%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU629^2 : 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 : n015.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 08:52:29 AM UTC 2026 % Result : Theorem 0.29s 0.55s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU629^2 : TPTP v9.2.1. Released v3.7.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n015.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:43:49 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.29/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.55 % SZS status Theorem % 0.29/0.55 % SZS output start Proof % 0.29/0.55 ( % 0.29/0.55 (declare-sort $$unsorted 0) % 0.29/0.55 (declare-const tptp.emptyset $$unsorted) % 0.29/0.55 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.29/0.55 (declare-const tptp.ubforcartprodlem2 Bool) % 0.29/0.55 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.29/0.55 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.29/0.55 (declare-const tptp.binunion (-> $$unsorted $$unsorted $$unsorted)) % 0.29/0.55 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 0.29/0.55 (define @t1 () (@var "B" $$unsorted)) % 0.29/0.55 (define @t2 () (@var "A" $$unsorted)) % 0.29/0.55 (define @t3 () (_ (_ tptp.binunion @t2) @t1)) % 0.29/0.55 (define @t4 () (_ tptp.powerset @t3)) % 0.29/0.55 (define @t5 () (_ tptp.powerset @t4)) % 0.29/0.55 (define @t6 () (@var "Xy" $$unsorted)) % 0.29/0.55 (define @t7 () (_ (_ tptp.setadjoin @t6) tptp.emptyset)) % 0.29/0.55 (define @t8 () (@var "Xx" $$unsorted)) % 0.29/0.55 (define @t9 () (_ tptp.setadjoin @t8)) % 0.29/0.55 (define @t10 () (_ @t9 @t7)) % 0.29/0.55 (define @t11 () (_ (_ tptp.setadjoin @t10) tptp.emptyset)) % 0.29/0.55 (define @t12 () (_ @t9 tptp.emptyset)) % 0.29/0.55 (define @t13 () (_ (_ tptp.setadjoin @t12) @t11)) % 0.29/0.55 (define @t14 () (_ (_ tptp.in @t13) @t5)) % 0.29/0.55 (define @t15 () (_ (_ tptp.in @t6) @t1)) % 0.29/0.55 (define @t16 () (@list @t6)) % 0.29/0.55 (define @t17 () (forall @t16 (=> @t15 @t14))) % 0.29/0.55 (define @t18 () (_ (_ tptp.in @t8) @t2)) % 0.29/0.55 (define @t19 () (=> @t18 @t17)) % 0.29/0.55 (define @t20 () (@list @t2 @t1 @t8)) % 0.29/0.55 (define @t21 () (forall @t20 @t19)) % 0.29/0.55 (define @t22 () (= tptp.ubforcartprodlem2 @t21)) % 0.29/0.55 (define @t23 () (=> @t15 (_ (_ tptp.in (_ (_ tptp.kpair @t8) @t6)) @t5))) % 0.29/0.55 (define @t24 () (forall @t16 @t23)) % 0.29/0.55 (define @t25 () (=> @t18 @t24)) % 0.29/0.55 (define @t26 () (forall @t20 @t25)) % 0.29/0.55 (define @t27 () (=> tptp.ubforcartprodlem2 @t26)) % 0.29/0.55 (define @t28 () (not @t27)) % 0.29/0.55 (define @t29 () (lambda (@list @t8 @t6) @t13)) % 0.29/0.55 (define @t30 () (tptp.binunion @t2 @t1)) % 0.29/0.55 (define @t31 () (tptp.powerset @t30)) % 0.29/0.55 (define @t32 () (tptp.powerset @t31)) % 0.29/0.55 (define @t33 () (@var "BOUND_VARIABLE_7497" $$unsorted)) % 0.29/0.55 (define @t34 () (tptp.setadjoin @t8 tptp.emptyset)) % 0.29/0.55 (define @t35 () (tptp.in (tptp.setadjoin @t34 (tptp.setadjoin (tptp.setadjoin @t8 (tptp.setadjoin @t33 tptp.emptyset)) tptp.emptyset)) @t32)) % 0.29/0.55 (define @t36 () (not (tptp.in @t33 @t1))) % 0.29/0.55 (define @t37 () (tptp.in @t8 @t2)) % 0.29/0.55 (define @t38 () (not @t37)) % 0.29/0.55 (define @t39 () (or @t38 @t36 @t35)) % 0.29/0.55 (define @t40 () (or @t36 @t35)) % 0.29/0.55 (define @t41 () (or @t38 @t40)) % 0.29/0.55 (define @t42 () (@list @t2 @t1 @t8 @t33)) % 0.29/0.55 (define @t43 () (forall @t42 @t41)) % 0.29/0.55 (define @t44 () (@list @t33)) % 0.29/0.55 (define @t45 () (forall @t44 @t41)) % 0.29/0.55 (define @t46 () (forall @t44 @t40)) % 0.29/0.55 (define @t47 () (or @t38 @t46)) % 0.29/0.55 (define @t48 () (tptp.setadjoin @t6 tptp.emptyset)) % 0.29/0.55 (define @t49 () (tptp.setadjoin @t8 @t48)) % 0.29/0.55 (define @t50 () (tptp.setadjoin @t49 tptp.emptyset)) % 0.29/0.55 (define @t51 () (tptp.setadjoin @t34 @t50)) % 0.29/0.55 (define @t52 () (tptp.in @t51 @t32)) % 0.29/0.55 (define @t53 () (tptp.in @t6 @t1)) % 0.29/0.55 (define @t54 () (forall @t16 (or (not @t53) @t52))) % 0.29/0.55 (define @t55 () (not @t18)) % 0.29/0.55 (define @t56 () (or @t55 @t54)) % 0.29/0.55 (define @t57 () (not @t15)) % 0.29/0.55 (define @t58 () (or @t57 @t14)) % 0.29/0.55 (define @t59 () (lambda @t16 @t13)) % 0.29/0.55 (define @t60 () (_ @t29 @t8)) % 0.29/0.55 (define @t61 () (=> @t15 (_ (_ tptp.in (_ @t60 @t6)) @t5))) % 0.29/0.55 (define @t62 () (forall @t16 @t61)) % 0.29/0.55 (define @t63 () (=> @t18 @t62)) % 0.29/0.55 (define @t64 () (forall @t20 @t63)) % 0.29/0.55 (define @t65 () (=> tptp.ubforcartprodlem2 @t64)) % 0.29/0.55 (define @t66 () (forall @t42 @t39)) % 0.29/0.55 (assume @p1 @t22) % 0.29/0.55 (assume @p2 @t28) % 0.29/0.55 (assume @p3 true) % 0.29/0.55 (step @p4 (= tptp.kpair @t29) :rule refl :args (@t29)) % 0.29/0.55 (step @p5 :rule aci_norm :args ((= @t41 @t39))) % 0.29/0.55 (step @p6 :rule cong :premises (@p5) :args (@t43)) % 0.29/0.55 (step @p7 :rule quant-merge-prenex :args ((= (forall @t20 @t45) @t43))) % 0.29/0.55 (step @p8 :rule alpha_equiv :args (@t46 (@list @t33) (@list @t6))) % 0.29/0.55 (step @p9 :rule refl :args (@t38)) % 0.29/0.55 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t47)) % 0.29/0.55 (step @p11 :rule quant-miniscope-or :args ((= @t45 @t47))) % 0.29/0.55 (step @p12 :rule trans :premises (@p11 @p10)) % 0.29/0.55 (step @p13 :rule symm :premises (@p12)) % 0.29/0.55 (step @p14 :rule cong :premises (@p13) :args ((forall @t20 (or @t38 @t54)))) % 0.29/0.55 (step @p15 :rule trans :premises (@p14 @p7)) % 0.29/0.55 (step @p16 :rule trans :premises (@p15 @p6)) % 0.29/0.55 (step @p17 :rule refl :args (@t54)) % 0.29/0.55 (step @p18 :rule refl :args (@t37)) % 0.29/0.55 (step @p19 :rule refl :args (@t18)) % 0.29/0.55 (step @p20 :rule cong :premises (@p19 @p18) :args ((= @t18 @t37))) % 0.29/0.55 (step @p21 :rule symm :premises (@p20)) % 0.29/0.55 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 0.29/0.55 (step @p23 :rule cong :premises (@p22) :args (@t55)) % 0.29/0.55 (step @p24 :rule nary_cong :premises (@p23 @p17) :args (@t56)) % 0.29/0.55 (step @p25 :rule cong :premises (@p24) :args ((forall @t20 @t56))) % 0.29/0.55 (step @p26 :rule trans :premises (@p25 @p16)) % 0.29/0.55 (step @p27 :rule bool-impl-elim :args (@t18 @t54)) % 0.29/0.55 (step @p28 :rule cong :premises (@p27) :args ((forall @t20 (=> @t18 @t54)))) % 0.29/0.55 (step @p29 :rule trans :premises (@p28 @p26)) % 0.29/0.55 (step @p30 :rule refl :args ((tptp.in @t13 @t5))) % 0.29/0.55 (step @p31 :rule refl :args ((tptp.powerset @t4))) % 0.29/0.55 (step @p32 :rule refl :args ((tptp.powerset @t3))) % 0.29/0.55 (step @p33 :rule refl :args (@t30)) % 0.29/0.55 (step @p34 :rule cong :premises (@p33) :args (@t31)) % 0.29/0.55 (step @p35 :rule trans :premises (@p34 @p32)) % 0.29/0.55 (step @p36 :rule cong :premises (@p35) :args (@t32)) % 0.29/0.55 (step @p37 :rule trans :premises (@p36 @p31)) % 0.29/0.55 (step @p38 :rule refl :args ((tptp.setadjoin @t12 @t11))) % 0.29/0.55 (step @p39 :rule refl :args ((tptp.setadjoin @t10 tptp.emptyset))) % 0.29/0.55 (step @p40 :rule refl :args (tptp.emptyset)) % 0.29/0.55 (step @p41 :rule refl :args ((tptp.setadjoin @t8 @t7))) % 0.29/0.55 (step @p42 :rule refl :args (@t48)) % 0.29/0.55 (step @p43 :rule refl :args (@t8)) % 0.29/0.55 (step @p44 :rule cong :premises (@p43 @p42) :args (@t49)) % 0.29/0.55 (step @p45 :rule trans :premises (@p44 @p41)) % 0.29/0.55 (step @p46 :rule cong :premises (@p45 @p40) :args (@t50)) % 0.29/0.55 (step @p47 :rule trans :premises (@p46 @p39)) % 0.29/0.55 (step @p48 :rule refl :args (@t34)) % 0.29/0.55 (step @p49 :rule cong :premises (@p48 @p47) :args (@t51)) % 0.29/0.55 (step @p50 :rule trans :premises (@p49 @p38)) % 0.29/0.55 (step @p51 :rule cong :premises (@p50 @p37) :args (@t52)) % 0.29/0.55 (step @p52 :rule trans :premises (@p51 @p30)) % 0.29/0.55 (step @p53 :rule refl :args (tptp.in)) % 0.29/0.55 (step @p54 :rule ho_cong :premises (@p53 @p50)) % 0.29/0.55 (step @p55 :rule ho_cong :premises (@p54 @p37)) % 0.29/0.55 (step @p56 :rule cong :premises (@p55 @p52) :args ((= (_ (_ tptp.in @t51) @t32) @t52))) % 0.29/0.55 (step @p57 :rule symm :premises (@p56)) % 0.29/0.55 (step @p58 :rule refl :args (@t14)) % 0.29/0.55 (step @p59 :rule eq_resolve :premises (@p58 @p57)) % 0.29/0.55 (step @p60 :rule refl :args (tptp.powerset)) % 0.29/0.55 (step @p61 :rule ho_cong :premises (@p60 @p35)) % 0.29/0.55 (step @p62 :rule cong :premises (@p61 @p37) :args ((= (_ tptp.powerset @t31) @t32))) % 0.29/0.55 (step @p63 :rule symm :premises (@p62)) % 0.29/0.55 (step @p64 :rule refl :args (@t5)) % 0.29/0.55 (step @p65 :rule eq_resolve :premises (@p64 @p63)) % 0.29/0.55 (step @p66 :rule ho_cong :premises (@p60 @p33)) % 0.29/0.55 (step @p67 :rule cong :premises (@p66 @p35) :args ((= (_ tptp.powerset @t30) @t31))) % 0.29/0.55 (step @p68 :rule symm :premises (@p67)) % 0.29/0.55 (step @p69 :rule refl :args (@t4)) % 0.29/0.55 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 0.29/0.55 (step @p71 :rule refl :args (@t3)) % 0.29/0.55 (step @p72 :rule cong :premises (@p71 @p33) :args ((= @t3 @t30))) % 0.29/0.55 (step @p73 :rule symm :premises (@p72)) % 0.29/0.55 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.29/0.55 (step @p75 :rule ho_cong :premises (@p60 @p74)) % 0.29/0.55 (step @p76 :rule trans :premises (@p75 @p70)) % 0.29/0.55 (step @p77 :rule ho_cong :premises (@p60 @p76)) % 0.29/0.55 (step @p78 :rule trans :premises (@p77 @p65)) % 0.29/0.55 (step @p79 :rule refl :args (tptp.setadjoin)) % 0.29/0.55 (step @p80 :rule ho_cong :premises (@p79 @p48)) % 0.29/0.55 (step @p81 :rule ho_cong :premises (@p80 @p47)) % 0.29/0.55 (step @p82 :rule cong :premises (@p81 @p50) :args ((= (_ (_ tptp.setadjoin @t34) @t50) @t51))) % 0.29/0.55 (step @p83 :rule symm :premises (@p82)) % 0.29/0.55 (step @p84 :rule refl :args (@t13)) % 0.29/0.55 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 0.29/0.55 (step @p86 :rule ho_cong :premises (@p79 @p45)) % 0.29/0.55 (step @p87 :rule ho_cong :premises (@p86 @p40)) % 0.29/0.55 (step @p88 :rule cong :premises (@p87 @p47) :args ((= (_ (_ tptp.setadjoin @t49) tptp.emptyset) @t50))) % 0.29/0.55 (step @p89 :rule symm :premises (@p88)) % 0.29/0.55 (step @p90 :rule refl :args (@t11)) % 0.29/0.55 (step @p91 :rule eq_resolve :premises (@p90 @p89)) % 0.29/0.55 (step @p92 :rule refl :args (@t9)) % 0.29/0.55 (step @p93 :rule ho_cong :premises (@p92 @p42)) % 0.29/0.55 (step @p94 :rule cong :premises (@p93 @p45) :args ((= (_ @t9 @t48) @t49))) % 0.29/0.55 (step @p95 :rule symm :premises (@p94)) % 0.29/0.55 (step @p96 :rule refl :args (@t10)) % 0.29/0.55 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.29/0.55 (step @p98 :rule refl :args (@t7)) % 0.29/0.55 (step @p99 :rule cong :premises (@p98 @p42) :args ((= @t7 @t48))) % 0.29/0.55 (step @p100 :rule symm :premises (@p99)) % 0.29/0.55 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.29/0.55 (step @p102 :rule ho_cong :premises (@p92 @p101)) % 0.29/0.55 (step @p103 :rule trans :premises (@p102 @p97)) % 0.29/0.55 (step @p104 :rule ho_cong :premises (@p79 @p103)) % 0.29/0.55 (step @p105 :rule ho_cong :premises (@p104 @p40)) % 0.29/0.55 (step @p106 :rule trans :premises (@p105 @p91)) % 0.29/0.55 (step @p107 :rule refl :args (@t12)) % 0.29/0.55 (step @p108 :rule cong :premises (@p107 @p48) :args ((= @t12 @t34))) % 0.29/0.55 (step @p109 :rule symm :premises (@p108)) % 0.29/0.55 (step @p110 :rule eq_resolve :premises (@p107 @p109)) % 0.29/0.55 (step @p111 :rule ho_cong :premises (@p79 @p110)) % 0.29/0.55 (step @p112 :rule ho_cong :premises (@p111 @p106)) % 0.29/0.55 (step @p113 :rule trans :premises (@p112 @p85)) % 0.29/0.55 (step @p114 :rule ho_cong :premises (@p53 @p113)) % 0.29/0.55 (step @p115 :rule ho_cong :premises (@p114 @p78)) % 0.29/0.55 (step @p116 :rule trans :premises (@p115 @p59)) % 0.29/0.55 (step @p117 :rule refl :args (@t53)) % 0.29/0.55 (step @p118 :rule refl :args (@t15)) % 0.29/0.55 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t15 @t53))) % 0.29/0.55 (step @p120 :rule symm :premises (@p119)) % 0.29/0.55 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 0.29/0.55 (step @p122 :rule cong :premises (@p121) :args (@t57)) % 0.29/0.55 (step @p123 :rule nary_cong :premises (@p122 @p116) :args (@t58)) % 0.29/0.55 (step @p124 :rule cong :premises (@p123) :args ((forall @t16 @t58))) % 0.29/0.55 (step @p125 :rule bool-impl-elim :args (@t15 @t14)) % 0.29/0.55 (step @p126 :rule cong :premises (@p125) :args (@t17)) % 0.29/0.55 (step @p127 :rule trans :premises (@p126 @p124)) % 0.29/0.55 (step @p128 :rule refl :args (@t5)) % 0.29/0.55 (step @p129 :rule beta-reduce :args ((= (_ @t59 @t6) @t13))) % 0.29/0.55 (step @p130 :rule refl :args (@t6)) % 0.29/0.55 (step @p131 :rule beta-reduce :args ((= @t60 @t59))) % 0.29/0.55 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.29/0.55 (step @p133 :rule trans :premises (@p132 @p129)) % 0.29/0.55 (step @p134 :rule refl :args (tptp.in)) % 0.29/0.55 (step @p135 :rule ho_cong :premises (@p134 @p133)) % 0.29/0.55 (step @p136 :rule ho_cong :premises (@p135 @p128)) % 0.29/0.55 (step @p137 :rule refl :args (@t15)) % 0.29/0.55 (step @p138 :rule cong :premises (@p137 @p136) :args (@t61)) % 0.29/0.55 (step @p139 :rule cong :premises (@p138) :args (@t62)) % 0.29/0.55 (step @p140 :rule trans :premises (@p139 @p127)) % 0.29/0.55 (step @p141 :rule refl :args (@t18)) % 0.29/0.55 (step @p142 :rule cong :premises (@p141 @p140) :args (@t63)) % 0.29/0.55 (step @p143 :rule cong :premises (@p142) :args (@t64)) % 0.29/0.55 (step @p144 :rule trans :premises (@p143 @p29)) % 0.29/0.55 (step @p145 :rule refl :args (tptp.ubforcartprodlem2)) % 0.29/0.55 (step @p146 :rule cong :premises (@p145 @p144) :args (@t65)) % 0.29/0.55 (step @p147 :rule cong :premises (@p146) :args ((not @t65))) % 0.29/0.55 (step @p148 :rule refl :args (@t8)) % 0.29/0.55 (step @p149 :rule ho_cong :premises (@p4 @p148)) % 0.29/0.55 (step @p150 :rule ho_cong :premises (@p149 @p130)) % 0.29/0.55 (step @p151 :rule ho_cong :premises (@p134 @p150)) % 0.29/0.55 (step @p152 :rule ho_cong :premises (@p151 @p128)) % 0.29/0.55 (step @p153 :rule cong :premises (@p137 @p152) :args (@t23)) % 0.29/0.55 (step @p154 :rule cong :premises (@p153) :args (@t24)) % 0.29/0.55 (step @p155 :rule cong :premises (@p141 @p154) :args (@t25)) % 0.29/0.55 (step @p156 :rule cong :premises (@p155) :args (@t26)) % 0.29/0.55 (step @p157 :rule cong :premises (@p145 @p156) :args (@t27)) % 0.29/0.55 (step @p158 :rule cong :premises (@p157) :args (@t28)) % 0.29/0.55 (step @p159 :rule trans :premises (@p158 @p147)) % 0.29/0.55 (step @p160 :rule eq_resolve :premises (@p2 @p159)) % 0.29/0.55 (step @p161 :rule not_implies_elim2 :premises (@p160)) % 0.29/0.55 (step @p162 :rule not_implies_elim1 :premises (@p160)) % 0.29/0.55 (step @p163 :rule cnf_equiv_pos1 :args ((= tptp.ubforcartprodlem2 @t66))) % 0.29/0.55 (step @p164 :rule chain_resolution :premises (@p163 @p162 @p161) :args ((@list false true) (@list tptp.ubforcartprodlem2 @t66))) % 0.29/0.55 (step @p165 :rule cong :premises (@p141 @p127) :args (@t19)) % 0.29/0.55 (step @p166 :rule cong :premises (@p165) :args (@t21)) % 0.29/0.55 (step @p167 :rule trans :premises (@p166 @p29)) % 0.29/0.55 (step @p168 :rule cong :premises (@p145 @p167) :args (@t22)) % 0.29/0.55 (step @p169 :rule eq_resolve :premises (@p1 @p168)) % 0.29/0.55 (step @p170 false :rule contra :premises (@p169 @p164)) % 0.29/0.55 ) % 0.29/0.55 % SZS output end Proof % 0.29/0.55 % cvc5 exiting %------------------------------------------------------------------------------