%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL735^5 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:43 AM UTC 2026 % Result : Theorem 52.93s 53.29s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL735^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.35 % Computer : n004.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 01:49:14 UTC 2026 % 0.12/0.35 % CPUTime : % 0.12/0.42 %----Proving TH0 % 52.93/53.29 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 52.93/53.29 % SZS status Theorem % 52.93/53.29 % SZS output start Proof % 52.93/53.29 ( % 52.93/53.29 (declare-sort tptp.b 0) % 52.93/53.29 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 52.93/53.29 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 52.93/53.29 (define @t3 () (_ @t2 @t1)) % 52.93/53.29 (define @t4 () (_ @t1 @t3)) % 52.93/53.29 (define @t5 () (@var "Xz" tptp.b)) % 52.93/53.29 (define @t6 () (_ @t1 @t5)) % 52.93/53.29 (define @t7 () (@list @t5)) % 52.93/53.29 (define @t8 () (exists @t7 @t6)) % 52.93/53.29 (define @t9 () (=> @t8 @t4)) % 52.93/53.29 (define @t10 () (@list @t1)) % 52.93/53.29 (define @t11 () (forall @t10 @t9)) % 52.93/53.29 (define @t12 () (@list @t2)) % 52.93/53.29 (define @t13 () (exists @t12 @t11)) % 52.93/53.29 (define @t14 () (@var "Xw" tptp.b)) % 52.93/53.29 (define @t15 () (@var "Xx" (-> tptp.b Bool))) % 52.93/53.29 (define @t16 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 52.93/53.29 (define @t17 () (_ @t16 @t15)) % 52.93/53.29 (define @t18 () (@var "Xb" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 52.93/53.29 (define @t19 () (_ @t18 @t15)) % 52.93/53.29 (define @t20 () (_ (_ @t19 @t17) @t14)) % 52.93/53.29 (define @t21 () (@var "Xa" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 52.93/53.29 (define @t22 () (_ @t21 @t15)) % 52.93/53.29 (define @t23 () (_ (_ @t22 @t17) @t14)) % 52.93/53.29 (define @t24 () (or @t23 @t20)) % 52.93/53.29 (define @t25 () (@list @t15 @t14)) % 52.93/53.29 (define @t26 () (forall @t25 @t24)) % 52.93/53.29 (define @t27 () (@list @t16)) % 52.93/53.29 (define @t28 () (exists @t27 @t26)) % 52.93/53.29 (define @t29 () (@var "Xy" tptp.b)) % 52.93/53.29 (define @t30 () (_ (_ @t19 @t29) @t14)) % 52.93/53.29 (define @t31 () (_ (_ @t22 @t29) @t14)) % 52.93/53.29 (define @t32 () (or @t31 @t30)) % 52.93/53.29 (define @t33 () (@list @t14)) % 52.93/53.29 (define @t34 () (forall @t33 @t32)) % 52.93/53.29 (define @t35 () (@list @t29)) % 52.93/53.29 (define @t36 () (exists @t35 @t34)) % 52.93/53.29 (define @t37 () (@list @t15)) % 52.93/53.29 (define @t38 () (forall @t37 @t36)) % 52.93/53.29 (define @t39 () (=> @t38 @t28)) % 52.93/53.29 (define @t40 () (@list @t21 @t18)) % 52.93/53.29 (define @t41 () (forall @t40 @t39)) % 52.93/53.29 (define @t42 () (=> @t41 @t13)) % 52.93/53.29 (define @t43 () (not @t42)) % 52.93/53.29 (define @t44 () (_ @t2 @t1)) % 52.93/53.29 (define @t45 () (_ @t1 @t44)) % 52.93/53.29 (define @t46 () (@var "BOUND_VARIABLE_7501" tptp.b)) % 52.93/53.29 (define @t47 () (not (_ @t1 @t46))) % 52.93/53.29 (define @t48 () (or @t47 @t45)) % 52.93/53.29 (define @t49 () (@list @t1 @t46)) % 52.93/53.29 (define @t50 () (forall @t49 @t48)) % 52.93/53.29 (define @t51 () (forall @t12 (not @t50))) % 52.93/53.29 (define @t52 () (@list @t46)) % 52.93/53.29 (define @t53 () (forall @t52 @t48)) % 52.93/53.29 (define @t54 () (forall @t52 @t47)) % 52.93/53.29 (define @t55 () (or @t54 @t45)) % 52.93/53.29 (define @t56 () (_ @t1 @t5)) % 52.93/53.29 (define @t57 () (forall @t7 (not @t56))) % 52.93/53.29 (define @t58 () (or @t57 @t4)) % 52.93/53.29 (define @t59 () (not @t57)) % 52.93/53.29 (define @t60 () (not @t6)) % 52.93/53.29 (define @t61 () (forall @t7 @t60)) % 52.93/53.29 (define @t62 () (not @t61)) % 52.93/53.29 (define @t63 () (_ @t18 @t15 @t29 @t14)) % 52.93/53.29 (define @t64 () (_ @t21 @t15 @t29 @t14)) % 52.93/53.29 (define @t65 () (forall @t33 (or @t64 @t63))) % 52.93/53.29 (define @t66 () (not (forall @t35 (not @t65)))) % 52.93/53.29 (define @t67 () (forall @t37 @t66)) % 52.93/53.29 (define @t68 () (_ @t16 @t15)) % 52.93/53.29 (define @t69 () (_ @t18 @t15 @t68 @t14)) % 52.93/53.29 (define @t70 () (_ @t21 @t15 @t68 @t14)) % 52.93/53.29 (define @t71 () (forall @t25 (or @t70 @t69))) % 52.93/53.29 (define @t72 () (not (forall @t27 (not @t71)))) % 52.93/53.29 (define @t73 () (@const 0 (-> (-> tptp.b Bool) tptp.b))) % 52.93/53.29 (define @t74 () (_ @t73 @t1)) % 52.93/53.29 (define @t75 () (@var "BOUND_VARIABLE_387794" (-> tptp.b Bool))) % 52.93/53.29 (define @t76 () (_ @t73 @t75)) % 52.93/53.29 (define @t77 () (@list @t75)) % 52.93/53.29 (define @t78 () (lambda @t77 @t76)) % 52.93/53.29 (define @t79 () (_ @t78 @t1)) % 52.93/53.29 (define @t80 () (_ @t1 @t79)) % 52.93/53.29 (define @t81 () (or @t47 @t80)) % 52.93/53.29 (define @t82 () (forall @t49 @t81)) % 52.93/53.29 (define @t83 () (not @t82)) % 52.93/53.29 (define @t84 () (forall @t49 (or @t47 (_ @t1 @t74)))) % 52.93/53.29 (define @t85 () (@quantifiers_skolemize @t84 1)) % 52.93/53.29 (define @t86 () (@quantifiers_skolemize @t84 0)) % 52.93/53.29 (define @t87 () (_ @t86 @t85)) % 52.93/53.29 (define @t88 () (_ @t86 (_ @t73 @t86))) % 52.93/53.29 (define @t89 () (not @t87)) % 52.93/53.29 (define @t90 () (or @t89 @t88)) % 52.93/53.29 (define @t91 () (@list true)) % 52.93/53.29 (define @t92 () (@list @t90)) % 52.93/53.29 (define @t93 () (@var "x" tptp.b)) % 52.93/53.29 (define @t94 () (@list @t93)) % 52.93/53.29 (define @t95 () (forall @t94 (not (_ @t86 @t93)))) % 52.93/53.29 (define @t96 () (or @t95 @t88)) % 52.93/53.29 (assume @p1 @t43) % 52.93/53.29 (assume @p2 true) % 52.93/53.29 (step @p3 :rule exists-elim :args ((= (exists @t12 @t50) (not @t51)))) % 52.93/53.29 (step @p4 :rule quant-merge-prenex :args ((= (forall @t10 @t53) @t50))) % 52.93/53.29 (step @p5 :rule refl :args (@t45)) % 52.93/53.29 (step @p6 :rule alpha_equiv :args (@t54 (@list @t46) (@list @t5))) % 52.93/53.29 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t55)) % 52.93/53.29 (step @p8 :rule quant-miniscope-or :args ((= @t53 @t55))) % 52.93/53.29 (step @p9 :rule trans :premises (@p8 @p7)) % 52.93/53.29 (step @p10 :rule symm :premises (@p9)) % 52.93/53.29 (step @p11 :rule cong :premises (@p10) :args ((forall @t10 (or @t57 @t45)))) % 52.93/53.29 (step @p12 :rule trans :premises (@p11 @p4)) % 52.93/53.29 (step @p13 :rule refl :args ((_ @t1 @t3))) % 52.93/53.29 (step @p14 :rule refl :args (@t44)) % 52.93/53.29 (step @p15 :rule cong :premises (@p14) :args (@t45)) % 52.93/53.29 (step @p16 :rule trans :premises (@p15 @p13)) % 52.93/53.29 (step @p17 :rule refl :args (@t1)) % 52.93/53.29 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 52.93/53.29 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t44) @t45))) % 52.93/53.29 (step @p20 :rule symm :premises (@p19)) % 52.93/53.29 (step @p21 :rule refl :args (@t4)) % 52.93/53.29 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 52.93/53.29 (step @p23 :rule refl :args (@t3)) % 52.93/53.29 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t3 @t44))) % 52.93/53.29 (step @p25 :rule symm :premises (@p24)) % 52.93/53.29 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 52.93/53.29 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 52.93/53.29 (step @p28 :rule trans :premises (@p27 @p22)) % 52.93/53.29 (step @p29 :rule refl :args (@t57)) % 52.93/53.29 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t58)) % 52.93/53.29 (step @p31 :rule cong :premises (@p30) :args ((forall @t10 @t58))) % 52.93/53.29 (step @p32 :rule trans :premises (@p31 @p12)) % 52.93/53.29 (step @p33 :rule bool-double-not-elim :args (@t57)) % 52.93/53.29 (step @p34 :rule nary_cong :premises (@p33 @p21) :args ((or (not @t59) @t4))) % 52.93/53.29 (step @p35 :rule bool-impl-elim :args (@t59 @t4)) % 52.93/53.29 (step @p36 :rule trans :premises (@p35 @p34)) % 52.93/53.29 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 (=> @t59 @t4)))) % 52.93/53.29 (step @p38 :rule trans :premises (@p37 @p32)) % 52.93/53.29 (step @p39 :rule refl :args (@t4)) % 52.93/53.29 (step @p40 :rule refl :args (@t56)) % 52.93/53.29 (step @p41 :rule refl :args (@t6)) % 52.93/53.29 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t6 @t56))) % 52.93/53.29 (step @p43 :rule symm :premises (@p42)) % 52.93/53.29 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 52.93/53.29 (step @p45 :rule cong :premises (@p44) :args (@t60)) % 52.93/53.29 (step @p46 :rule cong :premises (@p45) :args (@t61)) % 52.93/53.29 (step @p47 :rule cong :premises (@p46) :args (@t62)) % 52.93/53.29 (step @p48 :rule exists-elim :args ((= @t8 @t62))) % 52.93/53.29 (step @p49 :rule trans :premises (@p48 @p47)) % 52.93/53.29 (step @p50 :rule cong :premises (@p49 @p39) :args (@t9)) % 52.93/53.29 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 52.93/53.29 (step @p52 :rule trans :premises (@p51 @p38)) % 52.93/53.29 (step @p53 :rule cong :premises (@p52) :args (@t13)) % 52.93/53.29 (step @p54 :rule trans :premises (@p53 @p3)) % 52.93/53.29 (step @p55 :rule bool-impl-elim :args (@t67 @t72)) % 52.93/53.29 (step @p56 :rule cong :premises (@p55) :args ((forall @t40 (=> @t67 @t72)))) % 52.93/53.29 (step @p57 :rule exists-elim :args ((= (exists @t27 @t71) @t72))) % 52.93/53.29 (step @p58 :rule refl :args ((_ @t18 @t15 @t17 @t14))) % 52.93/53.29 (step @p59 :rule refl :args (@t14)) % 52.93/53.29 (step @p60 :rule refl :args (@t68)) % 52.93/53.29 (step @p61 :rule refl :args (@t15)) % 52.93/53.29 (step @p62 :rule cong :premises (@p61 @p60 @p59) :args (@t69)) % 52.93/53.29 (step @p63 :rule trans :premises (@p62 @p58)) % 52.93/53.29 (step @p64 :rule refl :args (@t19)) % 52.93/53.29 (step @p65 :rule ho_cong :premises (@p64 @p60)) % 52.93/53.29 (step @p66 :rule ho_cong :premises (@p65 @p59)) % 52.93/53.29 (step @p67 :rule cong :premises (@p66 @p63) :args ((= (_ (_ @t19 @t68) @t14) @t69))) % 52.93/53.29 (step @p68 :rule symm :premises (@p67)) % 52.93/53.29 (step @p69 :rule refl :args (@t20)) % 52.93/53.29 (step @p70 :rule eq_resolve :premises (@p69 @p68)) % 52.93/53.29 (step @p71 :rule refl :args (@t17)) % 52.93/53.29 (step @p72 :rule cong :premises (@p71 @p60) :args ((= @t17 @t68))) % 52.93/53.29 (step @p73 :rule symm :premises (@p72)) % 52.93/53.29 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 52.93/53.29 (step @p75 :rule ho_cong :premises (@p64 @p74)) % 52.93/53.29 (step @p76 :rule ho_cong :premises (@p75 @p59)) % 52.93/53.29 (step @p77 :rule trans :premises (@p76 @p70)) % 52.93/53.29 (step @p78 :rule refl :args ((_ @t21 @t15 @t17 @t14))) % 52.93/53.29 (step @p79 :rule cong :premises (@p61 @p60 @p59) :args (@t70)) % 52.93/53.29 (step @p80 :rule trans :premises (@p79 @p78)) % 52.93/53.29 (step @p81 :rule refl :args (@t22)) % 52.93/53.29 (step @p82 :rule ho_cong :premises (@p81 @p60)) % 52.93/53.29 (step @p83 :rule ho_cong :premises (@p82 @p59)) % 52.93/53.29 (step @p84 :rule cong :premises (@p83 @p80) :args ((= (_ (_ @t22 @t68) @t14) @t70))) % 52.93/53.29 (step @p85 :rule symm :premises (@p84)) % 52.93/53.29 (step @p86 :rule refl :args (@t23)) % 52.93/53.29 (step @p87 :rule eq_resolve :premises (@p86 @p85)) % 52.93/53.29 (step @p88 :rule ho_cong :premises (@p81 @p74)) % 52.93/53.29 (step @p89 :rule ho_cong :premises (@p88 @p59)) % 52.93/53.29 (step @p90 :rule trans :premises (@p89 @p87)) % 0.18/53.31 (step @p91 :rule nary_cong :premises (@p90 @p77) :args (@t24)) % 0.18/53.31 (step @p92 :rule cong :premises (@p91) :args (@t26)) % 0.18/53.31 (step @p93 :rule cong :premises (@p92) :args (@t28)) % 0.18/53.31 (step @p94 :rule trans :premises (@p93 @p57)) % 0.18/53.31 (step @p95 :rule exists-elim :args ((= (exists @t35 @t65) @t66))) % 0.18/53.31 (step @p96 :rule refl :args (@t63)) % 0.18/53.31 (step @p97 :rule refl :args (@t30)) % 0.18/53.31 (step @p98 :rule cong :premises (@p97 @p96) :args ((= @t30 @t63))) % 0.18/53.31 (step @p99 :rule symm :premises (@p98)) % 0.18/53.31 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.18/53.31 (step @p101 :rule refl :args (@t64)) % 0.18/53.31 (step @p102 :rule refl :args (@t31)) % 0.18/53.31 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t31 @t64))) % 0.18/53.31 (step @p104 :rule symm :premises (@p103)) % 0.18/53.31 (step @p105 :rule eq_resolve :premises (@p102 @p104)) % 0.18/53.31 (step @p106 :rule nary_cong :premises (@p105 @p100) :args (@t32)) % 0.18/53.31 (step @p107 :rule cong :premises (@p106) :args (@t34)) % 0.18/53.31 (step @p108 :rule cong :premises (@p107) :args (@t36)) % 0.18/53.31 (step @p109 :rule trans :premises (@p108 @p95)) % 0.18/53.31 (step @p110 :rule cong :premises (@p109) :args (@t38)) % 0.18/53.31 (step @p111 :rule cong :premises (@p110 @p94) :args (@t39)) % 0.18/53.31 (step @p112 :rule cong :premises (@p111) :args (@t41)) % 0.18/53.31 (step @p113 :rule trans :premises (@p112 @p56)) % 0.18/53.31 (step @p114 :rule cong :premises (@p113 @p54) :args (@t42)) % 0.18/53.31 (step @p115 :rule cong :premises (@p114) :args (@t43)) % 0.18/53.31 (step @p116 :rule eq_resolve :premises (@p1 @p115)) % 0.18/53.31 (step @p117 :rule not_implies_elim2 :premises (@p116)) % 0.18/53.31 (step @p118 :rule not_not_elim :premises (@p117)) % 0.18/53.31 (step @p119 :rule beta-reduce :args ((= @t79 @t74))) % 0.18/53.31 (step @p120 :rule cong :premises (@p119) :args (@t80)) % 0.18/53.31 (step @p121 :rule refl :args (@t47)) % 0.18/53.31 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t81)) % 0.18/53.31 (step @p123 :rule cong :premises (@p122) :args (@t82)) % 0.18/53.31 (step @p124 :rule cong :premises (@p123) :args (@t83)) % 0.18/53.31 (step @p125 :rule refl :args (@t51)) % 0.18/53.31 (step @p126 :rule cong :premises (@p125 @p124) :args ((=> @t51 @t83))) % 0.18/53.31 (assume-push @p156 @t51) % 0.18/53.31 (step @p128 :rule instantiate :premises (@p118) :args ((@list @t78))) % 0.18/53.31 (step-pop @p157 :rule scope :premises (@p128)) % 0.18/53.31 (step @p129 :rule process_scope :premises (@p157) :args (@t83)) % 0.18/53.31 (step @p131 :rule eq_resolve :premises (@p129 @p126)) % 0.18/53.31 (step @p132 :rule implies_elim :premises (@p131)) % 0.18/53.31 (step @p133 :rule chain_m_resolution :premises (@p132 @p118) :args ((not @t84) (@list false) (@list @t51))) % 0.18/53.31 (step @p134 :rule skolemize :premises (@p133)) % 0.18/53.31 (step @p135 :rule bool-double-not-elim :args (@t87)) % 0.18/53.31 (step @p136 :rule refl :args (@t90)) % 0.18/53.31 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or @t90 (not @t89)))) % 0.18/53.31 (step @p138 :rule cnf_or_neg :args (@t90 0)) % 0.18/53.31 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 0.18/53.31 (step @p140 :rule reordering :premises (@p139) :args ((or @t87 @t90))) % 0.18/53.31 (step @p141 :rule chain_m_resolution :premises (@p140 @p134) :args (@t87 @t91 @t92)) % 0.18/53.31 ; WARNING: add trust step for TRUST % 0.18/53.31 ; trust TRUST THEORY_LEMMA % 0.18/53.31 (step @p142 :rule trust :premises () :args ((forall @t77 (or (forall @t94 (not (_ @t75 @t93))) (_ @t75 @t76))))) % 0.18/53.31 (step @p143 :rule instantiate :premises (@p142) :args ((@list @t86))) % 0.18/53.31 (step @p144 :rule cnf_or_neg :args (@t90 1)) % 0.18/53.31 (step @p145 :rule chain_m_resolution :premises (@p144 @p134) :args ((not @t88) @t91 @t92)) % 0.18/53.31 (step @p146 :rule cnf_or_pos :args (@t96)) % 0.18/53.31 (step @p147 :rule reordering :premises (@p146) :args ((or @t88 @t95 (not @t96)))) % 0.18/53.31 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p143) :args (@t95 (@list true false) (@list @t88 @t96))) % 0.18/53.31 (assume-push @p158 @t95) % 0.18/53.31 (step @p150 :rule instantiate :premises (@p148) :args ((@list @t85))) % 0.18/53.31 (step-pop @p159 :rule scope :premises (@p150)) % 0.18/53.31 (step @p151 :rule process_scope :premises (@p159) :args (@t89)) % 0.18/53.31 (step @p153 :rule implies_elim :premises (@p151)) % 0.18/53.31 (step @p154 :rule reordering :premises (@p153) :args ((or @t89 (not @t95)))) % 0.18/53.31 (step @p155 false :rule chain_m_resolution :premises (@p154 @p148 @p141) :args (false (@list false false) (@list @t95 @t87))) % 0.18/53.31 ) % 0.18/53.31 % SZS output end Proof % 0.18/53.31 % cvc5 exiting %------------------------------------------------------------------------------