) % 0.37/0.56 (define @t41 () (or @t40 @t38 @t12)) % 0.37/0.56 (define @t42 () (=> tptp.setunionI @t34)) % 0.37/0.56 (define @t43 () (tptp.setadjoin @t2 @t1)) % 0.37/0.56 (define @t44 () (tptp.in @t2 @t43)) % 0.37/0.56 (define @t45 () (=> tptp.setadjoinIL @t42)) % 0.37/0.56 (define @t46 () (_ (_ tptp.setadjoin @t13) tptp.emptyset)) % 0.37/0.56 (define @t47 () (_ tptp.setadjoin @t10)) % 0.37/0.56 (define @t48 () (_ @t47 @t46)) % 0.37/0.56 (define @t49 () (_ tptp.setunion @t48)) % 0.37/0.56 (define @t50 () (_ @t5 @t49)) % 0.37/0.56 (define @t51 () (not @t20)) % 0.37/0.56 (define @t52 () (or @t51 @t50)) % 0.37/0.56 (define @t53 () (lambda (@list @t1) (_ tptp.setunion (_ @t47 @t27)))) % 0.37/0.56 (define @t54 () (_ @t28 @t10)) % 0.37/0.56 (define @t55 () (=> @t20 (_ @t5 (_ @t54 @t13)))) % 0.37/0.56 (define @t56 () (forall @t22 @t55)) % 0.37/0.56 (define @t57 () (=> tptp.setunionI @t56)) % 0.37/0.56 (define @t58 () (=> tptp.setadjoinIL @t57)) % 0.37/0.56 (define @t59 () (tptp.setadjoin (@quantifiers_skolemize @t34 1) tptp.emptyset)) % 0.37/0.56 (define @t60 () (@quantifiers_skolemize @t34 0)) % 0.37/0.56 (define @t61 () (tptp.setadjoin @t60 @t59)) % 0.37/0.56 (define @t62 () (@quantifiers_skolemize @t34 2)) % 0.37/0.56 (define @t63 () (tptp.in @t62 (tptp.setunion @t61))) % 0.37/0.56 (define @t64 () (tptp.in @t62 @t60)) % 0.37/0.56 (define @t65 () (not @t64)) % 0.37/0.56 (define @t66 () (or @t65 @t63)) % 0.37/0.56 (define @t67 () (@list true)) % 0.37/0.56 (define @t68 () (@list @t66)) % 0.37/0.56 (define @t69 () (tptp.in @t60 @t61)) % 0.37/0.56 (define @t70 () (not @t69)) % 0.37/0.56 (define @t71 () (or @t65 @t70 @t63)) % 0.37/0.56 (define @t72 () (not @t71)) % 0.37/0.56 (define @t73 () (forall @t17 (or (not @t39) (not @t37) @t36))) % 0.37/0.56 (assume @p1 @t9) % 0.37/0.56 (assume @p2 @t19) % 0.37/0.56 (assume @p3 @t26) % 0.37/0.56 (assume @p4 true) % 0.37/0.56 (step @p5 (= tptp.binunion @t28) :rule refl :args (@t28)) % 0.37/0.56 (step @p6 :rule refl :args (@t34)) % 0.37/0.56 (step @p7 :rule refl :args ((tptp.in @t2 @t11))) % 0.37/0.56 (step @p8 :rule refl :args (@t35)) % 0.37/0.56 (step @p9 :rule refl :args (@t2)) % 0.37/0.56 (step @p10 :rule cong :premises (@p9 @p8) :args (@t36)) % 0.37/0.56 (step @p11 :rule trans :premises (@p10 @p7)) % 0.37/0.56 (step @p12 :rule refl :args (@t5)) % 0.37/0.56 (step @p13 :rule ho_cong :premises (@p12 @p8)) % 0.37/0.56 (step @p14 :rule cong :premises (@p13 @p11) :args ((= (_ @t5 @t35) @t36))) % 0.37/0.56 (step @p15 :rule symm :premises (@p14)) % 0.37/0.56 (step @p16 :rule refl :args (@t12)) % 0.37/0.56 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 0.37/0.56 (step @p18 :rule refl :args (@t11)) % 0.37/0.56 (step @p19 :rule cong :premises (@p18 @p8) :args ((= @t11 @t35))) % 0.37/0.56 (step @p20 :rule symm :premises (@p19)) % 0.37/0.56 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.37/0.56 (step @p22 :rule ho_cong :premises (@p12 @p21)) % 0.37/0.56 (step @p23 :rule trans :premises (@p22 @p17)) % 0.37/0.56 (step @p24 :rule refl :args (@t37)) % 0.37/0.56 (step @p25 :rule refl :args (@t14)) % 0.37/0.56 (step @p26 :rule cong :premises (@p25 @p24) :args ((= @t14 @t37))) % 0.37/0.56 (step @p27 :rule symm :premises (@p26)) % 0.37/0.56 (step @p28 :rule eq_resolve :premises (@p25 @p27)) % 0.37/0.56 (step @p29 :rule cong :premises (@p28) :args (@t38)) % 0.37/0.56 (step @p30 :rule refl :args (@t39)) % 0.37/0.56 (step @p31 :rule refl :args (@t16)) % 0.37/0.56 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t16 @t39))) % 0.37/0.56 (step @p33 :rule symm :premises (@p32)) % 0.37/0.56 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.37/0.56 (step @p35 :rule cong :premises (@p34) :args (@t40)) % 0.37/0.56 (step @p36 :rule nary_cong :premises (@p35 @p29 @p23) :args (@t41)) % 0.37/0.56 (step @p37 :rule cong :premises (@p36) :args ((forall @t17 @t41))) % 0.37/0.56 (step @p38 :rule aci_norm :args ((= (or @t40 (or @t38 @t12)) @t41))) % 0.37/0.56 (step @p39 :rule bool-impl-elim :args (@t14 @t12)) % 0.37/0.56 (step @p40 :rule refl :args (@t40)) % 0.37/0.56 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t40 @t15))) % 0.37/0.56 (step @p42 :rule trans :premises (@p41 @p38)) % 0.37/0.56 (step @p43 :rule bool-impl-elim :args (@t16 @t15)) % 0.37/0.56 (step @p44 :rule trans :premises (@p43 @p42)) % 0.37/0.56 (step @p45 :rule cong :premises (@p44) :args (@t18)) % 0.37/0.56 (step @p46 :rule trans :premises (@p45 @p37)) % 0.37/0.56 (step @p47 :rule refl :args (tptp.setunionI)) % 0.37/0.56 (step @p48 :rule cong :premises (@p47 @p46) :args (@t19)) % 0.37/0.56 (step @p49 :rule eq_resolve :premises (@p2 @p48)) % 0.37/0.56 (step @p50 :rule cong :premises (@p49 @p6) :args (@t42)) % 0.37/0.56 (step @p51 :rule refl :args ((tptp.in @t2 @t4))) % 0.37/0.56 (step @p52 :rule refl :args (@t43)) % 0.37/0.56 (step @p53 :rule cong :premises (@p9 @p52) :args (@t44)) % 0.37/0.56 (step @p54 :rule trans :premises (@p53 @p51)) % 0.37/0.56 (step @p55 :rule ho_cong :premises (@p12 @p52)) % 0.37/0.56 (step @p56 :rule cong :premises (@p55 @p54) :args ((= (_ @t5 @t43) @t44))) % 0.37/0.56 (step @p57 :rule symm :premises (@p56)) % 0.37/0.56 (step @p58 :rule refl :args (@t6)) % 0.37/0.56 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.37/0.56 (step @p60 :rule refl :args (@t4)) % 0.37/0.56 (step @p61 :rule cong :premises (@p60 @p52) :args ((= @t4 @t43))) % 0.37/0.56 (step @p62 :rule symm :premises (@p61)) % 0.37/0.56 (step @p63 :rule eq_resolve :premises (@p60 @p62)) % 0.37/0.56 (step @p64 :rule ho_cong :premises (@p12 @p63)) % 0.37/0.56 (step @p65 :rule trans :premises (@p64 @p59)) % 0.37/0.56 (step @p66 :rule cong :premises (@p65) :args (@t8)) % 0.37/0.56 (step @p67 :rule refl :args (tptp.setadjoinIL)) % 0.37/0.56 (step @p68 :rule cong :premises (@p67 @p66) :args (@t9)) % 0.37/0.56 (step @p69 :rule eq_resolve :premises (@p1 @p68)) % 0.37/0.56 (step @p70 :rule cong :premises (@p69 @p50) :args (@t45)) % 0.37/0.56 (step @p71 :rule cong :premises (@p70) :args ((not @t45))) % 0.37/0.56 (step @p72 :rule refl :args ((tptp.in @t2 @t49))) % 0.37/0.56 (step @p73 :rule refl :args ((tptp.setunion @t48))) % 0.37/0.56 (step @p74 :rule refl :args ((tptp.setadjoin @t10 @t46))) % 0.37/0.56 (step @p75 :rule refl :args (@t29)) % 0.37/0.56 (step @p76 :rule refl :args (@t10)) % 0.37/0.56 (step @p77 :rule cong :premises (@p76 @p75) :args (@t30)) % 0.37/0.56 (step @p78 :rule trans :premises (@p77 @p74)) % 0.37/0.56 (step @p79 :rule cong :premises (@p78) :args (@t31)) % 0.37/0.56 (step @p80 :rule trans :premises (@p79 @p73)) % 0.37/0.56 (step @p81 :rule cong :premises (@p9 @p80) :args (@t32)) % 0.37/0.56 (step @p82 :rule trans :premises (@p81 @p72)) % 0.37/0.56 (step @p83 :rule ho_cong :premises (@p12 @p80)) % 0.37/0.56 (step @p84 :rule cong :premises (@p83 @p82) :args ((= (_ @t5 @t31) @t32))) % 0.37/0.56 (step @p85 :rule symm :premises (@p84)) % 0.37/0.56 (step @p86 :rule refl :args (@t50)) % 0.37/0.56 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 0.37/0.56 (step @p88 :rule refl :args (tptp.setunion)) % 0.37/0.56 (step @p89 :rule ho_cong :premises (@p88 @p78)) % 0.37/0.56 (step @p90 :rule cong :premises (@p89 @p80) :args ((= (_ tptp.setunion @t30) @t31))) % 0.37/0.56 (step @p91 :rule symm :premises (@p90)) % 0.37/0.56 (step @p92 :rule refl :args (@t49)) % 0.37/0.56 (step @p93 :rule eq_resolve :premises (@p92 @p91)) % 0.37/0.56 (step @p94 :rule refl :args (@t47)) % 0.37/0.56 (step @p95 :rule ho_cong :premises (@p94 @p75)) % 0.37/0.56 (step @p96 :rule cong :premises (@p95 @p78) :args ((= (_ @t47 @t29) @t30))) % 0.37/0.56 (step @p97 :rule symm :premises (@p96)) % 0.37/0.56 (step @p98 :rule refl :args (@t48)) % 0.37/0.56 (step @p99 :rule eq_resolve :premises (@p98 @p97)) % 0.37/0.56 (step @p100 :rule refl :args (@t46)) % 0.37/0.56 (step @p101 :rule cong :premises (@p100 @p75) :args ((= @t46 @t29))) % 0.37/0.56 (step @p102 :rule symm :premises (@p101)) % 0.37/0.56 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.37/0.56 (step @p104 :rule ho_cong :premises (@p94 @p103)) % 0.37/0.56 (step @p105 :rule trans :premises (@p104 @p99)) % 0.37/0.56 (step @p106 :rule ho_cong :premises (@p88 @p105)) % 0.37/0.56 (step @p107 :rule trans :premises (@p106 @p93)) % 0.37/0.56 (step @p108 :rule ho_cong :premises (@p12 @p107)) % 0.37/0.56 (step @p109 :rule trans :premises (@p108 @p87)) % 0.37/0.56 (step @p110 :rule refl :args (@t33)) % 0.37/0.56 (step @p111 :rule refl :args (@t20)) % 0.37/0.56 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t20 @t33))) % 0.37/0.56 (step @p113 :rule symm :premises (@p112)) % 0.37/0.56 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.37/0.56 (step @p115 :rule cong :premises (@p114) :args (@t51)) % 0.37/0.56 (step @p116 :rule nary_cong :premises (@p115 @p109) :args (@t52)) % 0.37/0.56 (step @p117 :rule cong :premises (@p116) :args ((forall @t22 @t52))) % 0.37/0.56 (step @p118 :rule bool-impl-elim :args (@t20 @t50)) % 0.37/0.56 (step @p119 :rule cong :premises (@p118) :args ((forall @t22 (=> @t20 @t50)))) % 0.37/0.56 (step @p120 :rule trans :premises (@p119 @p117)) % 0.37/0.56 (step @p121 :rule beta-reduce :args ((= (_ @t53 @t13) @t49))) % 0.37/0.56 (step @p122 :rule refl :args (@t13)) % 0.37/0.56 (step @p123 :rule beta-reduce :args ((= @t54 @t53))) % 0.37/0.56 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 0.37/0.56 (step @p125 :rule trans :premises (@p124 @p121)) % 0.37/0.56 (step @p126 :rule refl :args (@t5)) % 0.37/0.56 (step @p127 :rule ho_cong :premises (@p126 @p125)) % 0.37/0.56 (step @p128 :rule refl :args (@t20)) % 0.37/0.56 (step @p129 :rule cong :premises (@p128 @p127) :args (@t55)) % 0.37/0.56 (step @p130 :rule cong :premises (@p129) :args (@t56)) % 0.37/0.56 (step @p131 :rule trans :premises (@p130 @p120)) % 0.37/0.56 (step @p132 :rule cong :premises (@p47 @p131) :args (@t57)) % 0.37/0.56 (step @p133 :rule cong :premises (@p67 @p132) :args (@t58)) % 0.37/0.56 (step @p134 :rule cong :premises (@p133) :args ((not @t58))) % 0.37/0.56 (step @p135 :rule refl :args (@t10)) % 0.37/0.56 (step @p136 :rule ho_cong :premises (@p5 @p135)) % 0.37/0.56 (step @p137 :rule ho_cong :premises (@p136 @p122)) % 0.37/0.56 (step @p138 :rule ho_cong :premises (@p126 @p137)) % 0.37/0.56 (step @p139 :rule cong :premises (@p128 @p138) :args (@t21)) % 0.37/0.56 (step @p140 :rule cong :premises (@p139) :args (@t23)) % 0.37/0.56 (step @p141 :rule cong :premises (@p47 @p140) :args (@t24)) % 0.37/0.56 (step @p142 :rule cong :premises (@p67 @p141) :args (@t25)) % 0.37/0.56 (step @p143 :rule cong :premises (@p142) :args (@t26)) % 0.37/0.56 (step @p144 :rule trans :premises (@p143 @p134)) % 0.37/0.56 (step @p145 :rule trans :premises (@p144 @p71)) % 0.37/0.56 (step @p146 :rule eq_resolve :premises (@p3 @p145)) % 0.37/0.56 (step @p147 :rule not_implies_elim2 :premises (@p146)) % 0.37/0.56 (step @p148 :rule not_implies_elim1 :premises (@p147)) % 0.37/0.56 (step @p149 :rule not_implies_elim1 :premises (@p146)) % 0.37/0.56 (step @p150 :rule instantiate :premises (@p149) :args ((@list @t60 @t59))) % 0.37/0.56 (step @p151 :rule not_implies_elim2 :premises (@p147)) % 0.37/0.56 (step @p152 :rule skolemize :premises (@p151)) % 0.37/0.56 (step @p153 :rule cnf_or_neg :args (@t66 1)) % 0.37/0.56 (step @p154 :rule chain_m_resolution :premises (@p153 @p152) :args ((not @t63) @t67 @t68)) % 0.37/0.56 (step @p155 :rule bool-double-not-elim :args (@t64)) % 0.37/0.56 (step @p156 :rule refl :args (@t66)) % 0.37/0.56 (step @p157 :rule nary_cong :premises (@p156 @p155) :args ((or @t66 (not @t65)))) % 0.37/0.56 (step @p158 :rule cnf_or_neg :args (@t66 0)) % 0.37/0.56 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.37/0.56 (step @p160 :rule reordering :premises (@p159) :args ((or @t64 @t66))) % 0.37/0.56 (step @p161 :rule chain_m_resolution :premises (@p160 @p152) :args (@t64 @t67 @t68)) % 0.37/0.56 (step @p162 :rule cnf_or_pos :args (@t71)) % 0.37/0.56 (step @p163 :rule reordering :premises (@p162) :args ((or @t65 @t63 @t70 @t72))) % 0.37/0.56 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p154 @p150) :args (@t72 (@list false true false) (@list @t64 @t63 @t69))) % 0.37/0.56 (assume-push @p171 @t73) % 0.37/0.56 (step @p166 :rule instantiate :premises (@p148) :args ((@list @t61 @t62 @t60))) % 0.37/0.56 (step-pop @p172 :rule scope :premises (@p166)) % 0.37/0.56 (step @p167 :rule process_scope :premises (@p172) :args (@t71)) % 0.37/0.56 (step @p169 :rule implies_elim :premises (@p167)) % 0.37/0.57 (step @p170 false :rule chain_m_resolution :premises (@p169 @p164 @p148) :args (false (@list true false) (@list @t71 @t73))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------