%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ104^5 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:44:12 AM UTC 2026 % Result : Theorem 0.38s 0.57s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ104^5 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n021.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 13:19:20 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.38/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.57 % SZS status Theorem % 0.38/0.57 % SZS output start Proof % 0.38/0.57 ( % 0.38/0.57 (declare-sort $$unsorted 0) % 0.38/0.57 (declare-const tptp.s (-> $$unsorted $$unsorted)) % 0.38/0.57 (declare-const tptp.c1 $$unsorted) % 0.38/0.57 (define tptp.cCKB6_NUM () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xp" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Xw" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (and (_ _let_2 tptp.c1) (forall (@list _let_3) (=> (_ _let_2 _let_3) (_ _let_2 (_ tptp.s _let_3))))) (_ _let_2 _let_1)))))))) % 0.38/0.57 (define @t1 () (@var "Xx" $$unsorted)) % 0.38/0.57 (define @t2 () (_ tptp.s @t1)) % 0.38/0.57 (define @t3 () (_ tptp.s @t2)) % 0.38/0.57 (define @t4 () (=> (_ tptp.cCKB6_NUM @t1) (_ tptp.cCKB6_NUM @t3))) % 0.38/0.57 (define @t5 () (@list @t1)) % 0.38/0.57 (define @t6 () (forall @t5 @t4)) % 0.38/0.57 (define @t7 () (not @t6)) % 0.38/0.57 (define @t8 () (@var "Xp" (-> $$unsorted Bool))) % 0.38/0.57 (define @t9 () (_ @t8 @t1)) % 0.38/0.57 (define @t10 () (@var "Xw" $$unsorted)) % 0.38/0.57 (define @t11 () (_ tptp.s @t10)) % 0.38/0.57 (define @t12 () (_ @t8 @t11)) % 0.38/0.57 (define @t13 () (_ @t8 @t10)) % 0.38/0.57 (define @t14 () (@list @t10)) % 0.38/0.57 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.38/0.57 (define @t16 () (_ @t8 tptp.c1)) % 0.38/0.57 (define @t17 () (and @t16 @t15)) % 0.38/0.57 (define @t18 () (=> @t17 @t9)) % 0.38/0.57 (define @t19 () (@list @t8)) % 0.38/0.57 (define @t20 () (forall @t19 @t18)) % 0.38/0.57 (define @t21 () (lambda @t5 @t20)) % 0.38/0.57 (define @t22 () (tptp.s @t1)) % 0.38/0.57 (define @t23 () (tptp.s @t22)) % 0.38/0.57 (define @t24 () (@var "BOUND_VARIABLE_7489" (-> $$unsorted Bool))) % 0.38/0.57 (define @t25 () (_ @t24 @t23)) % 0.38/0.57 (define @t26 () (tptp.s @t10)) % 0.38/0.57 (define @t27 () (not (forall @t14 (or (not (_ @t24 @t10)) (_ @t24 @t26))))) % 0.38/0.57 (define @t28 () (not (_ @t24 tptp.c1))) % 0.38/0.57 (define @t29 () (_ @t8 @t1)) % 0.38/0.57 (define @t30 () (_ @t8 @t26)) % 0.38/0.57 (define @t31 () (_ @t8 @t10)) % 0.38/0.57 (define @t32 () (forall @t14 (or (not @t31) @t30))) % 0.38/0.57 (define @t33 () (not @t32)) % 0.38/0.57 (define @t34 () (_ @t8 tptp.c1)) % 0.38/0.57 (define @t35 () (not @t34)) % 0.38/0.57 (define @t36 () (forall @t19 (or @t35 @t33 @t29))) % 0.38/0.57 (define @t37 () (not @t36)) % 0.38/0.57 (define @t38 () (or @t37 @t28 @t27 @t25)) % 0.38/0.57 (define @t39 () (or @t28 @t27 @t25)) % 0.38/0.57 (define @t40 () (or @t37 @t39)) % 0.38/0.57 (define @t41 () (@list @t1 @t24)) % 0.38/0.57 (define @t42 () (forall @t41 @t40)) % 0.38/0.57 (define @t43 () (@list @t24)) % 0.38/0.57 (define @t44 () (forall @t43 @t40)) % 0.38/0.57 (define @t45 () (forall @t43 @t39)) % 0.38/0.57 (define @t46 () (or @t37 @t45)) % 0.38/0.57 (define @t47 () (forall @t19 (or @t35 @t33 (_ @t8 @t23)))) % 0.38/0.57 (define @t48 () (_ @t8 @t3)) % 0.38/0.57 (define @t49 () (or @t35 @t33 @t48)) % 0.38/0.57 (define @t50 () (forall @t19 @t49)) % 0.38/0.57 (define @t51 () (lambda @t5 @t36)) % 0.38/0.57 (define @t52 () (_ @t51 @t3)) % 0.38/0.57 (define @t53 () (_ @t51 @t1)) % 0.38/0.57 (define @t54 () (=> @t53 @t52)) % 0.38/0.57 (define @t55 () (forall @t5 @t54)) % 0.38/0.57 (define @t56 () (not @t16)) % 0.38/0.57 (define @t57 () (or @t56 @t33 @t9)) % 0.38/0.57 (define @t58 () (and @t16 @t32)) % 0.38/0.57 (define @t59 () (not @t13)) % 0.38/0.57 (define @t60 () (or @t59 @t12)) % 0.38/0.57 (define @t61 () (forall @t41 @t38)) % 0.38/0.57 (define @t62 () (@quantifiers_skolemize @t61 0)) % 0.38/0.57 (define @t63 () (forall @t19 (or @t35 @t33 (_ @t8 @t62)))) % 0.38/0.57 (define @t64 () (tptp.s @t62)) % 0.38/0.57 (define @t65 () (@quantifiers_skolemize @t61 1)) % 0.38/0.57 (define @t66 () (_ @t65 (tptp.s @t64))) % 0.38/0.57 (define @t67 () (forall @t14 (or (not (_ @t65 @t10)) (_ @t65 @t26)))) % 0.38/0.57 (define @t68 () (not @t67)) % 0.38/0.57 (define @t69 () (_ @t65 tptp.c1)) % 0.38/0.57 (define @t70 () (not @t69)) % 0.38/0.57 (define @t71 () (not @t63)) % 0.38/0.57 (define @t72 () (or @t71 @t70 @t68 @t66)) % 0.38/0.57 (define @t73 () (@list true)) % 0.38/0.57 (define @t74 () (@list @t72)) % 0.38/0.57 (define @t75 () (_ @t65 @t64)) % 0.38/0.57 (define @t76 () (not @t75)) % 0.38/0.57 (define @t77 () (or @t76 @t66)) % 0.38/0.57 (define @t78 () (@list true false)) % 0.38/0.57 (define @t79 () (_ @t65 @t62)) % 0.38/0.57 (define @t80 () (not @t79)) % 0.38/0.57 (define @t81 () (or @t80 @t75)) % 0.38/0.57 (define @t82 () (or @t70 @t68 @t79)) % 0.38/0.57 (define @t83 () (not @t82)) % 0.38/0.57 (assume @p1 @t7) % 0.38/0.57 (assume @p2 true) % 0.38/0.57 (step @p3 (= tptp.cCKB6_NUM @t21) :rule refl :args (@t21)) % 0.38/0.57 (step @p4 :rule aci_norm :args ((= @t40 @t38))) % 0.38/0.57 (step @p5 :rule cong :premises (@p4) :args (@t42)) % 0.38/0.57 (step @p6 :rule quant-merge-prenex :args ((= (forall @t5 @t44) @t42))) % 0.38/0.57 (step @p7 :rule alpha_equiv :args (@t45 (@list @t24) (@list @t8))) % 0.38/0.57 (step @p8 :rule refl :args (@t37)) % 0.38/0.57 (step @p9 :rule nary_cong :premises (@p8 @p7) :args (@t46)) % 0.38/0.57 (step @p10 :rule quant-miniscope-or :args ((= @t44 @t46))) % 0.38/0.57 (step @p11 :rule trans :premises (@p10 @p9)) % 0.38/0.57 (step @p12 :rule symm :premises (@p11)) % 0.38/0.57 (step @p13 :rule cong :premises (@p12) :args ((forall @t5 (or @t37 @t47)))) % 0.38/0.57 (step @p14 :rule trans :premises (@p13 @p6)) % 0.38/0.57 (step @p15 :rule trans :premises (@p14 @p5)) % 0.38/0.57 (step @p16 :rule bool-impl-elim :args (@t36 @t47)) % 0.38/0.57 (step @p17 :rule cong :premises (@p16) :args ((forall @t5 (=> @t36 @t47)))) % 0.38/0.57 (step @p18 :rule trans :premises (@p17 @p15)) % 0.38/0.57 (step @p19 :rule refl :args ((tptp.s @t2))) % 0.38/0.57 (step @p20 :rule refl :args (@t22)) % 0.38/0.57 (step @p21 :rule cong :premises (@p20) :args (@t23)) % 0.38/0.57 (step @p22 :rule trans :premises (@p21 @p19)) % 0.38/0.57 (step @p23 :rule refl :args (tptp.s)) % 0.38/0.57 (step @p24 :rule ho_cong :premises (@p23 @p20)) % 0.38/0.57 (step @p25 :rule cong :premises (@p24 @p22) :args ((= (_ tptp.s @t22) @t23))) % 0.38/0.57 (step @p26 :rule symm :premises (@p25)) % 0.38/0.57 (step @p27 :rule refl :args (@t3)) % 0.38/0.57 (step @p28 :rule eq_resolve :premises (@p27 @p26)) % 0.38/0.57 (step @p29 :rule refl :args (@t2)) % 0.38/0.57 (step @p30 :rule cong :premises (@p29 @p20) :args ((= @t2 @t22))) % 0.38/0.57 (step @p31 :rule symm :premises (@p30)) % 0.38/0.57 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 0.38/0.57 (step @p33 :rule ho_cong :premises (@p23 @p32)) % 0.38/0.57 (step @p34 :rule trans :premises (@p33 @p28)) % 0.38/0.57 (step @p35 :rule cong :premises (@p34) :args (@t48)) % 0.38/0.57 (step @p36 :rule refl :args (@t33)) % 0.38/0.57 (step @p37 :rule refl :args (@t35)) % 0.38/0.57 (step @p38 :rule nary_cong :premises (@p37 @p36 @p35) :args (@t49)) % 0.38/0.57 (step @p39 :rule cong :premises (@p38) :args (@t50)) % 0.38/0.57 (step @p40 :rule beta-reduce :args ((= @t52 @t50))) % 0.38/0.57 (step @p41 :rule trans :premises (@p40 @p39)) % 0.38/0.57 (step @p42 :rule beta-reduce :args ((= @t53 @t36))) % 0.38/0.57 (step @p43 :rule cong :premises (@p42 @p41) :args (@t54)) % 0.38/0.57 (step @p44 :rule cong :premises (@p43) :args (@t55)) % 0.38/0.57 (step @p45 :rule trans :premises (@p44 @p18)) % 0.38/0.57 (step @p46 :rule cong :premises (@p45) :args ((not @t55))) % 0.38/0.57 (step @p47 :rule refl :args (@t3)) % 0.38/0.57 (step @p48 :rule refl :args (@t29)) % 0.38/0.57 (step @p49 :rule refl :args (@t9)) % 0.38/0.57 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t9 @t29))) % 0.38/0.57 (step @p51 :rule symm :premises (@p50)) % 0.38/0.57 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.38/0.57 (step @p53 :rule refl :args (@t34)) % 0.38/0.57 (step @p54 :rule refl :args (@t16)) % 0.38/0.57 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t16 @t34))) % 0.38/0.57 (step @p56 :rule symm :premises (@p55)) % 0.38/0.57 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.38/0.57 (step @p58 :rule cong :premises (@p57) :args (@t56)) % 0.38/0.57 (step @p59 :rule nary_cong :premises (@p58 @p36 @p52) :args (@t57)) % 0.38/0.57 (step @p60 :rule cong :premises (@p59) :args ((forall @t19 @t57))) % 0.38/0.57 (step @p61 :rule aci_norm :args ((= (or (or @t56 @t33) @t9) @t57))) % 0.38/0.57 (step @p62 :rule bool-and-de-morgan :args (@t16 @t32 true)) % 0.38/0.57 (step @p63 :rule nary_cong :premises (@p62 @p49) :args ((or (not @t58) @t9))) % 0.38/0.57 (step @p64 :rule trans :premises (@p63 @p61)) % 0.38/0.57 (step @p65 :rule bool-impl-elim :args (@t58 @t9)) % 0.38/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.38/0.57 (step @p67 :rule cong :premises (@p66) :args ((forall @t19 (=> @t58 @t9)))) % 0.38/0.57 (step @p68 :rule trans :premises (@p67 @p60)) % 0.38/0.57 (step @p69 :rule refl :args (@t9)) % 0.38/0.57 (step @p70 :rule refl :args ((_ @t8 @t11))) % 0.38/0.57 (step @p71 :rule refl :args (@t26)) % 0.38/0.57 (step @p72 :rule cong :premises (@p71) :args (@t30)) % 0.38/0.57 (step @p73 :rule trans :premises (@p72 @p70)) % 0.38/0.57 (step @p74 :rule refl :args (@t8)) % 0.38/0.57 (step @p75 :rule ho_cong :premises (@p74 @p71)) % 0.38/0.57 (step @p76 :rule cong :premises (@p75 @p73) :args ((= (_ @t8 @t26) @t30))) % 0.38/0.57 (step @p77 :rule symm :premises (@p76)) % 0.38/0.57 (step @p78 :rule refl :args (@t12)) % 0.38/0.57 (step @p79 :rule eq_resolve :premises (@p78 @p77)) % 0.38/0.57 (step @p80 :rule refl :args (@t11)) % 0.38/0.57 (step @p81 :rule cong :premises (@p80 @p71) :args ((= @t11 @t26))) % 0.38/0.57 (step @p82 :rule symm :premises (@p81)) % 0.38/0.57 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.38/0.57 (step @p84 :rule ho_cong :premises (@p74 @p83)) % 0.38/0.57 (step @p85 :rule trans :premises (@p84 @p79)) % 0.38/0.57 (step @p86 :rule refl :args (@t31)) % 0.38/0.57 (step @p87 :rule refl :args (@t13)) % 0.38/0.57 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t13 @t31))) % 0.38/0.57 (step @p89 :rule symm :premises (@p88)) % 0.38/0.57 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.38/0.57 (step @p91 :rule cong :premises (@p90) :args (@t59)) % 0.38/0.57 (step @p92 :rule nary_cong :premises (@p91 @p85) :args (@t60)) % 0.38/0.57 (step @p93 :rule cong :premises (@p92) :args ((forall @t14 @t60))) % 0.38/0.57 (step @p94 :rule bool-impl-elim :args (@t13 @t12)) % 0.38/0.57 (step @p95 :rule cong :premises (@p94) :args (@t15)) % 0.38/0.57 (step @p96 :rule trans :premises (@p95 @p93)) % 0.38/0.57 (step @p97 :rule refl :args (@t16)) % 0.38/0.57 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t17)) % 0.38/0.57 (step @p99 :rule cong :premises (@p98 @p69) :args (@t18)) % 0.38/0.57 (step @p100 :rule cong :premises (@p99) :args (@t20)) % 0.38/0.57 (step @p101 :rule trans :premises (@p100 @p68)) % 0.38/0.57 (step @p102 :rule cong :premises (@p101) :args (@t21)) % 0.38/0.57 (step @p103 :rule trans :premises (@p3 @p102)) % 0.38/0.57 (step @p104 :rule ho_cong :premises (@p103 @p47)) % 0.38/0.57 (step @p105 :rule refl :args (@t1)) % 0.38/0.57 (step @p106 :rule ho_cong :premises (@p103 @p105)) % 0.38/0.57 (step @p107 :rule cong :premises (@p106 @p104) :args (@t4)) % 0.38/0.57 (step @p108 :rule cong :premises (@p107) :args (@t6)) % 0.38/0.57 (step @p109 :rule cong :premises (@p108) :args (@t7)) % 0.38/0.57 (step @p110 :rule trans :premises (@p109 @p46)) % 0.38/0.57 (step @p111 :rule eq_resolve :premises (@p1 @p110)) % 0.38/0.57 (step @p112 :rule skolemize :premises (@p111)) % 0.38/0.57 (step @p113 :rule bool-double-not-elim :args (@t63)) % 0.38/0.57 (step @p114 :rule refl :args (@t72)) % 0.38/0.57 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t72 (not @t71)))) % 0.38/0.57 (step @p116 :rule cnf_or_neg :args (@t72 0)) % 0.38/0.57 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.38/0.57 (step @p118 :rule reordering :premises (@p117) :args ((or @t63 @t72))) % 0.38/0.57 (step @p119 :rule chain_m_resolution :premises (@p118 @p112) :args (@t63 @t73 @t74)) % 0.38/0.57 (step @p120 :rule bool-double-not-elim :args (@t67)) % 0.38/0.57 (step @p121 :rule nary_cong :premises (@p114 @p120) :args ((or @t72 (not @t68)))) % 0.38/0.57 (step @p122 :rule cnf_or_neg :args (@t72 2)) % 0.38/0.57 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.38/0.57 (step @p124 :rule reordering :premises (@p123) :args ((or @t67 @t72))) % 0.38/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p112) :args (@t67 @t73 @t74)) % 0.38/0.57 (step @p126 :rule instantiate :premises (@p125) :args ((@list @t62))) % 0.38/0.57 (step @p127 :rule instantiate :premises (@p125) :args ((@list @t64))) % 0.38/0.57 (step @p128 :rule cnf_or_neg :args (@t72 3)) % 0.38/0.57 (step @p129 :rule chain_m_resolution :premises (@p128 @p112) :args ((not @t66) @t73 @t74)) % 0.38/0.57 (step @p130 :rule cnf_or_pos :args (@t77)) % 0.38/0.57 (step @p131 :rule reordering :premises (@p130) :args ((or @t66 @t76 (not @t77)))) % 0.38/0.57 (step @p132 :rule chain_m_resolution :premises (@p131 @p129 @p127) :args (@t76 @t78 (@list @t66 @t77))) % 0.38/0.57 (step @p133 :rule cnf_or_pos :args (@t81)) % 0.38/0.57 (step @p134 :rule reordering :premises (@p133) :args ((or @t80 @t75 (not @t81)))) % 0.38/0.57 (step @p135 :rule chain_m_resolution :premises (@p134 @p132 @p126) :args (@t80 @t78 (@list @t75 @t81))) % 0.38/0.57 (step @p136 :rule bool-double-not-elim :args (@t69)) % 0.38/0.57 (step @p137 :rule nary_cong :premises (@p114 @p136) :args ((or @t72 (not @t70)))) % 0.38/0.57 (step @p138 :rule cnf_or_neg :args (@t72 1)) % 0.38/0.57 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.38/0.57 (step @p140 :rule reordering :premises (@p139) :args ((or @t69 @t72))) % 0.38/0.57 (step @p141 :rule chain_m_resolution :premises (@p140 @p112) :args (@t69 @t73 @t74)) % 0.38/0.57 (step @p142 :rule cnf_or_pos :args (@t82)) % 0.38/0.57 (step @p143 :rule reordering :premises (@p142) :args ((or @t70 @t68 @t79 @t83))) % 0.38/0.57 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p125 @p135) :args (@t83 (@list false false true) (@list @t69 @t67 @t79))) % 0.38/0.57 (assume-push @p151 @t63) % 0.38/0.57 (step @p146 :rule instantiate :premises (@p119) :args ((@list @t65))) % 0.38/0.57 (step-pop @p152 :rule scope :premises (@p146)) % 0.38/0.57 (step @p147 :rule process_scope :premises (@p152) :args (@t82)) % 0.38/0.57 (step @p149 :rule implies_elim :premises (@p147)) % 0.38/0.57 (step @p150 false :rule chain_m_resolution :premises (@p149 @p144 @p119) :args (false @t78 (@list @t82 @t63))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------