%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU618^2 : 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 : n006.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 08:52:26 AM UTC 2026 % Result : Theorem 0.37s 0.55s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU618^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n006.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 17:43:19 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.37/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.55 % SZS status Theorem % 0.37/0.55 % SZS output start Proof % 0.37/0.55 ( % 0.37/0.55 (declare-sort $$unsorted 0) % 0.37/0.55 (declare-const tptp.secondinupair Bool) % 0.37/0.55 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.55 (declare-const tptp.emptyset $$unsorted) % 0.37/0.55 (declare-const tptp.setunionI Bool) % 0.37/0.55 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.55 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.37/0.55 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.55 (define @t2 () (_ tptp.setunion @t1)) % 0.37/0.55 (define @t3 () (@var "Xx" $$unsorted)) % 0.37/0.55 (define @t4 () (_ tptp.in @t3)) % 0.37/0.55 (define @t5 () (_ @t4 @t2)) % 0.37/0.55 (define @t6 () (@var "B" $$unsorted)) % 0.37/0.55 (define @t7 () (_ (_ tptp.in @t6) @t1)) % 0.37/0.55 (define @t8 () (=> @t7 @t5)) % 0.37/0.55 (define @t9 () (_ @t4 @t6)) % 0.37/0.55 (define @t10 () (@list @t1 @t3 @t6)) % 0.37/0.55 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.37/0.55 (define @t12 () (= tptp.setunionI @t11)) % 0.37/0.55 (define @t13 () (@var "Xy" $$unsorted)) % 0.37/0.55 (define @t14 () (_ (_ tptp.setadjoin @t13) tptp.emptyset)) % 0.37/0.55 (define @t15 () (_ tptp.setadjoin @t3)) % 0.37/0.55 (define @t16 () (_ @t15 @t14)) % 0.37/0.55 (define @t17 () (_ tptp.in @t13)) % 0.37/0.55 (define @t18 () (_ @t17 @t16)) % 0.37/0.55 (define @t19 () (@list @t3 @t13)) % 0.37/0.55 (define @t20 () (forall @t19 @t18)) % 0.37/0.55 (define @t21 () (= tptp.secondinupair @t20)) % 0.37/0.55 (define @t22 () (_ (_ tptp.setadjoin @t16) tptp.emptyset)) % 0.37/0.55 (define @t23 () (_ @t15 tptp.emptyset)) % 0.37/0.55 (define @t24 () (_ (_ tptp.setadjoin @t23) @t22)) % 0.37/0.55 (define @t25 () (_ tptp.setunion @t24)) % 0.37/0.55 (define @t26 () (_ @t17 @t25)) % 0.37/0.55 (define @t27 () (forall @t19 @t26)) % 0.37/0.55 (define @t28 () (=> tptp.secondinupair @t27)) % 0.37/0.55 (define @t29 () (=> tptp.setunionI @t28)) % 0.37/0.55 (define @t30 () (not @t29)) % 0.37/0.55 (define @t31 () (tptp.setadjoin @t13 tptp.emptyset)) % 0.37/0.55 (define @t32 () (tptp.setadjoin @t3 @t31)) % 0.37/0.55 (define @t33 () (tptp.setadjoin @t32 tptp.emptyset)) % 0.37/0.55 (define @t34 () (tptp.setadjoin @t3 tptp.emptyset)) % 0.37/0.55 (define @t35 () (tptp.setadjoin @t34 @t33)) % 0.37/0.55 (define @t36 () (tptp.setunion @t35)) % 0.37/0.55 (define @t37 () (tptp.in @t13 @t36)) % 0.37/0.55 (define @t38 () (forall @t19 @t37)) % 0.37/0.55 (define @t39 () (tptp.in @t13 @t32)) % 0.37/0.55 (define @t40 () (=> tptp.secondinupair @t38)) % 0.37/0.55 (define @t41 () (tptp.setunion @t1)) % 0.37/0.55 (define @t42 () (tptp.in @t3 @t41)) % 0.37/0.55 (define @t43 () (tptp.in @t6 @t1)) % 0.37/0.55 (define @t44 () (not @t7)) % 0.37/0.55 (define @t45 () (tptp.in @t3 @t6)) % 0.37/0.55 (define @t46 () (not @t9)) % 0.37/0.55 (define @t47 () (or @t46 @t44 @t5)) % 0.37/0.55 (define @t48 () (=> tptp.setunionI @t40)) % 0.37/0.55 (define @t49 () (@quantifiers_skolemize @t38 1)) % 0.37/0.55 (define @t50 () (@quantifiers_skolemize @t38 0)) % 0.37/0.55 (define @t51 () (tptp.setadjoin @t50 (tptp.setadjoin @t49 tptp.emptyset))) % 0.37/0.55 (define @t52 () (tptp.setadjoin @t50 tptp.emptyset)) % 0.37/0.55 (define @t53 () (tptp.setadjoin @t52 (tptp.setadjoin @t51 tptp.emptyset))) % 0.37/0.55 (define @t54 () (tptp.in @t49 (tptp.setunion @t53))) % 0.37/0.55 (define @t55 () (tptp.in @t51 @t53)) % 0.37/0.55 (define @t56 () (not @t55)) % 0.37/0.55 (define @t57 () (tptp.in @t49 @t51)) % 0.37/0.55 (define @t58 () (not @t57)) % 0.37/0.55 (define @t59 () (or @t58 @t56 @t54)) % 0.37/0.55 (define @t60 () (not @t59)) % 0.37/0.55 (define @t61 () (forall @t10 (or (not @t45) (not @t43) @t42))) % 0.37/0.55 (assume @p1 @t12) % 0.37/0.55 (assume @p2 @t21) % 0.37/0.55 (assume @p3 @t30) % 0.37/0.55 (assume @p4 true) % 0.37/0.55 (step @p5 :rule refl :args (@t38)) % 0.37/0.55 (step @p6 :rule refl :args ((tptp.in @t13 @t16))) % 0.37/0.55 (step @p7 :rule refl :args ((tptp.setadjoin @t3 @t14))) % 0.37/0.55 (step @p8 :rule refl :args (@t31)) % 0.37/0.55 (step @p9 :rule refl :args (@t3)) % 0.37/0.55 (step @p10 :rule cong :premises (@p9 @p8) :args (@t32)) % 0.37/0.55 (step @p11 :rule trans :premises (@p10 @p7)) % 0.37/0.55 (step @p12 :rule refl :args (@t13)) % 0.37/0.55 (step @p13 :rule cong :premises (@p12 @p11) :args (@t39)) % 0.37/0.55 (step @p14 :rule trans :premises (@p13 @p6)) % 0.37/0.55 (step @p15 :rule refl :args (@t17)) % 0.37/0.55 (step @p16 :rule ho_cong :premises (@p15 @p11)) % 0.37/0.55 (step @p17 :rule cong :premises (@p16 @p14) :args ((= (_ @t17 @t32) @t39))) % 0.37/0.55 (step @p18 :rule symm :premises (@p17)) % 0.37/0.55 (step @p19 :rule refl :args (@t18)) % 0.37/0.55 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 0.37/0.55 (step @p21 :rule refl :args (@t15)) % 0.37/0.55 (step @p22 :rule ho_cong :premises (@p21 @p8)) % 0.37/0.55 (step @p23 :rule cong :premises (@p22 @p11) :args ((= (_ @t15 @t31) @t32))) % 0.37/0.55 (step @p24 :rule symm :premises (@p23)) % 0.37/0.55 (step @p25 :rule refl :args (@t16)) % 0.37/0.55 (step @p26 :rule eq_resolve :premises (@p25 @p24)) % 0.37/0.55 (step @p27 :rule refl :args (@t14)) % 0.37/0.55 (step @p28 :rule cong :premises (@p27 @p8) :args ((= @t14 @t31))) % 0.37/0.55 (step @p29 :rule symm :premises (@p28)) % 0.37/0.55 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.37/0.55 (step @p31 :rule ho_cong :premises (@p21 @p30)) % 0.37/0.55 (step @p32 :rule trans :premises (@p31 @p26)) % 0.37/0.55 (step @p33 :rule ho_cong :premises (@p15 @p32)) % 0.37/0.55 (step @p34 :rule trans :premises (@p33 @p20)) % 0.37/0.55 (step @p35 :rule cong :premises (@p34) :args (@t20)) % 0.37/0.55 (step @p36 :rule refl :args (tptp.secondinupair)) % 0.37/0.55 (step @p37 :rule cong :premises (@p36 @p35) :args (@t21)) % 0.37/0.55 (step @p38 :rule eq_resolve :premises (@p2 @p37)) % 0.37/0.55 (step @p39 :rule cong :premises (@p38 @p5) :args (@t40)) % 0.37/0.55 (step @p40 :rule refl :args ((tptp.in @t3 @t2))) % 0.37/0.55 (step @p41 :rule refl :args (@t41)) % 0.37/0.55 (step @p42 :rule cong :premises (@p9 @p41) :args (@t42)) % 0.37/0.55 (step @p43 :rule trans :premises (@p42 @p40)) % 0.37/0.55 (step @p44 :rule refl :args (@t4)) % 0.37/0.55 (step @p45 :rule ho_cong :premises (@p44 @p41)) % 0.37/0.55 (step @p46 :rule cong :premises (@p45 @p43) :args ((= (_ @t4 @t41) @t42))) % 0.37/0.55 (step @p47 :rule symm :premises (@p46)) % 0.37/0.55 (step @p48 :rule refl :args (@t5)) % 0.37/0.55 (step @p49 :rule eq_resolve :premises (@p48 @p47)) % 0.37/0.55 (step @p50 :rule refl :args (@t2)) % 0.37/0.55 (step @p51 :rule cong :premises (@p50 @p41) :args ((= @t2 @t41))) % 0.37/0.55 (step @p52 :rule symm :premises (@p51)) % 0.37/0.55 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.37/0.55 (step @p54 :rule ho_cong :premises (@p44 @p53)) % 0.37/0.55 (step @p55 :rule trans :premises (@p54 @p49)) % 0.37/0.55 (step @p56 :rule refl :args (@t43)) % 0.37/0.55 (step @p57 :rule refl :args (@t7)) % 0.37/0.55 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t7 @t43))) % 0.37/0.55 (step @p59 :rule symm :premises (@p58)) % 0.37/0.55 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.37/0.55 (step @p61 :rule cong :premises (@p60) :args (@t44)) % 0.37/0.55 (step @p62 :rule refl :args (@t45)) % 0.37/0.55 (step @p63 :rule refl :args (@t9)) % 0.37/0.55 (step @p64 :rule cong :premises (@p63 @p62) :args ((= @t9 @t45))) % 0.37/0.55 (step @p65 :rule symm :premises (@p64)) % 0.37/0.55 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.37/0.55 (step @p67 :rule cong :premises (@p66) :args (@t46)) % 0.37/0.55 (step @p68 :rule nary_cong :premises (@p67 @p61 @p55) :args (@t47)) % 0.37/0.55 (step @p69 :rule cong :premises (@p68) :args ((forall @t10 @t47))) % 0.37/0.55 (step @p70 :rule aci_norm :args ((= (or @t46 (or @t44 @t5)) @t47))) % 0.37/0.55 (step @p71 :rule bool-impl-elim :args (@t7 @t5)) % 0.37/0.55 (step @p72 :rule refl :args (@t46)) % 0.37/0.55 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or @t46 @t8))) % 0.37/0.55 (step @p74 :rule trans :premises (@p73 @p70)) % 0.37/0.55 (step @p75 :rule bool-impl-elim :args (@t9 @t8)) % 0.37/0.55 (step @p76 :rule trans :premises (@p75 @p74)) % 0.37/0.55 (step @p77 :rule cong :premises (@p76) :args (@t11)) % 0.37/0.55 (step @p78 :rule trans :premises (@p77 @p69)) % 0.37/0.55 (step @p79 :rule refl :args (tptp.setunionI)) % 0.37/0.55 (step @p80 :rule cong :premises (@p79 @p78) :args (@t12)) % 0.37/0.55 (step @p81 :rule eq_resolve :premises (@p1 @p80)) % 0.37/0.55 (step @p82 :rule cong :premises (@p81 @p39) :args (@t48)) % 0.37/0.55 (step @p83 :rule cong :premises (@p82) :args ((not @t48))) % 0.37/0.55 (step @p84 :rule refl :args ((tptp.in @t13 @t25))) % 0.37/0.55 (step @p85 :rule refl :args ((tptp.setunion @t24))) % 0.37/0.55 (step @p86 :rule refl :args ((tptp.setadjoin @t23 @t22))) % 0.37/0.55 (step @p87 :rule refl :args ((tptp.setadjoin @t16 tptp.emptyset))) % 0.37/0.55 (step @p88 :rule refl :args (tptp.emptyset)) % 0.37/0.55 (step @p89 :rule cong :premises (@p11 @p88) :args (@t33)) % 0.37/0.55 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.55 (step @p91 :rule refl :args (@t34)) % 0.37/0.55 (step @p92 :rule cong :premises (@p91 @p90) :args (@t35)) % 0.37/0.55 (step @p93 :rule trans :premises (@p92 @p86)) % 0.37/0.55 (step @p94 :rule cong :premises (@p93) :args (@t36)) % 0.37/0.55 (step @p95 :rule trans :premises (@p94 @p85)) % 0.37/0.55 (step @p96 :rule cong :premises (@p12 @p95) :args (@t37)) % 0.37/0.55 (step @p97 :rule trans :premises (@p96 @p84)) % 0.37/0.55 (step @p98 :rule ho_cong :premises (@p15 @p95)) % 0.37/0.55 (step @p99 :rule cong :premises (@p98 @p97) :args ((= (_ @t17 @t36) @t37))) % 0.37/0.55 (step @p100 :rule symm :premises (@p99)) % 0.37/0.55 (step @p101 :rule refl :args (@t26)) % 0.37/0.55 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 0.37/0.55 (step @p103 :rule refl :args (tptp.setunion)) % 0.37/0.55 (step @p104 :rule ho_cong :premises (@p103 @p93)) % 0.37/0.55 (step @p105 :rule cong :premises (@p104 @p95) :args ((= (_ tptp.setunion @t35) @t36))) % 0.37/0.55 (step @p106 :rule symm :premises (@p105)) % 0.37/0.55 (step @p107 :rule refl :args (@t25)) % 0.37/0.55 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.37/0.56 (step @p109 :rule refl :args (tptp.setadjoin)) % 0.37/0.56 (step @p110 :rule ho_cong :premises (@p109 @p91)) % 0.37/0.56 (step @p111 :rule ho_cong :premises (@p110 @p90)) % 0.37/0.56 (step @p112 :rule cong :premises (@p111 @p93) :args ((= (_ (_ tptp.setadjoin @t34) @t33) @t35))) % 0.37/0.56 (step @p113 :rule symm :premises (@p112)) % 0.37/0.56 (step @p114 :rule refl :args (@t24)) % 0.37/0.56 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 0.37/0.56 (step @p116 :rule ho_cong :premises (@p109 @p11)) % 0.37/0.56 (step @p117 :rule ho_cong :premises (@p116 @p88)) % 0.37/0.56 (step @p118 :rule cong :premises (@p117 @p90) :args ((= (_ (_ tptp.setadjoin @t32) tptp.emptyset) @t33))) % 0.37/0.56 (step @p119 :rule symm :premises (@p118)) % 0.37/0.56 (step @p120 :rule refl :args (@t22)) % 0.37/0.56 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.37/0.56 (step @p122 :rule ho_cong :premises (@p109 @p32)) % 0.37/0.56 (step @p123 :rule ho_cong :premises (@p122 @p88)) % 0.37/0.56 (step @p124 :rule trans :premises (@p123 @p121)) % 0.37/0.56 (step @p125 :rule refl :args (@t23)) % 0.37/0.56 (step @p126 :rule cong :premises (@p125 @p91) :args ((= @t23 @t34))) % 0.37/0.56 (step @p127 :rule symm :premises (@p126)) % 0.37/0.56 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 0.37/0.56 (step @p129 :rule ho_cong :premises (@p109 @p128)) % 0.37/0.56 (step @p130 :rule ho_cong :premises (@p129 @p124)) % 0.37/0.56 (step @p131 :rule trans :premises (@p130 @p115)) % 0.37/0.56 (step @p132 :rule ho_cong :premises (@p103 @p131)) % 0.37/0.56 (step @p133 :rule trans :premises (@p132 @p108)) % 0.37/0.56 (step @p134 :rule ho_cong :premises (@p15 @p133)) % 0.37/0.56 (step @p135 :rule trans :premises (@p134 @p102)) % 0.37/0.56 (step @p136 :rule cong :premises (@p135) :args (@t27)) % 0.37/0.56 (step @p137 :rule cong :premises (@p36 @p136) :args (@t28)) % 0.37/0.56 (step @p138 :rule cong :premises (@p79 @p137) :args (@t29)) % 0.37/0.56 (step @p139 :rule cong :premises (@p138) :args (@t30)) % 0.37/0.56 (step @p140 :rule trans :premises (@p139 @p83)) % 0.37/0.56 (step @p141 :rule eq_resolve :premises (@p3 @p140)) % 0.37/0.56 (step @p142 :rule not_implies_elim1 :premises (@p141)) % 0.37/0.56 (step @p143 :rule not_implies_elim2 :premises (@p141)) % 0.37/0.56 (step @p144 :rule not_implies_elim1 :premises (@p143)) % 0.37/0.56 (step @p145 :rule instantiate :premises (@p144) :args ((@list @t52 @t51))) % 0.37/0.56 (step @p146 :rule instantiate :premises (@p144) :args ((@list @t50 @t49))) % 0.37/0.56 (step @p147 :rule not_implies_elim2 :premises (@p143)) % 0.37/0.56 (step @p148 :rule skolemize :premises (@p147)) % 0.37/0.56 (step @p149 :rule cnf_or_pos :args (@t59)) % 0.37/0.56 (step @p150 :rule reordering :premises (@p149) :args ((or @t54 @t58 @t56 @t60))) % 0.37/0.56 (step @p151 :rule chain_m_resolution :premises (@p150 @p148 @p146 @p145) :args (@t60 (@list true false false) (@list @t54 @t57 @t55))) % 0.37/0.56 (assume-push @p158 @t61) % 0.37/0.56 (step @p153 :rule instantiate :premises (@p142) :args ((@list @t53 @t49 @t51))) % 0.37/0.56 (step-pop @p159 :rule scope :premises (@p153)) % 0.37/0.56 (step @p154 :rule process_scope :premises (@p159) :args (@t59)) % 0.37/0.56 (step @p156 :rule implies_elim :premises (@p154)) % 0.37/0.56 (step @p157 false :rule chain_m_resolution :premises (@p156 @p151 @p142) :args (false (@list true false) (@list @t59 @t61))) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------