%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU602^2 : 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 : n008.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 08:52:22 AM UTC 2026 % Result : Theorem 0.33s 0.58s % Output : Proof 0.33s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU602^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n008.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:43:03 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.33/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.33/0.58 % SZS status Theorem % 0.33/0.58 % SZS output start Proof % 0.33/0.58 ( % 0.33/0.58 (declare-sort $$unsorted 0) % 0.33/0.58 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.33/0.58 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.33/0.58 (declare-const tptp.dsetconstrEL Bool) % 0.33/0.58 (define tptp.setminus () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_1) (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_2) (not (_ (_ tptp.in _let_2) _let_1))))))))) % 0.33/0.58 (define @t1 () (@var "A" $$unsorted)) % 0.33/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.33/0.58 (define @t3 () (_ tptp.in @t2)) % 0.33/0.58 (define @t4 () (_ @t3 @t1)) % 0.33/0.58 (define @t5 () (@var "Xy" $$unsorted)) % 0.33/0.58 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.33/0.58 (define @t7 () (_ @t6 @t5)) % 0.33/0.58 (define @t8 () (@list @t5)) % 0.33/0.58 (define @t9 () (lambda @t8 @t7)) % 0.33/0.58 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.33/0.58 (define @t11 () (_ @t10 @t9)) % 0.33/0.58 (define @t12 () (_ @t3 @t11)) % 0.33/0.58 (define @t13 () (@list @t1 @t6 @t2)) % 0.33/0.58 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.33/0.58 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.33/0.58 (define @t16 () (@var "B" $$unsorted)) % 0.33/0.58 (define @t17 () (=> (_ @t3 (_ (_ tptp.setminus @t1) @t16)) @t4)) % 0.33/0.58 (define @t18 () (@list @t1 @t16 @t2)) % 0.33/0.58 (define @t19 () (forall @t18 @t17)) % 0.33/0.58 (define @t20 () (=> tptp.dsetconstrEL @t19)) % 0.33/0.58 (define @t21 () (not @t20)) % 0.33/0.58 (define @t22 () (lambda (@list @t2) (not (_ @t3 @t16)))) % 0.33/0.58 (define @t23 () (_ @t10 @t22)) % 0.33/0.58 (define @t24 () (lambda (@list @t1 @t16) @t23)) % 0.33/0.58 (define @t25 () (tptp.in @t2 @t1)) % 0.33/0.58 (define @t26 () (@var "BOUND_VARIABLE_7485" $$unsorted)) % 0.33/0.58 (define @t27 () (tptp.in @t26 @t16)) % 0.33/0.58 (define @t28 () (not @t27)) % 0.33/0.58 (define @t29 () (@list @t26)) % 0.33/0.58 (define @t30 () (lambda @t29 @t28)) % 0.33/0.58 (define @t31 () (tptp.dsetconstr @t1 @t30)) % 0.33/0.58 (define @t32 () (tptp.in @t2 @t31)) % 0.33/0.58 (define @t33 () (forall @t18 (or (not @t32) @t25))) % 0.33/0.58 (define @t34 () (_ @t6 @t5)) % 0.33/0.58 (define @t35 () (lambda @t8 @t34)) % 0.33/0.58 (define @t36 () (tptp.dsetconstr @t1 @t35)) % 0.33/0.58 (define @t37 () (tptp.in @t2 @t36)) % 0.33/0.58 (define @t38 () (not @t37)) % 0.33/0.58 (define @t39 () (or @t38 @t25)) % 0.33/0.58 (define @t40 () (not @t12)) % 0.33/0.58 (define @t41 () (or @t40 @t4)) % 0.33/0.58 (define @t42 () (=> tptp.dsetconstrEL @t33)) % 0.33/0.58 (define @t43 () (_ (_ tptp.in @t26) @t16)) % 0.33/0.58 (define @t44 () (not @t43)) % 0.33/0.58 (define @t45 () (lambda @t29 @t44)) % 0.33/0.58 (define @t46 () (_ @t10 @t45)) % 0.33/0.58 (define @t47 () (_ @t3 @t46)) % 0.33/0.58 (define @t48 () (not @t47)) % 0.33/0.58 (define @t49 () (or @t48 @t4)) % 0.33/0.58 (define @t50 () (=> (_ @t3 @t23) @t4)) % 0.33/0.58 (define @t51 () (lambda (@list @t16) @t23)) % 0.33/0.58 (define @t52 () (_ @t24 @t1)) % 0.33/0.58 (define @t53 () (=> (_ @t3 (_ @t52 @t16)) @t4)) % 0.33/0.58 (define @t54 () (forall @t18 @t53)) % 0.33/0.58 (define @t55 () (=> tptp.dsetconstrEL @t54)) % 0.33/0.58 (define @t56 () (@quantifiers_skolemize @t33 0)) % 0.33/0.58 (define @t57 () (@quantifiers_skolemize @t33 2)) % 0.33/0.58 (define @t58 () (tptp.in @t57 @t56)) % 0.33/0.58 (define @t59 () (lambda @t29 (not (tptp.in @t26 (@quantifiers_skolemize @t33 1))))) % 0.33/0.58 (define @t60 () (@purify @t59)) % 0.33/0.58 (define @t61 () (or (not (tptp.in @t57 (tptp.dsetconstr @t56 @t60))) @t58)) % 0.33/0.58 (define @t62 () (not @t61)) % 0.33/0.58 (define @t63 () (not @t33)) % 0.33/0.58 (define @t64 () (tptp.dsetconstr @t56 @t59)) % 0.33/0.58 (define @t65 () (tptp.in @t57 @t64)) % 0.33/0.58 (define @t66 () (not @t65)) % 0.33/0.58 (define @t67 () (or @t66 @t58)) % 0.33/0.58 (define @t68 () (not @t67)) % 0.33/0.58 (define @t69 () (forall @t13 (or (not (tptp.in @t2 (tptp.dsetconstr @t1 @t6))) @t25))) % 0.33/0.58 (assume @p1 @t15) % 0.33/0.58 (assume @p2 @t21) % 0.33/0.58 (assume @p3 true) % 0.33/0.58 (step @p4 (= tptp.setminus @t24) :rule refl :args (@t24)) % 0.33/0.58 (step @p5 :rule refl :args (@t33)) % 0.33/0.58 (step @p6 :rule refl :args (@t25)) % 0.33/0.58 (step @p7 :rule lambda-elim :args ((= @t35 @t6))) % 0.33/0.58 (step @p8 :rule refl :args (@t1)) % 0.33/0.58 (step @p9 :rule cong :premises (@p8 @p7) :args (@t36)) % 0.33/0.58 (step @p10 :rule refl :args (@t2)) % 0.33/0.58 (step @p11 :rule cong :premises (@p10 @p9) :args (@t37)) % 0.33/0.58 (step @p12 :rule cong :premises (@p11) :args (@t38)) % 0.33/0.58 (step @p13 :rule nary_cong :premises (@p12 @p6) :args (@t39)) % 0.33/0.58 (step @p14 :rule cong :premises (@p13) :args ((forall @t13 @t39))) % 0.33/0.58 (step @p15 :rule refl :args (@t25)) % 0.33/0.58 (step @p16 :rule refl :args (@t4)) % 0.33/0.58 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t4 @t25))) % 0.33/0.58 (step @p18 :rule symm :premises (@p17)) % 0.33/0.58 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.33/0.58 (step @p20 :rule refl :args ((tptp.in @t2 @t11))) % 0.33/0.58 (step @p21 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.33/0.58 (step @p22 :rule refl :args (@t34)) % 0.33/0.58 (step @p23 :rule cong :premises (@p22) :args (@t35)) % 0.33/0.58 (step @p24 :rule refl :args (@t1)) % 0.33/0.58 (step @p25 :rule cong :premises (@p24 @p23) :args (@t36)) % 0.33/0.58 (step @p26 :rule trans :premises (@p25 @p21)) % 0.33/0.58 (step @p27 :rule refl :args (@t2)) % 0.33/0.58 (step @p28 :rule cong :premises (@p27 @p26) :args (@t37)) % 0.33/0.58 (step @p29 :rule trans :premises (@p28 @p20)) % 0.33/0.58 (step @p30 :rule refl :args (@t3)) % 0.33/0.58 (step @p31 :rule ho_cong :premises (@p30 @p26)) % 0.33/0.58 (step @p32 :rule cong :premises (@p31 @p29) :args ((= (_ @t3 @t36) @t37))) % 0.33/0.58 (step @p33 :rule symm :premises (@p32)) % 0.33/0.58 (step @p34 :rule refl :args (@t12)) % 0.33/0.58 (step @p35 :rule eq_resolve :premises (@p34 @p33)) % 0.33/0.58 (step @p36 :rule refl :args (@t10)) % 0.33/0.58 (step @p37 :rule ho_cong :premises (@p36 @p23)) % 0.33/0.58 (step @p38 :rule cong :premises (@p37 @p26) :args ((= (_ @t10 @t35) @t36))) % 0.33/0.58 (step @p39 :rule symm :premises (@p38)) % 0.33/0.58 (step @p40 :rule refl :args (@t11)) % 0.33/0.58 (step @p41 :rule eq_resolve :premises (@p40 @p39)) % 0.33/0.58 (step @p42 :rule refl :args (@t7)) % 0.33/0.58 (step @p43 :rule cong :premises (@p42 @p22) :args ((= @t7 @t34))) % 0.33/0.58 (step @p44 :rule symm :premises (@p43)) % 0.33/0.58 (step @p45 :rule eq_resolve :premises (@p42 @p44)) % 0.33/0.58 (step @p46 :rule cong :premises (@p45) :args (@t9)) % 0.33/0.58 (step @p47 :rule ho_cong :premises (@p36 @p46)) % 0.33/0.58 (step @p48 :rule trans :premises (@p47 @p41)) % 0.33/0.58 (step @p49 :rule ho_cong :premises (@p30 @p48)) % 0.33/0.58 (step @p50 :rule trans :premises (@p49 @p35)) % 0.33/0.58 (step @p51 :rule cong :premises (@p50) :args (@t40)) % 0.33/0.58 (step @p52 :rule nary_cong :premises (@p51 @p19) :args (@t41)) % 0.33/0.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t13 @t41))) % 0.33/0.58 (step @p54 :rule trans :premises (@p53 @p14)) % 0.33/0.58 (step @p55 :rule bool-impl-elim :args (@t12 @t4)) % 0.33/0.58 (step @p56 :rule cong :premises (@p55) :args (@t14)) % 0.33/0.58 (step @p57 :rule trans :premises (@p56 @p54)) % 0.33/0.58 (step @p58 :rule refl :args (tptp.dsetconstrEL)) % 0.33/0.58 (step @p59 :rule cong :premises (@p58 @p57) :args (@t15)) % 0.33/0.58 (step @p60 :rule eq_resolve :premises (@p1 @p59)) % 0.33/0.58 (step @p61 :rule cong :premises (@p60 @p5) :args (@t42)) % 0.33/0.58 (step @p62 :rule cong :premises (@p61) :args ((not @t42))) % 0.33/0.58 (step @p63 :rule refl :args ((tptp.in @t2 @t46))) % 0.33/0.58 (step @p64 :rule refl :args ((tptp.dsetconstr @t1 @t45))) % 0.33/0.58 (step @p65 :rule refl :args (@t27)) % 0.33/0.58 (step @p66 :rule cong :premises (@p65) :args (@t28)) % 0.33/0.58 (step @p67 :rule cong :premises (@p66) :args (@t30)) % 0.33/0.58 (step @p68 :rule cong :premises (@p24 @p67) :args (@t31)) % 0.33/0.58 (step @p69 :rule trans :premises (@p68 @p64)) % 0.33/0.58 (step @p70 :rule cong :premises (@p27 @p69) :args (@t32)) % 0.33/0.58 (step @p71 :rule trans :premises (@p70 @p63)) % 0.33/0.58 (step @p72 :rule ho_cong :premises (@p30 @p69)) % 0.33/0.58 (step @p73 :rule cong :premises (@p72 @p71) :args ((= (_ @t3 @t31) @t32))) % 0.33/0.58 (step @p74 :rule symm :premises (@p73)) % 0.33/0.58 (step @p75 :rule refl :args (@t47)) % 0.33/0.58 (step @p76 :rule eq_resolve :premises (@p75 @p74)) % 0.33/0.58 (step @p77 :rule ho_cong :premises (@p36 @p67)) % 0.33/0.58 (step @p78 :rule cong :premises (@p77 @p69) :args ((= (_ @t10 @t30) @t31))) % 0.33/0.58 (step @p79 :rule symm :premises (@p78)) % 0.33/0.58 (step @p80 :rule refl :args (@t46)) % 0.33/0.58 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.33/0.58 (step @p82 :rule refl :args (@t43)) % 0.33/0.58 (step @p83 :rule cong :premises (@p82 @p65) :args ((= @t43 @t27))) % 0.33/0.58 (step @p84 :rule symm :premises (@p83)) % 0.33/0.58 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.33/0.58 (step @p86 :rule cong :premises (@p85) :args (@t44)) % 0.33/0.58 (step @p87 :rule cong :premises (@p86) :args (@t45)) % 0.33/0.58 (step @p88 :rule ho_cong :premises (@p36 @p87)) % 0.33/0.58 (step @p89 :rule trans :premises (@p88 @p81)) % 0.33/0.58 (step @p90 :rule ho_cong :premises (@p30 @p89)) % 0.33/0.58 (step @p91 :rule trans :premises (@p90 @p76)) % 0.33/0.58 (step @p92 :rule cong :premises (@p91) :args (@t48)) % 0.33/0.58 (step @p93 :rule nary_cong :premises (@p92 @p19) :args (@t49)) % 0.33/0.58 (step @p94 :rule cong :premises (@p93) :args ((forall @t18 @t49))) % 0.33/0.58 (step @p95 :rule bool-impl-elim :args (@t47 @t4)) % 0.33/0.58 (step @p96 :rule cong :premises (@p95) :args ((forall @t18 (=> @t47 @t4)))) % 0.33/0.58 (step @p97 :rule trans :premises (@p96 @p94)) % 0.33/0.58 (step @p98 :rule alpha_equiv :args (@t22 (@list @t2) (@list @t26))) % 0.33/0.58 (step @p99 :rule ho_cong :premises (@p36 @p98)) % 0.33/0.58 (step @p100 :rule ho_cong :premises (@p30 @p99)) % 0.33/0.58 (step @p101 :rule cong :premises (@p100 @p16) :args (@t50)) % 0.33/0.58 (step @p102 :rule cong :premises (@p101) :args ((forall @t18 @t50))) % 0.33/0.58 (step @p103 :rule trans :premises (@p102 @p97)) % 0.33/0.58 (step @p104 :rule refl :args (@t4)) % 0.33/0.58 (step @p105 :rule beta-reduce :args ((= (_ @t51 @t16) @t23))) % 0.33/0.58 (step @p106 :rule refl :args (@t16)) % 0.33/0.58 (step @p107 :rule beta-reduce :args ((= @t52 @t51))) % 0.33/0.58 (step @p108 :rule ho_cong :premises (@p107 @p106)) % 0.33/0.58 (step @p109 :rule trans :premises (@p108 @p105)) % 0.33/0.58 (step @p110 :rule refl :args (@t3)) % 0.33/0.58 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.33/0.58 (step @p112 :rule cong :premises (@p111 @p104) :args (@t53)) % 0.33/0.58 (step @p113 :rule cong :premises (@p112) :args (@t54)) % 0.33/0.58 (step @p114 :rule trans :premises (@p113 @p103)) % 0.33/0.58 (step @p115 :rule cong :premises (@p58 @p114) :args (@t55)) % 0.33/0.58 (step @p116 :rule cong :premises (@p115) :args ((not @t55))) % 0.33/0.58 (step @p117 :rule ho_cong :premises (@p4 @p8)) % 0.33/0.58 (step @p118 :rule ho_cong :premises (@p117 @p106)) % 0.33/0.58 (step @p119 :rule ho_cong :premises (@p110 @p118)) % 0.33/0.58 (step @p120 :rule cong :premises (@p119 @p104) :args (@t17)) % 0.33/0.58 (step @p121 :rule cong :premises (@p120) :args (@t19)) % 0.33/0.58 (step @p122 :rule cong :premises (@p58 @p121) :args (@t20)) % 0.33/0.58 (step @p123 :rule cong :premises (@p122) :args (@t21)) % 0.33/0.58 (step @p124 :rule trans :premises (@p123 @p116)) % 0.33/0.58 (step @p125 :rule trans :premises (@p124 @p62)) % 0.33/0.58 (step @p126 :rule eq_resolve :premises (@p2 @p125)) % 0.33/0.58 (step @p127 :rule not_implies_elim1 :premises (@p126)) % 0.33/0.58 (step @p128 :rule not_implies_elim2 :premises (@p126)) % 0.33/0.58 (step @p129 :rule refl :args (@t62)) % 0.33/0.58 (step @p130 :rule bool-double-not-elim :args (@t33)) % 0.33/0.58 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or (not @t63) @t62))) % 0.33/0.58 (step @p132 :rule refl :args (@t58)) % 0.33/0.58 (step @p133 :rule eq-refl :args (@t59)) % 0.33/0.58 (step @p134 :rule skolem_intro :args (@t60)) % 0.33/0.58 (step @p135 :rule refl :args (@t59)) % 0.33/0.58 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t59 @t60))) % 0.33/0.58 (step @p137 :rule trans :premises (@p136 @p133)) % 0.33/0.58 (step @p138 :rule true_elim :premises (@p137)) % 0.33/0.58 (step @p139 :rule refl :args (@t56)) % 0.33/0.58 (step @p140 :rule cong :premises (@p139 @p138) :args (@t64)) % 0.33/0.58 (step @p141 :rule refl :args (@t57)) % 0.33/0.58 (step @p142 :rule cong :premises (@p141 @p140) :args (@t65)) % 0.33/0.58 (step @p143 :rule cong :premises (@p142) :args (@t66)) % 0.33/0.58 (step @p144 :rule nary_cong :premises (@p143 @p132) :args (@t67)) % 0.33/0.58 (step @p145 :rule cong :premises (@p144) :args (@t68)) % 0.33/0.58 (step @p146 :rule refl :args (@t63)) % 0.33/0.58 (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t63 @t68))) % 0.33/0.58 (assume-push @p162 @t63) % 0.33/0.58 (step @p149 :rule skolemize :premises (@p128)) % 0.33/0.58 (step-pop @p163 :rule scope :premises (@p149)) % 0.33/0.58 (step @p150 :rule process_scope :premises (@p163) :args (@t68)) % 0.33/0.58 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 0.33/0.58 (step @p153 :rule implies_elim :premises (@p152)) % 0.33/0.58 (step @p154 :rule eq_resolve :premises (@p153 @p131)) % 0.33/0.58 (step @p155 :rule chain_m_resolution :premises (@p154 @p128) :args (@t62 (@list true) (@list @t33))) % 0.33/0.58 (assume-push @p164 @t69) % 0.33/0.58 (step @p157 :rule instantiate :premises (@p127) :args ((@list @t56 @t60 @t57))) % 0.33/0.58 (step-pop @p165 :rule scope :premises (@p157)) % 0.33/0.58 (step @p158 :rule process_scope :premises (@p165) :args (@t61)) % 0.33/0.58 (step @p160 :rule implies_elim :premises (@p158)) % 0.33/0.58 (step @p161 false :rule chain_m_resolution :premises (@p160 @p155 @p127) :args (false (@list true false) (@list @t61 @t69))) % 0.33/0.58 ) % 0.33/0.58 % SZS output end Proof % 0.33/0.58 % cvc5 exiting %------------------------------------------------------------------------------