%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU580^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 0.31s 0.54s % Output : Proof 0.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU580^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.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 17:42:32 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.49 %----Proving TH0 % 0.31/0.54 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.54 % SZS status Theorem % 0.31/0.54 % SZS output start Proof % 0.31/0.54 ( % 0.31/0.54 (declare-sort $$unsorted 0) % 0.31/0.54 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.31/0.54 (declare-const tptp.dsetconstrEL Bool) % 0.31/0.54 (declare-const tptp.powersetI Bool) % 0.31/0.54 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.31/0.54 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.31/0.54 (define @t1 () (@var "A" $$unsorted)) % 0.31/0.54 (define @t2 () (@var "Xx" $$unsorted)) % 0.31/0.54 (define @t3 () (_ tptp.in @t2)) % 0.31/0.54 (define @t4 () (_ @t3 @t1)) % 0.31/0.54 (define @t5 () (@var "Xy" $$unsorted)) % 0.31/0.54 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.31/0.54 (define @t7 () (_ @t6 @t5)) % 0.31/0.54 (define @t8 () (@list @t5)) % 0.31/0.54 (define @t9 () (lambda @t8 @t7)) % 0.31/0.54 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.31/0.54 (define @t11 () (_ @t10 @t9)) % 0.31/0.54 (define @t12 () (_ @t3 @t11)) % 0.31/0.54 (define @t13 () (@list @t1 @t6 @t2)) % 0.31/0.54 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.31/0.54 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.31/0.54 (define @t16 () (_ tptp.powerset @t1)) % 0.31/0.54 (define @t17 () (@var "B" $$unsorted)) % 0.31/0.54 (define @t18 () (_ tptp.in @t17)) % 0.31/0.54 (define @t19 () (_ @t18 @t16)) % 0.31/0.54 (define @t20 () (_ @t3 @t17)) % 0.31/0.54 (define @t21 () (@list @t2)) % 0.31/0.54 (define @t22 () (forall @t21 (=> @t20 @t4))) % 0.31/0.54 (define @t23 () (=> @t22 @t19)) % 0.31/0.54 (define @t24 () (@list @t1 @t17)) % 0.31/0.54 (define @t25 () (forall @t24 @t23)) % 0.31/0.54 (define @t26 () (= tptp.powersetI @t25)) % 0.31/0.54 (define @t27 () (_ @t6 @t2)) % 0.31/0.54 (define @t28 () (lambda @t21 @t27)) % 0.31/0.54 (define @t29 () (_ @t10 @t28)) % 0.31/0.54 (define @t30 () (_ (_ tptp.in @t29) @t16)) % 0.31/0.54 (define @t31 () (@list @t1 @t6)) % 0.31/0.54 (define @t32 () (forall @t31 @t30)) % 0.31/0.54 (define @t33 () (=> tptp.powersetI @t32)) % 0.31/0.54 (define @t34 () (=> tptp.dsetconstrEL @t33)) % 0.31/0.54 (define @t35 () (not @t34)) % 0.31/0.54 (define @t36 () (tptp.powerset @t1)) % 0.31/0.54 (define @t37 () (tptp.dsetconstr @t1 @t6)) % 0.31/0.54 (define @t38 () (forall @t31 (tptp.in @t37 @t36))) % 0.31/0.54 (define @t39 () (tptp.in @t17 @t36)) % 0.31/0.54 (define @t40 () (tptp.in @t2 @t1)) % 0.31/0.54 (define @t41 () (tptp.in @t2 @t17)) % 0.31/0.54 (define @t42 () (forall @t21 (or (not @t41) @t40))) % 0.31/0.54 (define @t43 () (not @t42)) % 0.31/0.54 (define @t44 () (or @t43 @t19)) % 0.31/0.54 (define @t45 () (not @t20)) % 0.31/0.54 (define @t46 () (or @t45 @t4)) % 0.31/0.54 (define @t47 () (=> tptp.powersetI @t38)) % 0.31/0.54 (define @t48 () (_ @t6 @t5)) % 0.31/0.54 (define @t49 () (lambda @t8 @t48)) % 0.31/0.54 (define @t50 () (tptp.dsetconstr @t1 @t49)) % 0.31/0.54 (define @t51 () (tptp.in @t2 @t50)) % 0.31/0.54 (define @t52 () (not @t51)) % 0.31/0.54 (define @t53 () (or @t52 @t40)) % 0.31/0.54 (define @t54 () (not @t12)) % 0.31/0.54 (define @t55 () (or @t54 @t4)) % 0.31/0.54 (define @t56 () (=> tptp.dsetconstrEL @t47)) % 0.31/0.54 (define @t57 () (_ @t6 @t2)) % 0.31/0.54 (define @t58 () (lambda @t21 @t57)) % 0.31/0.54 (define @t59 () (tptp.dsetconstr @t1 @t58)) % 0.31/0.54 (define @t60 () (tptp.in @t59 @t36)) % 0.31/0.54 (define @t61 () (@quantifiers_skolemize @t38 1)) % 0.31/0.54 (define @t62 () (@quantifiers_skolemize @t38 0)) % 0.31/0.54 (define @t63 () (tptp.dsetconstr @t62 @t61)) % 0.31/0.54 (define @t64 () (tptp.in @t63 (tptp.powerset @t62))) % 0.31/0.54 (define @t65 () (forall @t21 (or (not (tptp.in @t2 @t63)) (tptp.in @t2 @t62)))) % 0.31/0.54 (define @t66 () (not @t65)) % 0.31/0.54 (define @t67 () (or @t66 @t64)) % 0.31/0.54 (define @t68 () (@list true false)) % 0.31/0.54 (define @t69 () (forall @t13 (or (not (tptp.in @t2 @t37)) @t40))) % 0.31/0.54 (define @t70 () (@quantifiers_skolemize @t65 0)) % 0.31/0.54 (define @t71 () (or (not (tptp.in @t70 @t63)) (tptp.in @t70 @t62))) % 0.31/0.54 (assume @p1 @t15) % 0.31/0.54 (assume @p2 @t26) % 0.31/0.54 (assume @p3 @t35) % 0.31/0.54 (assume @p4 true) % 0.31/0.54 (step @p5 :rule refl :args (@t38)) % 0.31/0.54 (step @p6 :rule refl :args ((tptp.in @t17 @t16))) % 0.31/0.54 (step @p7 :rule refl :args (@t36)) % 0.31/0.54 (step @p8 :rule refl :args (@t17)) % 0.31/0.54 (step @p9 :rule cong :premises (@p8 @p7) :args (@t39)) % 0.31/0.54 (step @p10 :rule trans :premises (@p9 @p6)) % 0.31/0.54 (step @p11 :rule refl :args (@t18)) % 0.31/0.54 (step @p12 :rule ho_cong :premises (@p11 @p7)) % 0.31/0.54 (step @p13 :rule cong :premises (@p12 @p10) :args ((= (_ @t18 @t36) @t39))) % 0.31/0.54 (step @p14 :rule symm :premises (@p13)) % 0.31/0.54 (step @p15 :rule refl :args (@t19)) % 0.31/0.54 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.31/0.54 (step @p17 :rule refl :args (@t16)) % 0.31/0.54 (step @p18 :rule cong :premises (@p17 @p7) :args ((= @t16 @t36))) % 0.31/0.54 (step @p19 :rule symm :premises (@p18)) % 0.31/0.54 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.31/0.54 (step @p21 :rule ho_cong :premises (@p11 @p20)) % 0.31/0.54 (step @p22 :rule trans :premises (@p21 @p16)) % 0.31/0.54 (step @p23 :rule refl :args (@t43)) % 0.31/0.54 (step @p24 :rule nary_cong :premises (@p23 @p22) :args (@t44)) % 0.31/0.54 (step @p25 :rule cong :premises (@p24) :args ((forall @t24 @t44))) % 0.31/0.54 (step @p26 :rule bool-impl-elim :args (@t42 @t19)) % 0.31/0.54 (step @p27 :rule cong :premises (@p26) :args ((forall @t24 (=> @t42 @t19)))) % 0.31/0.54 (step @p28 :rule trans :premises (@p27 @p25)) % 0.31/0.54 (step @p29 :rule refl :args (@t19)) % 0.31/0.54 (step @p30 :rule refl :args (@t40)) % 0.31/0.54 (step @p31 :rule refl :args (@t4)) % 0.31/0.54 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t4 @t40))) % 0.31/0.54 (step @p33 :rule symm :premises (@p32)) % 0.31/0.54 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.31/0.54 (step @p35 :rule refl :args (@t41)) % 0.31/0.54 (step @p36 :rule refl :args (@t20)) % 0.31/0.54 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t20 @t41))) % 0.31/0.54 (step @p38 :rule symm :premises (@p37)) % 0.31/0.54 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.31/0.54 (step @p40 :rule cong :premises (@p39) :args (@t45)) % 0.31/0.54 (step @p41 :rule nary_cong :premises (@p40 @p34) :args (@t46)) % 0.31/0.54 (step @p42 :rule cong :premises (@p41) :args ((forall @t21 @t46))) % 0.31/0.54 (step @p43 :rule bool-impl-elim :args (@t20 @t4)) % 0.31/0.54 (step @p44 :rule cong :premises (@p43) :args (@t22)) % 0.31/0.54 (step @p45 :rule trans :premises (@p44 @p42)) % 0.31/0.54 (step @p46 :rule cong :premises (@p45 @p29) :args (@t23)) % 0.31/0.54 (step @p47 :rule cong :premises (@p46) :args (@t25)) % 0.31/0.54 (step @p48 :rule trans :premises (@p47 @p28)) % 0.31/0.54 (step @p49 :rule refl :args (tptp.powersetI)) % 0.31/0.54 (step @p50 :rule cong :premises (@p49 @p48) :args (@t26)) % 0.31/0.54 (step @p51 :rule eq_resolve :premises (@p2 @p50)) % 0.31/0.54 (step @p52 :rule cong :premises (@p51 @p5) :args (@t47)) % 0.31/0.54 (step @p53 :rule refl :args (@t40)) % 0.31/0.54 (step @p54 :rule lambda-elim :args ((= @t49 @t6))) % 0.31/0.54 (step @p55 :rule refl :args (@t1)) % 0.31/0.54 (step @p56 :rule cong :premises (@p55 @p54) :args (@t50)) % 0.31/0.54 (step @p57 :rule refl :args (@t2)) % 0.31/0.54 (step @p58 :rule cong :premises (@p57 @p56) :args (@t51)) % 0.31/0.54 (step @p59 :rule cong :premises (@p58) :args (@t52)) % 0.31/0.54 (step @p60 :rule nary_cong :premises (@p59 @p53) :args (@t53)) % 0.31/0.54 (step @p61 :rule cong :premises (@p60) :args ((forall @t13 @t53))) % 0.31/0.54 (step @p62 :rule refl :args ((tptp.in @t2 @t11))) % 0.31/0.54 (step @p63 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.31/0.54 (step @p64 :rule refl :args (@t48)) % 0.31/0.54 (step @p65 :rule cong :premises (@p64) :args (@t49)) % 0.31/0.54 (step @p66 :rule refl :args (@t1)) % 0.31/0.54 (step @p67 :rule cong :premises (@p66 @p65) :args (@t50)) % 0.31/0.54 (step @p68 :rule trans :premises (@p67 @p63)) % 0.31/0.54 (step @p69 :rule refl :args (@t2)) % 0.31/0.54 (step @p70 :rule cong :premises (@p69 @p68) :args (@t51)) % 0.31/0.54 (step @p71 :rule trans :premises (@p70 @p62)) % 0.31/0.54 (step @p72 :rule refl :args (@t3)) % 0.31/0.54 (step @p73 :rule ho_cong :premises (@p72 @p68)) % 0.31/0.54 (step @p74 :rule cong :premises (@p73 @p71) :args ((= (_ @t3 @t50) @t51))) % 0.31/0.54 (step @p75 :rule symm :premises (@p74)) % 0.31/0.54 (step @p76 :rule refl :args (@t12)) % 0.31/0.54 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.31/0.54 (step @p78 :rule refl :args (@t10)) % 0.31/0.54 (step @p79 :rule ho_cong :premises (@p78 @p65)) % 0.31/0.54 (step @p80 :rule cong :premises (@p79 @p68) :args ((= (_ @t10 @t49) @t50))) % 0.31/0.54 (step @p81 :rule symm :premises (@p80)) % 0.31/0.54 (step @p82 :rule refl :args (@t11)) % 0.31/0.54 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.31/0.54 (step @p84 :rule refl :args (@t7)) % 0.31/0.54 (step @p85 :rule cong :premises (@p84 @p64) :args ((= @t7 @t48))) % 0.31/0.54 (step @p86 :rule symm :premises (@p85)) % 0.31/0.54 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.31/0.54 (step @p88 :rule cong :premises (@p87) :args (@t9)) % 0.31/0.54 (step @p89 :rule ho_cong :premises (@p78 @p88)) % 0.31/0.54 (step @p90 :rule trans :premises (@p89 @p83)) % 0.31/0.54 (step @p91 :rule ho_cong :premises (@p72 @p90)) % 0.31/0.54 (step @p92 :rule trans :premises (@p91 @p77)) % 0.31/0.54 (step @p93 :rule cong :premises (@p92) :args (@t54)) % 0.31/0.54 (step @p94 :rule nary_cong :premises (@p93 @p34) :args (@t55)) % 0.31/0.54 (step @p95 :rule cong :premises (@p94) :args ((forall @t13 @t55))) % 0.31/0.54 (step @p96 :rule trans :premises (@p95 @p61)) % 0.31/0.54 (step @p97 :rule bool-impl-elim :args (@t12 @t4)) % 0.31/0.54 (step @p98 :rule cong :premises (@p97) :args (@t14)) % 0.31/0.54 (step @p99 :rule trans :premises (@p98 @p96)) % 0.31/0.54 (step @p100 :rule refl :args (tptp.dsetconstrEL)) % 0.31/0.54 (step @p101 :rule cong :premises (@p100 @p99) :args (@t15)) % 0.31/0.54 (step @p102 :rule eq_resolve :premises (@p1 @p101)) % 0.31/0.54 (step @p103 :rule cong :premises (@p102 @p52) :args (@t56)) % 0.31/0.54 (step @p104 :rule cong :premises (@p103) :args ((not @t56))) % 0.31/0.54 (step @p105 :rule refl :args (@t36)) % 0.31/0.54 (step @p106 :rule lambda-elim :args ((= @t58 @t6))) % 0.31/0.54 (step @p107 :rule cong :premises (@p55 @p106) :args (@t59)) % 0.31/0.54 (step @p108 :rule cong :premises (@p107 @p105) :args (@t60)) % 0.31/0.54 (step @p109 :rule cong :premises (@p108) :args ((forall @t31 @t60))) % 0.31/0.54 (step @p110 :rule refl :args ((tptp.in @t29 @t16))) % 0.31/0.54 (step @p111 :rule refl :args ((tptp.dsetconstr @t1 @t28))) % 0.31/0.54 (step @p112 :rule refl :args (@t57)) % 0.31/0.54 (step @p113 :rule cong :premises (@p112) :args (@t58)) % 0.31/0.54 (step @p114 :rule cong :premises (@p66 @p113) :args (@t59)) % 0.31/0.54 (step @p115 :rule trans :premises (@p114 @p111)) % 0.31/0.54 (step @p116 :rule cong :premises (@p115 @p7) :args (@t60)) % 0.31/0.54 (step @p117 :rule trans :premises (@p116 @p110)) % 0.31/0.54 (step @p118 :rule refl :args (tptp.in)) % 0.31/0.54 (step @p119 :rule ho_cong :premises (@p118 @p115)) % 0.31/0.54 (step @p120 :rule ho_cong :premises (@p119 @p7)) % 0.31/0.54 (step @p121 :rule cong :premises (@p120 @p117) :args ((= (_ (_ tptp.in @t59) @t36) @t60))) % 0.31/0.54 (step @p122 :rule symm :premises (@p121)) % 0.31/0.54 (step @p123 :rule refl :args (@t30)) % 0.31/0.54 (step @p124 :rule eq_resolve :premises (@p123 @p122)) % 0.31/0.54 (step @p125 :rule ho_cong :premises (@p78 @p113)) % 0.31/0.54 (step @p126 :rule cong :premises (@p125 @p115) :args ((= (_ @t10 @t58) @t59))) % 0.31/0.54 (step @p127 :rule symm :premises (@p126)) % 0.31/0.54 (step @p128 :rule refl :args (@t29)) % 0.31/0.54 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.31/0.54 (step @p130 :rule refl :args (@t27)) % 0.31/0.54 (step @p131 :rule cong :premises (@p130 @p112) :args ((= @t27 @t57))) % 0.31/0.54 (step @p132 :rule symm :premises (@p131)) % 0.31/0.54 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.31/0.54 (step @p134 :rule cong :premises (@p133) :args (@t28)) % 0.31/0.54 (step @p135 :rule ho_cong :premises (@p78 @p134)) % 0.31/0.54 (step @p136 :rule trans :premises (@p135 @p129)) % 0.31/0.54 (step @p137 :rule ho_cong :premises (@p118 @p136)) % 0.31/0.54 (step @p138 :rule ho_cong :premises (@p137 @p20)) % 0.31/0.54 (step @p139 :rule trans :premises (@p138 @p124)) % 0.31/0.54 (step @p140 :rule cong :premises (@p139) :args (@t32)) % 0.31/0.54 (step @p141 :rule trans :premises (@p140 @p109)) % 0.31/0.54 (step @p142 :rule cong :premises (@p49 @p141) :args (@t33)) % 0.31/0.54 (step @p143 :rule cong :premises (@p100 @p142) :args (@t34)) % 0.31/0.54 (step @p144 :rule cong :premises (@p143) :args (@t35)) % 0.31/0.54 (step @p145 :rule trans :premises (@p144 @p104)) % 0.31/0.54 (step @p146 :rule eq_resolve :premises (@p3 @p145)) % 0.31/0.54 (step @p147 :rule not_implies_elim1 :premises (@p146)) % 0.31/0.54 (step @p148 :rule not_implies_elim2 :premises (@p146)) % 0.31/0.54 (step @p149 :rule not_implies_elim1 :premises (@p148)) % 0.31/0.54 (step @p150 :rule instantiate :premises (@p149) :args ((@list @t62 @t63))) % 0.31/0.54 (step @p151 :rule not_implies_elim2 :premises (@p148)) % 0.31/0.54 (step @p152 :rule skolemize :premises (@p151)) % 0.31/0.54 (step @p153 :rule cnf_or_pos :args (@t67)) % 0.31/0.54 (step @p154 :rule reordering :premises (@p153) :args ((or @t64 @t66 (not @t67)))) % 0.31/0.54 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p150) :args (@t66 @t68 (@list @t64 @t67))) % 0.31/0.54 (step @p156 :rule skolemize :premises (@p155)) % 0.31/0.54 (assume-push @p163 @t69) % 0.31/0.54 (step @p158 :rule instantiate :premises (@p147) :args ((@list @t62 @t61 @t70))) % 0.31/0.54 (step-pop @p164 :rule scope :premises (@p158)) % 0.31/0.54 (step @p159 :rule process_scope :premises (@p164) :args (@t71)) % 0.31/0.54 (step @p161 :rule implies_elim :premises (@p159)) % 0.31/0.54 (step @p162 false :rule chain_m_resolution :premises (@p161 @p156 @p147) :args (false @t68 (@list @t71 @t69))) % 0.31/0.54 ) % 0.31/0.54 % SZS output end Proof % 0.31/0.54 % cvc5 exiting %------------------------------------------------------------------------------