%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU648^2 : 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 : 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 08:52:34 AM UTC 2026 % Result : Theorem 0.32s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SEU648^2 : 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 : n016.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 17:44:54 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 0.32/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.32/0.57 % SZS status Theorem % 0.32/0.57 % SZS output start Proof % 0.32/0.57 ( % 0.32/0.57 (declare-sort $$unsorted 0) % 0.32/0.57 (declare-const tptp.emptyset $$unsorted) % 0.32/0.57 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.32/0.57 (declare-const tptp.setukpairinjL2 Bool) % 0.32/0.57 (define tptp.kpair () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.setadjoin _let_2))) (lambda (@list _let_2 _let_1) (_ (_ tptp.setadjoin (_ _let_3 tptp.emptyset)) (_ (_ tptp.setadjoin (_ _let_3 (_ (_ tptp.setadjoin _let_1) tptp.emptyset))) tptp.emptyset))))))) % 0.32/0.57 (define @t1 () (@var "Xz" $$unsorted)) % 0.32/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.32/0.57 (define @t3 () (= @t2 @t1)) % 0.32/0.57 (define @t4 () (@var "Xu" $$unsorted)) % 0.32/0.57 (define @t5 () (_ (_ tptp.setadjoin @t4) tptp.emptyset)) % 0.32/0.57 (define @t6 () (_ tptp.setadjoin @t1)) % 0.32/0.57 (define @t7 () (_ @t6 @t5)) % 0.32/0.57 (define @t8 () (_ (_ tptp.setadjoin @t7) tptp.emptyset)) % 0.32/0.57 (define @t9 () (_ @t6 tptp.emptyset)) % 0.32/0.57 (define @t10 () (_ tptp.setadjoin @t9)) % 0.32/0.57 (define @t11 () (_ @t10 @t8)) % 0.32/0.57 (define @t12 () (@var "Xy" $$unsorted)) % 0.32/0.57 (define @t13 () (_ (_ tptp.setadjoin @t12) tptp.emptyset)) % 0.32/0.57 (define @t14 () (_ tptp.setadjoin @t2)) % 0.32/0.57 (define @t15 () (_ @t14 @t13)) % 0.32/0.57 (define @t16 () (_ (_ tptp.setadjoin @t15) tptp.emptyset)) % 0.32/0.57 (define @t17 () (_ @t14 tptp.emptyset)) % 0.32/0.57 (define @t18 () (_ (_ tptp.setadjoin @t17) @t16)) % 0.32/0.57 (define @t19 () (= @t18 @t11)) % 0.32/0.57 (define @t20 () (@list @t2 @t12 @t1 @t4)) % 0.32/0.57 (define @t21 () (forall @t20 (=> @t19 @t3))) % 0.32/0.57 (define @t22 () (= tptp.setukpairinjL2 @t21)) % 0.32/0.57 (define @t23 () (= (_ (_ tptp.kpair @t2) @t12) (_ (_ tptp.kpair @t1) @t4))) % 0.32/0.57 (define @t24 () (=> @t23 @t3)) % 0.32/0.57 (define @t25 () (forall @t20 @t24)) % 0.32/0.57 (define @t26 () (=> tptp.setukpairinjL2 @t25)) % 0.32/0.57 (define @t27 () (not @t26)) % 0.32/0.57 (define @t28 () (lambda (@list @t2 @t12) @t18)) % 0.32/0.57 (define @t29 () (tptp.setadjoin @t4 tptp.emptyset)) % 0.32/0.57 (define @t30 () (tptp.setadjoin @t1 @t29)) % 0.32/0.57 (define @t31 () (tptp.setadjoin @t30 tptp.emptyset)) % 0.32/0.57 (define @t32 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.32/0.57 (define @t33 () (tptp.setadjoin @t32 @t31)) % 0.32/0.57 (define @t34 () (tptp.setadjoin @t12 tptp.emptyset)) % 0.32/0.57 (define @t35 () (tptp.setadjoin @t2 @t34)) % 0.32/0.57 (define @t36 () (tptp.setadjoin @t35 tptp.emptyset)) % 0.32/0.57 (define @t37 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.32/0.57 (define @t38 () (tptp.setadjoin @t37 @t36)) % 0.32/0.57 (define @t39 () (not @t19)) % 0.32/0.57 (define @t40 () (or @t39 @t3)) % 0.32/0.57 (define @t41 () (@list @t12)) % 0.32/0.57 (define @t42 () (lambda @t41 (_ @t10 (_ (_ tptp.setadjoin (_ @t6 @t13)) tptp.emptyset)))) % 0.32/0.57 (define @t43 () (_ @t28 @t1)) % 0.32/0.57 (define @t44 () (lambda @t41 @t18)) % 0.32/0.57 (define @t45 () (_ @t28 @t2)) % 0.32/0.57 (define @t46 () (= (_ @t45 @t12) (_ @t43 @t4))) % 0.32/0.57 (define @t47 () (=> @t46 @t3)) % 0.32/0.57 (define @t48 () (forall @t20 @t47)) % 0.32/0.57 (define @t49 () (=> tptp.setukpairinjL2 @t48)) % 0.32/0.57 (define @t50 () (forall @t20 (or (not (= @t38 @t33)) @t3))) % 0.32/0.57 (assume @p1 @t22) % 0.32/0.57 (assume @p2 @t27) % 0.32/0.57 (assume @p3 true) % 0.32/0.57 (step @p4 (= tptp.kpair @t28) :rule refl :args (@t28)) % 0.32/0.57 (step @p5 :rule refl :args (@t3)) % 0.32/0.57 (step @p6 :rule refl :args ((tptp.setadjoin @t9 @t8))) % 0.32/0.57 (step @p7 :rule refl :args ((tptp.setadjoin @t7 tptp.emptyset))) % 0.32/0.57 (step @p8 :rule refl :args (tptp.emptyset)) % 0.32/0.57 (step @p9 :rule refl :args ((tptp.setadjoin @t1 @t5))) % 0.32/0.57 (step @p10 :rule refl :args (@t29)) % 0.32/0.57 (step @p11 :rule refl :args (@t1)) % 0.32/0.57 (step @p12 :rule cong :premises (@p11 @p10) :args (@t30)) % 0.32/0.57 (step @p13 :rule trans :premises (@p12 @p9)) % 0.32/0.57 (step @p14 :rule cong :premises (@p13 @p8) :args (@t31)) % 0.32/0.57 (step @p15 :rule trans :premises (@p14 @p7)) % 0.32/0.57 (step @p16 :rule refl :args (@t32)) % 0.32/0.57 (step @p17 :rule cong :premises (@p16 @p15) :args (@t33)) % 0.32/0.57 (step @p18 :rule trans :premises (@p17 @p6)) % 0.32/0.57 (step @p19 :rule refl :args (tptp.setadjoin)) % 0.32/0.57 (step @p20 :rule ho_cong :premises (@p19 @p16)) % 0.32/0.57 (step @p21 :rule ho_cong :premises (@p20 @p15)) % 0.32/0.57 (step @p22 :rule cong :premises (@p21 @p18) :args ((= (_ (_ tptp.setadjoin @t32) @t31) @t33))) % 0.32/0.57 (step @p23 :rule symm :premises (@p22)) % 0.32/0.57 (step @p24 :rule refl :args (@t11)) % 0.32/0.57 (step @p25 :rule eq_resolve :premises (@p24 @p23)) % 0.32/0.57 (step @p26 :rule ho_cong :premises (@p19 @p13)) % 0.32/0.57 (step @p27 :rule ho_cong :premises (@p26 @p8)) % 0.32/0.57 (step @p28 :rule cong :premises (@p27 @p15) :args ((= (_ (_ tptp.setadjoin @t30) tptp.emptyset) @t31))) % 0.32/0.57 (step @p29 :rule symm :premises (@p28)) % 0.32/0.57 (step @p30 :rule refl :args (@t8)) % 0.32/0.57 (step @p31 :rule eq_resolve :premises (@p30 @p29)) % 0.32/0.57 (step @p32 :rule refl :args (@t6)) % 0.32/0.57 (step @p33 :rule ho_cong :premises (@p32 @p10)) % 0.32/0.57 (step @p34 :rule cong :premises (@p33 @p13) :args ((= (_ @t6 @t29) @t30))) % 0.32/0.57 (step @p35 :rule symm :premises (@p34)) % 0.32/0.57 (step @p36 :rule refl :args (@t7)) % 0.32/0.57 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.32/0.57 (step @p38 :rule refl :args (@t5)) % 0.32/0.57 (step @p39 :rule cong :premises (@p38 @p10) :args ((= @t5 @t29))) % 0.32/0.57 (step @p40 :rule symm :premises (@p39)) % 0.32/0.57 (step @p41 :rule eq_resolve :premises (@p38 @p40)) % 0.32/0.57 (step @p42 :rule ho_cong :premises (@p32 @p41)) % 0.32/0.57 (step @p43 :rule trans :premises (@p42 @p37)) % 0.32/0.57 (step @p44 :rule ho_cong :premises (@p19 @p43)) % 0.32/0.57 (step @p45 :rule ho_cong :premises (@p44 @p8)) % 0.32/0.57 (step @p46 :rule trans :premises (@p45 @p31)) % 0.32/0.57 (step @p47 :rule refl :args (@t9)) % 0.32/0.57 (step @p48 :rule cong :premises (@p47 @p16) :args ((= @t9 @t32))) % 0.32/0.57 (step @p49 :rule symm :premises (@p48)) % 0.32/0.57 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.32/0.57 (step @p51 :rule ho_cong :premises (@p19 @p50)) % 0.32/0.57 (step @p52 :rule ho_cong :premises (@p51 @p46)) % 0.32/0.57 (step @p53 :rule trans :premises (@p52 @p25)) % 0.32/0.57 (step @p54 :rule refl :args ((tptp.setadjoin @t17 @t16))) % 0.32/0.57 (step @p55 :rule refl :args ((tptp.setadjoin @t15 tptp.emptyset))) % 0.32/0.57 (step @p56 :rule refl :args ((tptp.setadjoin @t2 @t13))) % 0.32/0.57 (step @p57 :rule refl :args (@t34)) % 0.32/0.57 (step @p58 :rule refl :args (@t2)) % 0.32/0.57 (step @p59 :rule cong :premises (@p58 @p57) :args (@t35)) % 0.32/0.57 (step @p60 :rule trans :premises (@p59 @p56)) % 0.32/0.57 (step @p61 :rule cong :premises (@p60 @p8) :args (@t36)) % 0.32/0.57 (step @p62 :rule trans :premises (@p61 @p55)) % 0.32/0.57 (step @p63 :rule refl :args (@t37)) % 0.32/0.57 (step @p64 :rule cong :premises (@p63 @p62) :args (@t38)) % 0.32/0.57 (step @p65 :rule trans :premises (@p64 @p54)) % 0.32/0.57 (step @p66 :rule ho_cong :premises (@p19 @p63)) % 0.32/0.57 (step @p67 :rule ho_cong :premises (@p66 @p62)) % 0.32/0.57 (step @p68 :rule cong :premises (@p67 @p65) :args ((= (_ (_ tptp.setadjoin @t37) @t36) @t38))) % 0.32/0.57 (step @p69 :rule symm :premises (@p68)) % 0.32/0.57 (step @p70 :rule refl :args (@t18)) % 0.32/0.57 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.32/0.57 (step @p72 :rule ho_cong :premises (@p19 @p60)) % 0.32/0.57 (step @p73 :rule ho_cong :premises (@p72 @p8)) % 0.32/0.57 (step @p74 :rule cong :premises (@p73 @p62) :args ((= (_ (_ tptp.setadjoin @t35) tptp.emptyset) @t36))) % 0.32/0.57 (step @p75 :rule symm :premises (@p74)) % 0.32/0.57 (step @p76 :rule refl :args (@t16)) % 0.32/0.57 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.32/0.57 (step @p78 :rule refl :args (@t14)) % 0.32/0.57 (step @p79 :rule ho_cong :premises (@p78 @p57)) % 0.32/0.57 (step @p80 :rule cong :premises (@p79 @p60) :args ((= (_ @t14 @t34) @t35))) % 0.32/0.57 (step @p81 :rule symm :premises (@p80)) % 0.32/0.57 (step @p82 :rule refl :args (@t15)) % 0.32/0.57 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 0.32/0.57 (step @p84 :rule refl :args (@t13)) % 0.32/0.57 (step @p85 :rule cong :premises (@p84 @p57) :args ((= @t13 @t34))) % 0.32/0.57 (step @p86 :rule symm :premises (@p85)) % 0.32/0.57 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.32/0.57 (step @p88 :rule ho_cong :premises (@p78 @p87)) % 0.32/0.57 (step @p89 :rule trans :premises (@p88 @p83)) % 0.32/0.57 (step @p90 :rule ho_cong :premises (@p19 @p89)) % 0.32/0.57 (step @p91 :rule ho_cong :premises (@p90 @p8)) % 0.32/0.57 (step @p92 :rule trans :premises (@p91 @p77)) % 0.32/0.57 (step @p93 :rule refl :args (@t17)) % 0.32/0.57 (step @p94 :rule cong :premises (@p93 @p63) :args ((= @t17 @t37))) % 0.32/0.57 (step @p95 :rule symm :premises (@p94)) % 0.32/0.57 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.32/0.57 (step @p97 :rule ho_cong :premises (@p19 @p96)) % 0.32/0.57 (step @p98 :rule ho_cong :premises (@p97 @p92)) % 0.32/0.57 (step @p99 :rule trans :premises (@p98 @p71)) % 0.32/0.57 (step @p100 :rule cong :premises (@p99 @p53) :args (@t19)) % 0.32/0.57 (step @p101 :rule cong :premises (@p100) :args (@t39)) % 0.32/0.57 (step @p102 :rule nary_cong :premises (@p101 @p5) :args (@t40)) % 0.32/0.57 (step @p103 :rule cong :premises (@p102) :args ((forall @t20 @t40))) % 0.32/0.57 (step @p104 :rule bool-impl-elim :args (@t19 @t3)) % 0.32/0.57 (step @p105 :rule cong :premises (@p104) :args (@t21)) % 0.32/0.57 (step @p106 :rule trans :premises (@p105 @p103)) % 0.32/0.57 (step @p107 :rule refl :args (@t3)) % 0.32/0.57 (step @p108 :rule beta-reduce :args ((= (_ @t42 @t4) @t11))) % 0.32/0.57 (step @p109 :rule refl :args (@t4)) % 0.39/0.57 (step @p110 :rule beta-reduce :args ((= @t43 @t42))) % 0.39/0.57 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.39/0.57 (step @p112 :rule trans :premises (@p111 @p108)) % 0.39/0.57 (step @p113 :rule beta-reduce :args ((= (_ @t44 @t12) @t18))) % 0.39/0.57 (step @p114 :rule refl :args (@t12)) % 0.39/0.57 (step @p115 :rule beta-reduce :args ((= @t45 @t44))) % 0.39/0.57 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.39/0.57 (step @p117 :rule trans :premises (@p116 @p113)) % 0.39/0.57 (step @p118 :rule cong :premises (@p117 @p112) :args (@t46)) % 0.39/0.57 (step @p119 :rule cong :premises (@p118 @p107) :args (@t47)) % 0.39/0.57 (step @p120 :rule cong :premises (@p119) :args (@t48)) % 0.39/0.57 (step @p121 :rule trans :premises (@p120 @p106)) % 0.39/0.57 (step @p122 :rule refl :args (tptp.setukpairinjL2)) % 0.39/0.57 (step @p123 :rule cong :premises (@p122 @p121) :args (@t49)) % 0.39/0.57 (step @p124 :rule cong :premises (@p123) :args ((not @t49))) % 0.39/0.57 (step @p125 :rule refl :args (@t1)) % 0.39/0.57 (step @p126 :rule ho_cong :premises (@p4 @p125)) % 0.39/0.57 (step @p127 :rule ho_cong :premises (@p126 @p109)) % 0.39/0.57 (step @p128 :rule refl :args (@t2)) % 0.39/0.57 (step @p129 :rule ho_cong :premises (@p4 @p128)) % 0.39/0.57 (step @p130 :rule ho_cong :premises (@p129 @p114)) % 0.39/0.57 (step @p131 :rule cong :premises (@p130 @p127) :args (@t23)) % 0.39/0.57 (step @p132 :rule cong :premises (@p131 @p107) :args (@t24)) % 0.39/0.57 (step @p133 :rule cong :premises (@p132) :args (@t25)) % 0.39/0.57 (step @p134 :rule cong :premises (@p122 @p133) :args (@t26)) % 0.39/0.57 (step @p135 :rule cong :premises (@p134) :args (@t27)) % 0.39/0.57 (step @p136 :rule trans :premises (@p135 @p124)) % 0.39/0.57 (step @p137 :rule eq_resolve :premises (@p2 @p136)) % 0.39/0.57 (step @p138 :rule not_implies_elim2 :premises (@p137)) % 0.39/0.57 (step @p139 :rule not_implies_elim1 :premises (@p137)) % 0.39/0.57 (step @p140 :rule cnf_equiv_pos1 :args ((= tptp.setukpairinjL2 @t50))) % 0.39/0.57 (step @p141 :rule chain_resolution :premises (@p140 @p139 @p138) :args ((@list false true) (@list tptp.setukpairinjL2 @t50))) % 0.39/0.57 (step @p142 :rule cong :premises (@p122 @p106) :args (@t22)) % 0.39/0.57 (step @p143 :rule eq_resolve :premises (@p1 @p142)) % 0.39/0.57 (step @p144 false :rule contra :premises (@p143 @p141)) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------