%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU633^2 : 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 : n026.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 08:52:30 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU633^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n026.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 17:43:55 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (declare-const tptp.setunionE Bool) % 0.39/0.57 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.39/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.39/0.57 (define @t1 () (@var "Xphi" Bool)) % 0.39/0.57 (define @t2 () (@var "A" $$unsorted)) % 0.39/0.57 (define @t3 () (@var "B" $$unsorted)) % 0.39/0.57 (define @t4 () (_ (_ tptp.in @t3) @t2)) % 0.39/0.57 (define @t5 () (=> @t4 @t1)) % 0.39/0.57 (define @t6 () (@var "Xx" $$unsorted)) % 0.39/0.57 (define @t7 () (_ tptp.in @t6)) % 0.39/0.57 (define @t8 () (_ @t7 @t3)) % 0.39/0.57 (define @t9 () (@list @t3)) % 0.39/0.57 (define @t10 () (forall @t9 (=> @t8 @t5))) % 0.39/0.57 (define @t11 () (=> @t10 @t1)) % 0.39/0.57 (define @t12 () (@list @t1)) % 0.39/0.57 (define @t13 () (forall @t12 @t11)) % 0.39/0.57 (define @t14 () (_ tptp.setunion @t2)) % 0.39/0.57 (define @t15 () (_ @t7 @t14)) % 0.39/0.57 (define @t16 () (=> @t15 @t13)) % 0.39/0.57 (define @t17 () (@list @t2 @t6)) % 0.39/0.57 (define @t18 () (forall @t17 @t16)) % 0.39/0.57 (define @t19 () (= tptp.setunionE @t18)) % 0.39/0.57 (define @t20 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t21 () (_ @t7 @t20)) % 0.39/0.57 (define @t22 () (_ (_ tptp.in @t20) @t2)) % 0.39/0.57 (define @t23 () (and @t22 @t21)) % 0.39/0.57 (define @t24 () (@list @t20)) % 0.39/0.57 (define @t25 () (exists @t24 @t23)) % 0.39/0.57 (define @t26 () (=> @t15 @t25)) % 0.39/0.57 (define @t27 () (forall @t17 @t26)) % 0.39/0.57 (define @t28 () (=> tptp.setunionE @t27)) % 0.39/0.57 (define @t29 () (not @t28)) % 0.39/0.57 (define @t30 () (tptp.in @t6 @t20)) % 0.39/0.57 (define @t31 () (not @t30)) % 0.39/0.57 (define @t32 () (tptp.in @t20 @t2)) % 0.39/0.57 (define @t33 () (not @t32)) % 0.39/0.57 (define @t34 () (or @t33 @t31)) % 0.39/0.57 (define @t35 () (forall @t24 @t34)) % 0.39/0.57 (define @t36 () (not @t35)) % 0.39/0.57 (define @t37 () (tptp.setunion @t2)) % 0.39/0.57 (define @t38 () (tptp.in @t6 @t37)) % 0.39/0.57 (define @t39 () (not @t38)) % 0.39/0.57 (define @t40 () (or @t39 @t36)) % 0.39/0.57 (define @t41 () (forall @t17 @t40)) % 0.39/0.57 (define @t42 () (tptp.in @t3 @t2)) % 0.39/0.57 (define @t43 () (tptp.in @t6 @t3)) % 0.39/0.57 (define @t44 () (forall @t9 (or (not @t43) (not @t42)))) % 0.39/0.57 (define @t45 () (not @t44)) % 0.39/0.57 (define @t46 () (not @t15)) % 0.39/0.57 (define @t47 () (or @t46 @t45)) % 0.39/0.57 (define @t48 () (not false)) % 0.39/0.57 (define @t49 () (and @t48 @t45)) % 0.39/0.57 (define @t50 () (or @t49 false)) % 0.39/0.57 (define @t51 () (not @t1)) % 0.39/0.57 (define @t52 () (and @t51 @t45)) % 0.39/0.57 (define @t53 () (or @t1 @t52 @t1)) % 0.39/0.57 (define @t54 () (or @t52 @t1)) % 0.39/0.57 (define @t55 () (or @t1 @t44)) % 0.39/0.57 (define @t56 () (not @t4)) % 0.39/0.57 (define @t57 () (not @t8)) % 0.39/0.57 (define @t58 () (or @t57 @t56)) % 0.39/0.57 (define @t59 () (forall @t9 @t58)) % 0.39/0.57 (define @t60 () (or @t1 @t59)) % 0.39/0.57 (define @t61 () (or @t1 @t58)) % 0.39/0.57 (define @t62 () (or @t57 @t56 @t1)) % 0.39/0.57 (define @t63 () (=> tptp.setunionE @t41)) % 0.39/0.57 (define @t64 () (or @t46 @t36)) % 0.39/0.57 (define @t65 () (not @t21)) % 0.39/0.57 (define @t66 () (not @t22)) % 0.39/0.57 (define @t67 () (or @t66 @t65)) % 0.39/0.57 (define @t68 () (forall @t24 (not @t23))) % 0.39/0.57 (define @t69 () (not @t68)) % 0.39/0.57 (define @t70 () (or @t31 @t33)) % 0.39/0.57 (define @t71 () (forall @t17 (or @t39 (not (forall @t24 @t70))))) % 0.39/0.57 (define @t72 () (@var "BOUND_VARIABLE_7550" $$unsorted)) % 0.39/0.57 (define @t73 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.39/0.57 (define @t74 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.39/0.57 (define @t75 () (@list @t73 @t74 @t72)) % 0.39/0.57 (define @t76 () (forall @t17 (or @t39 @t45))) % 0.39/0.57 (define @t77 () (@list false)) % 0.39/0.57 (assume @p1 @t19) % 0.39/0.57 (assume @p2 @t29) % 0.39/0.57 (assume @p3 true) % 0.39/0.57 (step @p4 :rule refl :args (@t41)) % 0.39/0.57 (step @p5 :rule refl :args (@t45)) % 0.39/0.57 (step @p6 :rule refl :args ((tptp.in @t6 @t14))) % 0.39/0.57 (step @p7 :rule refl :args (@t37)) % 0.39/0.57 (step @p8 :rule refl :args (@t6)) % 0.39/0.57 (step @p9 :rule cong :premises (@p8 @p7) :args (@t38)) % 0.39/0.57 (step @p10 :rule trans :premises (@p9 @p6)) % 0.39/0.57 (step @p11 :rule refl :args (@t7)) % 0.39/0.57 (step @p12 :rule ho_cong :premises (@p11 @p7)) % 0.39/0.57 (step @p13 :rule cong :premises (@p12 @p10) :args ((= (_ @t7 @t37) @t38))) % 0.39/0.57 (step @p14 :rule symm :premises (@p13)) % 0.39/0.57 (step @p15 :rule refl :args (@t15)) % 0.39/0.57 (step @p16 :rule eq_resolve :premises (@p15 @p14)) % 0.39/0.57 (step @p17 :rule refl :args (@t14)) % 0.39/0.57 (step @p18 :rule cong :premises (@p17 @p7) :args ((= @t14 @t37))) % 0.39/0.57 (step @p19 :rule symm :premises (@p18)) % 0.39/0.57 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.39/0.57 (step @p21 :rule ho_cong :premises (@p11 @p20)) % 0.39/0.57 (step @p22 :rule trans :premises (@p21 @p16)) % 0.39/0.57 (step @p23 :rule cong :premises (@p22) :args (@t46)) % 0.39/0.57 (step @p24 :rule nary_cong :premises (@p23 @p5) :args (@t47)) % 0.39/0.57 (step @p25 :rule cong :premises (@p24) :args ((forall @t17 @t47))) % 0.39/0.57 (step @p26 :rule bool-impl-elim :args (@t15 @t45)) % 0.39/0.57 (step @p27 :rule cong :premises (@p26) :args ((forall @t17 (=> @t15 @t45)))) % 0.39/0.57 (step @p28 :rule trans :premises (@p27 @p25)) % 0.39/0.57 (step @p29 :rule aci_norm :args ((= (and true @t45) @t45))) % 0.39/0.57 (step @p30 :rule refl :args (@t45)) % 0.39/0.57 (step @p31 :rule evaluate :args (@t48)) % 0.39/0.57 (step @p32 :rule nary_cong :premises (@p31 @p30) :args (@t49)) % 0.39/0.57 (step @p33 :rule trans :premises (@p32 @p29)) % 0.39/0.57 (step @p34 :rule aci_norm :args ((= @t50 @t49))) % 0.39/0.57 (step @p35 :rule trans :premises (@p34 @p33)) % 0.39/0.57 (step @p36 :rule quant-var-elim-eq :args ((= (forall @t12 (or (not (= @t1 false)) @t52 @t1)) @t50))) % 0.39/0.57 (step @p37 :rule refl :args (@t1)) % 0.39/0.57 (step @p38 :rule refl :args (@t52)) % 0.39/0.57 (step @p39 :rule bool-eq-false :args (@t1)) % 0.39/0.57 (step @p40 :rule symm :premises (@p39)) % 0.39/0.57 (step @p41 :rule cong :premises (@p40) :args ((not @t51))) % 0.39/0.57 (step @p42 :rule bool-double-not-elim :args (@t1)) % 0.39/0.57 (step @p43 :rule symm :premises (@p42)) % 0.39/0.57 (step @p44 :rule trans :premises (@p43 @p41)) % 0.39/0.57 (step @p45 :rule nary_cong :premises (@p44 @p38 @p37) :args (@t53)) % 0.39/0.57 (step @p46 :rule aci_norm :args ((= @t54 @t53))) % 0.39/0.57 (step @p47 :rule trans :premises (@p46 @p45)) % 0.39/0.57 (step @p48 :rule cong :premises (@p47) :args ((forall @t12 @t54))) % 0.39/0.57 (step @p49 :rule trans :premises (@p48 @p36)) % 0.39/0.57 (step @p50 :rule trans :premises (@p49 @p35)) % 0.39/0.57 (step @p51 :rule bool-or-de-morgan :args (@t1 @t44 false)) % 0.39/0.57 (step @p52 :rule nary_cong :premises (@p51 @p37) :args ((or (not @t55) @t1))) % 0.39/0.57 (step @p53 :rule bool-impl-elim :args (@t55 @t1)) % 0.39/0.57 (step @p54 :rule trans :premises (@p53 @p52)) % 0.39/0.57 (step @p55 :rule cong :premises (@p54) :args ((forall @t12 (=> @t55 @t1)))) % 0.39/0.57 (step @p56 :rule trans :premises (@p55 @p50)) % 0.39/0.57 (step @p57 :rule refl :args (@t1)) % 0.39/0.57 (step @p58 :rule refl :args (@t42)) % 0.39/0.57 (step @p59 :rule refl :args (@t4)) % 0.39/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t4 @t42))) % 0.39/0.57 (step @p61 :rule symm :premises (@p60)) % 0.39/0.57 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.39/0.57 (step @p63 :rule cong :premises (@p62) :args (@t56)) % 0.39/0.57 (step @p64 :rule refl :args (@t43)) % 0.39/0.57 (step @p65 :rule refl :args (@t8)) % 0.39/0.57 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t8 @t43))) % 0.39/0.57 (step @p67 :rule symm :premises (@p66)) % 0.39/0.57 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.39/0.57 (step @p69 :rule cong :premises (@p68) :args (@t57)) % 0.39/0.57 (step @p70 :rule nary_cong :premises (@p69 @p63) :args (@t58)) % 0.39/0.57 (step @p71 :rule cong :premises (@p70) :args (@t59)) % 0.39/0.57 (step @p72 :rule nary_cong :premises (@p57 @p71) :args (@t60)) % 0.39/0.57 (step @p73 :rule quant-miniscope-or :args ((= (forall @t9 @t61) @t60))) % 0.39/0.57 (step @p74 :rule aci_norm :args ((= @t62 @t61))) % 0.39/0.57 (step @p75 :rule cong :premises (@p74) :args ((forall @t9 @t62))) % 0.39/0.57 (step @p76 :rule trans :premises (@p75 @p73)) % 0.39/0.57 (step @p77 :rule trans :premises (@p76 @p72)) % 0.39/0.57 (step @p78 :rule aci_norm :args ((= (or @t57 (or @t56 @t1)) @t62))) % 0.39/0.57 (step @p79 :rule bool-impl-elim :args (@t4 @t1)) % 0.39/0.57 (step @p80 :rule refl :args (@t57)) % 0.39/0.57 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or @t57 @t5))) % 0.39/0.57 (step @p82 :rule trans :premises (@p81 @p78)) % 0.39/0.57 (step @p83 :rule bool-impl-elim :args (@t8 @t5)) % 0.39/0.57 (step @p84 :rule trans :premises (@p83 @p82)) % 0.39/0.57 (step @p85 :rule cong :premises (@p84) :args (@t10)) % 0.39/0.57 (step @p86 :rule trans :premises (@p85 @p77)) % 0.39/0.57 (step @p87 :rule cong :premises (@p86 @p57) :args (@t11)) % 0.39/0.57 (step @p88 :rule cong :premises (@p87) :args (@t13)) % 0.39/0.57 (step @p89 :rule trans :premises (@p88 @p56)) % 0.39/0.57 (step @p90 :rule refl :args (@t15)) % 0.39/0.57 (step @p91 :rule cong :premises (@p90 @p89) :args (@t16)) % 0.39/0.57 (step @p92 :rule cong :premises (@p91) :args (@t18)) % 0.39/0.57 (step @p93 :rule trans :premises (@p92 @p28)) % 0.39/0.57 (step @p94 :rule refl :args (tptp.setunionE)) % 0.39/0.57 (step @p95 :rule cong :premises (@p94 @p93) :args (@t19)) % 0.39/0.57 (step @p96 :rule eq_resolve :premises (@p1 @p95)) % 0.39/0.57 (step @p97 :rule cong :premises (@p96 @p4) :args (@t63)) % 0.39/0.57 (step @p98 :rule cong :premises (@p97) :args ((not @t63))) % 0.39/0.57 (step @p99 :rule refl :args (@t36)) % 0.39/0.57 (step @p100 :rule nary_cong :premises (@p23 @p99) :args (@t64)) % 0.39/0.57 (step @p101 :rule cong :premises (@p100) :args ((forall @t17 @t64))) % 0.39/0.57 (step @p102 :rule bool-impl-elim :args (@t15 @t36)) % 0.39/0.57 (step @p103 :rule cong :premises (@p102) :args ((forall @t17 (=> @t15 @t36)))) % 0.39/0.57 (step @p104 :rule trans :premises (@p103 @p101)) % 0.39/0.57 (step @p105 :rule refl :args (@t30)) % 0.39/0.57 (step @p106 :rule refl :args (@t21)) % 0.39/0.57 (step @p107 :rule cong :premises (@p106 @p105) :args ((= @t21 @t30))) % 0.39/0.57 (step @p108 :rule symm :premises (@p107)) % 0.39/0.57 (step @p109 :rule eq_resolve :premises (@p106 @p108)) % 0.39/0.57 (step @p110 :rule cong :premises (@p109) :args (@t65)) % 0.39/0.57 (step @p111 :rule refl :args (@t32)) % 0.39/0.57 (step @p112 :rule refl :args (@t22)) % 0.39/0.57 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t22 @t32))) % 0.39/0.57 (step @p114 :rule symm :premises (@p113)) % 0.39/0.57 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.39/0.57 (step @p116 :rule cong :premises (@p115) :args (@t66)) % 0.39/0.57 (step @p117 :rule nary_cong :premises (@p116 @p110) :args (@t67)) % 0.39/0.57 (step @p118 :rule cong :premises (@p117) :args ((forall @t24 @t67))) % 0.39/0.57 (step @p119 :rule bool-and-de-morgan :args (@t22 @t21 true)) % 0.39/0.57 (step @p120 :rule cong :premises (@p119) :args (@t68)) % 0.39/0.57 (step @p121 :rule trans :premises (@p120 @p118)) % 0.39/0.57 (step @p122 :rule cong :premises (@p121) :args (@t69)) % 0.39/0.57 (step @p123 :rule exists-elim :args ((= @t25 @t69))) % 0.39/0.57 (step @p124 :rule trans :premises (@p123 @p122)) % 0.39/0.57 (step @p125 :rule cong :premises (@p90 @p124) :args (@t26)) % 0.39/0.57 (step @p126 :rule cong :premises (@p125) :args (@t27)) % 0.39/0.57 (step @p127 :rule trans :premises (@p126 @p104)) % 0.39/0.57 (step @p128 :rule cong :premises (@p94 @p127) :args (@t28)) % 0.39/0.57 (step @p129 :rule cong :premises (@p128) :args (@t29)) % 0.39/0.57 (step @p130 :rule trans :premises (@p129 @p98)) % 0.39/0.57 (step @p131 :rule eq_resolve :premises (@p2 @p130)) % 0.39/0.57 (step @p132 :rule not_implies_elim1 :premises (@p131)) % 0.39/0.57 (step @p133 :rule aci_norm :args ((= @t34 @t70))) % 0.39/0.57 (step @p134 :rule cong :premises (@p133) :args (@t35)) % 0.39/0.57 (step @p135 :rule cong :premises (@p134) :args (@t36)) % 0.39/0.57 (step @p136 :rule refl :args (@t39)) % 0.39/0.57 (step @p137 :rule nary_cong :premises (@p136 @p135) :args (@t40)) % 0.39/0.57 (step @p138 :rule cong :premises (@p137) :args (@t41)) % 0.39/0.57 (step @p139 :rule symm :premises (@p138)) % 0.39/0.57 (step @p140 :rule true_intro :premises (@p139)) % 0.39/0.57 (step @p141 :rule eq-symm :args (@t41 @t71)) % 0.39/0.57 (step @p142 :rule trans :premises (@p141 @p140)) % 0.39/0.57 (step @p143 :rule cong :premises (@p139 @p138) :args ((= @t71 @t41))) % 0.39/0.57 (step @p144 :rule trans :premises (@p143 @p142)) % 0.39/0.57 (step @p145 :rule true_elim :premises (@p144)) % 0.39/0.57 (step @p146 :rule alpha_equiv :args ((forall (@list @t72 @t74) (or (not (tptp.in @t74 (tptp.setunion @t72))) (not (forall (@list @t73) (or (not (tptp.in @t74 @t73)) (not (tptp.in @t73 @t72))))))) @t75 (@list @t20 @t6 @t2))) % 0.39/0.57 (step @p147 :rule alpha_equiv :args (@t76 (@list @t3 @t6 @t2) @t75)) % 0.39/0.57 (step @p148 :rule trans :premises (@p147 @p146 @p145)) % 0.39/0.57 (step @p149 :rule equiv_elim1 :premises (@p148)) % 0.39/0.57 (step @p150 :rule reordering :premises (@p149) :args ((or @t41 (not @t76)))) % 0.39/0.57 (step @p151 :rule chain_m_resolution :premises (@p150 @p132) :args (@t41 @t77 (@list @t76))) % 0.39/0.57 (step @p152 :rule not_implies_elim2 :premises (@p131)) % 0.39/0.57 (step @p153 false :rule chain_m_resolution :premises (@p152 @p151) :args (false @t77 (@list @t41))) % 0.39/0.57 ) % 0.39/0.57 % SZS output end Proof % 0.39/0.57 % cvc5 exiting %------------------------------------------------------------------------------