%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL740^5 : 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 : n011.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 11:23:44 AM UTC 2026 % Result : Theorem 121.31s 121.97s % Output : Proof 121.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL740^5 : 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 : n011.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 : Fri Sep 4 14:39:58 UTC 2026 % 0.09/0.36 % CPUTime : % 0.13/0.42 %----Proving TH0 % 121.31/121.97 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 121.31/121.97 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 121.31/121.97 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 121.31/121.97 % SZS status Theorem % 121.31/121.97 % SZS output start Proof % 121.31/121.97 ( % 121.31/121.97 (declare-sort tptp.b 0) % 121.31/121.97 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 121.31/121.97 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 121.31/121.97 (define @t3 () (_ @t2 @t1)) % 121.31/121.97 (define @t4 () (_ @t1 @t3)) % 121.31/121.97 (define @t5 () (@var "Xz" tptp.b)) % 121.31/121.97 (define @t6 () (_ @t1 @t5)) % 121.31/121.97 (define @t7 () (@list @t5)) % 121.31/121.97 (define @t8 () (exists @t7 @t6)) % 121.31/121.97 (define @t9 () (=> @t8 @t4)) % 121.31/121.97 (define @t10 () (@list @t1)) % 121.31/121.97 (define @t11 () (forall @t10 @t9)) % 121.31/121.97 (define @t12 () (@list @t2)) % 121.31/121.97 (define @t13 () (exists @t12 @t11)) % 121.31/121.97 (define @t14 () (@var "Xw_4" tptp.b)) % 121.31/121.97 (define @t15 () (@var "Xy" tptp.b)) % 121.31/121.97 (define @t16 () (@var "Xx" (-> tptp.b Bool))) % 121.31/121.97 (define @t17 () (@var "Xr_13" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 121.31/121.97 (define @t18 () (_ @t17 @t16)) % 121.31/121.97 (define @t19 () (_ (_ @t18 @t15) @t14)) % 121.31/121.97 (define @t20 () (@var "Xr_12" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 121.31/121.97 (define @t21 () (_ @t20 @t16)) % 121.31/121.97 (define @t22 () (_ (_ @t21 @t15) @t14)) % 121.31/121.97 (define @t23 () (or @t22 @t19)) % 121.31/121.97 (define @t24 () (@list @t14)) % 121.31/121.97 (define @t25 () (forall @t24 @t23)) % 121.31/121.97 (define @t26 () (@list @t15)) % 121.31/121.97 (define @t27 () (exists @t26 @t25)) % 121.31/121.97 (define @t28 () (forall (@list @t16) @t27)) % 121.31/121.97 (define @t29 () (not @t28)) % 121.31/121.97 (define @t30 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 121.31/121.97 (define @t31 () (_ @t30 @t16)) % 121.31/121.97 (define @t32 () (_ (_ @t18 @t31) @t14)) % 121.31/121.97 (define @t33 () (_ (_ @t21 @t31) @t14)) % 121.31/121.97 (define @t34 () (or @t33 @t32)) % 121.31/121.97 (define @t35 () (@list @t16 @t14)) % 121.31/121.97 (define @t36 () (forall @t35 @t34)) % 121.31/121.97 (define @t37 () (@list @t30)) % 121.31/121.97 (define @t38 () (exists @t37 @t36)) % 121.31/121.97 (define @t39 () (or @t38 @t29)) % 121.31/121.97 (define @t40 () (forall (@list @t20 @t17) @t39)) % 121.31/121.97 (define @t41 () (=> @t40 @t13)) % 121.31/121.97 (define @t42 () (not @t41)) % 121.31/121.97 (define @t43 () (_ @t2 @t1)) % 121.31/121.97 (define @t44 () (_ @t1 @t43)) % 121.31/121.97 (define @t45 () (@var "BOUND_VARIABLE_7500" tptp.b)) % 121.31/121.97 (define @t46 () (not (_ @t1 @t45))) % 121.31/121.97 (define @t47 () (or @t46 @t44)) % 121.31/121.97 (define @t48 () (@list @t1 @t45)) % 121.31/121.97 (define @t49 () (forall @t48 @t47)) % 121.31/121.97 (define @t50 () (forall @t12 (not @t49))) % 121.31/121.97 (define @t51 () (@list @t45)) % 121.31/121.97 (define @t52 () (forall @t51 @t47)) % 121.31/121.97 (define @t53 () (forall @t51 @t46)) % 121.31/121.97 (define @t54 () (or @t53 @t44)) % 121.31/121.97 (define @t55 () (_ @t1 @t5)) % 121.31/121.97 (define @t56 () (forall @t7 (not @t55))) % 121.31/121.97 (define @t57 () (or @t56 @t4)) % 121.31/121.97 (define @t58 () (not @t56)) % 121.31/121.97 (define @t59 () (not @t6)) % 121.31/121.97 (define @t60 () (forall @t7 @t59)) % 121.31/121.97 (define @t61 () (not @t60)) % 121.31/121.97 (define @t62 () (_ @t17 @t16 @t15 @t14)) % 121.31/121.97 (define @t63 () (_ @t20 @t16 @t15 @t14)) % 121.31/121.97 (define @t64 () (forall @t24 (or @t63 @t62))) % 121.31/121.97 (define @t65 () (_ @t30 @t16)) % 121.31/121.97 (define @t66 () (_ @t17 @t16 @t65 @t14)) % 121.31/121.97 (define @t67 () (_ @t20 @t16 @t65 @t14)) % 121.31/121.97 (define @t68 () (forall @t35 (or @t67 @t66))) % 121.31/121.97 (define @t69 () (@const 0 (-> (-> tptp.b Bool) tptp.b))) % 121.31/121.97 (define @t70 () (_ @t69 @t1)) % 121.31/121.97 (define @t71 () (@var "BOUND_VARIABLE_23847" (-> tptp.b Bool))) % 121.31/121.97 (define @t72 () (_ @t69 @t71)) % 121.31/121.97 (define @t73 () (@list @t71)) % 121.31/121.97 (define @t74 () (lambda @t73 @t72)) % 121.31/121.97 (define @t75 () (_ @t74 @t1)) % 121.31/121.97 (define @t76 () (_ @t1 @t75)) % 121.31/121.97 (define @t77 () (or @t46 @t76)) % 121.31/121.97 (define @t78 () (forall @t48 @t77)) % 121.31/121.97 (define @t79 () (not @t78)) % 121.31/121.97 (define @t80 () (forall @t48 (or @t46 (_ @t1 @t70)))) % 121.31/121.97 (define @t81 () (@quantifiers_skolemize @t80 1)) % 121.31/121.97 (define @t82 () (@quantifiers_skolemize @t80 0)) % 121.31/121.97 (define @t83 () (_ @t82 @t81)) % 121.31/121.97 (define @t84 () (_ @t82 (_ @t69 @t82))) % 121.31/121.97 (define @t85 () (not @t83)) % 121.31/121.97 (define @t86 () (or @t85 @t84)) % 121.31/121.97 (define @t87 () (@list true)) % 121.31/121.97 (define @t88 () (@list @t86)) % 121.31/121.97 (define @t89 () (@var "x" tptp.b)) % 121.31/121.97 (define @t90 () (@list @t89)) % 121.31/121.97 (define @t91 () (forall @t90 (not (_ @t82 @t89)))) % 121.31/121.97 (define @t92 () (or @t91 @t84)) % 121.31/121.97 (assume @p1 @t42) % 121.31/121.97 (assume @p2 true) % 121.31/121.97 (step @p3 :rule exists-elim :args ((= (exists @t12 @t49) (not @t50)))) % 121.31/121.97 (step @p4 :rule quant-merge-prenex :args ((= (forall @t10 @t52) @t49))) % 121.31/121.97 (step @p5 :rule refl :args (@t44)) % 121.31/121.97 (step @p6 :rule alpha_equiv :args (@t53 (@list @t45) (@list @t5))) % 121.31/121.97 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t54)) % 121.31/121.97 (step @p8 :rule quant-miniscope-or :args ((= @t52 @t54))) % 121.31/121.97 (step @p9 :rule trans :premises (@p8 @p7)) % 121.31/121.97 (step @p10 :rule symm :premises (@p9)) % 121.31/121.97 (step @p11 :rule cong :premises (@p10) :args ((forall @t10 (or @t56 @t44)))) % 121.31/121.97 (step @p12 :rule trans :premises (@p11 @p4)) % 121.31/121.97 (step @p13 :rule refl :args ((_ @t1 @t3))) % 121.31/121.97 (step @p14 :rule refl :args (@t43)) % 121.31/121.97 (step @p15 :rule cong :premises (@p14) :args (@t44)) % 121.31/121.97 (step @p16 :rule trans :premises (@p15 @p13)) % 121.31/121.97 (step @p17 :rule refl :args (@t1)) % 121.31/121.97 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 121.31/121.97 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t43) @t44))) % 121.31/121.97 (step @p20 :rule symm :premises (@p19)) % 121.31/121.97 (step @p21 :rule refl :args (@t4)) % 121.31/121.97 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 121.31/121.97 (step @p23 :rule refl :args (@t3)) % 121.31/121.97 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t3 @t43))) % 121.31/121.97 (step @p25 :rule symm :premises (@p24)) % 121.31/121.97 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 121.31/121.97 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 121.31/121.97 (step @p28 :rule trans :premises (@p27 @p22)) % 121.31/121.97 (step @p29 :rule refl :args (@t56)) % 121.31/121.97 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t57)) % 121.31/121.97 (step @p31 :rule cong :premises (@p30) :args ((forall @t10 @t57))) % 121.31/121.97 (step @p32 :rule trans :premises (@p31 @p12)) % 121.31/121.97 (step @p33 :rule bool-double-not-elim :args (@t56)) % 121.31/121.97 (step @p34 :rule nary_cong :premises (@p33 @p21) :args ((or (not @t58) @t4))) % 121.31/121.97 (step @p35 :rule bool-impl-elim :args (@t58 @t4)) % 121.31/121.97 (step @p36 :rule trans :premises (@p35 @p34)) % 121.31/121.97 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 (=> @t58 @t4)))) % 121.31/121.97 (step @p38 :rule trans :premises (@p37 @p32)) % 121.31/121.97 (step @p39 :rule refl :args (@t4)) % 121.31/121.97 (step @p40 :rule refl :args (@t55)) % 121.31/121.97 (step @p41 :rule refl :args (@t6)) % 121.31/121.97 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t6 @t55))) % 121.31/121.97 (step @p43 :rule symm :premises (@p42)) % 121.31/121.97 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 121.31/121.97 (step @p45 :rule cong :premises (@p44) :args (@t59)) % 121.31/121.97 (step @p46 :rule cong :premises (@p45) :args (@t60)) % 121.31/121.97 (step @p47 :rule cong :premises (@p46) :args (@t61)) % 121.31/121.97 (step @p48 :rule exists-elim :args ((= @t8 @t61))) % 121.31/121.97 (step @p49 :rule trans :premises (@p48 @p47)) % 121.31/121.97 (step @p50 :rule cong :premises (@p49 @p39) :args (@t9)) % 121.31/121.97 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 121.31/121.97 (step @p52 :rule trans :premises (@p51 @p38)) % 121.31/121.97 (step @p53 :rule cong :premises (@p52) :args (@t13)) % 121.31/121.97 (step @p54 :rule trans :premises (@p53 @p3)) % 121.31/121.97 (step @p55 :rule exists-elim :args ((= (exists @t26 @t64) (not (forall @t26 (not @t64)))))) % 121.31/121.97 (step @p56 :rule refl :args (@t62)) % 121.31/121.97 (step @p57 :rule refl :args (@t19)) % 121.31/121.97 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t19 @t62))) % 121.31/121.97 (step @p59 :rule symm :premises (@p58)) % 121.31/121.97 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 121.31/121.97 (step @p61 :rule refl :args (@t63)) % 121.31/121.97 (step @p62 :rule refl :args (@t22)) % 121.31/121.97 (step @p63 :rule cong :premises (@p62 @p61) :args ((= @t22 @t63))) % 121.31/121.97 (step @p64 :rule symm :premises (@p63)) % 121.31/121.97 (step @p65 :rule eq_resolve :premises (@p62 @p64)) % 121.31/121.97 (step @p66 :rule nary_cong :premises (@p65 @p60) :args (@t23)) % 121.31/121.97 (step @p67 :rule cong :premises (@p66) :args (@t25)) % 121.31/121.97 (step @p68 :rule cong :premises (@p67) :args (@t27)) % 121.31/121.97 (step @p69 :rule trans :premises (@p68 @p55)) % 121.31/121.97 (step @p70 :rule cong :premises (@p69) :args (@t28)) % 121.31/121.97 (step @p71 :rule cong :premises (@p70) :args (@t29)) % 121.31/121.97 (step @p72 :rule exists-elim :args ((= (exists @t37 @t68) (not (forall @t37 (not @t68)))))) % 121.31/121.97 (step @p73 :rule refl :args ((_ @t17 @t16 @t31 @t14))) % 121.31/121.97 (step @p74 :rule refl :args (@t14)) % 121.31/121.97 (step @p75 :rule refl :args (@t65)) % 121.31/121.97 (step @p76 :rule refl :args (@t16)) % 121.31/121.97 (step @p77 :rule cong :premises (@p76 @p75 @p74) :args (@t66)) % 121.31/121.97 (step @p78 :rule trans :premises (@p77 @p73)) % 121.31/121.97 (step @p79 :rule refl :args (@t18)) % 121.31/121.97 (step @p80 :rule ho_cong :premises (@p79 @p75)) % 121.31/121.97 (step @p81 :rule ho_cong :premises (@p80 @p74)) % 121.31/121.97 (step @p82 :rule cong :premises (@p81 @p78) :args ((= (_ (_ @t18 @t65) @t14) @t66))) % 121.31/121.97 (step @p83 :rule symm :premises (@p82)) % 121.31/121.97 (step @p84 :rule refl :args (@t32)) % 121.31/121.97 (step @p85 :rule eq_resolve :premises (@p84 @p83)) % 121.31/121.98 (step @p86 :rule refl :args (@t31)) % 121.31/121.98 (step @p87 :rule cong :premises (@p86 @p75) :args ((= @t31 @t65))) % 121.31/121.98 (step @p88 :rule symm :premises (@p87)) % 121.31/121.98 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 121.31/121.98 (step @p90 :rule ho_cong :premises (@p79 @p89)) % 121.31/121.98 (step @p91 :rule ho_cong :premises (@p90 @p74)) % 121.31/121.98 (step @p92 :rule trans :premises (@p91 @p85)) % 121.31/121.98 (step @p93 :rule refl :args ((_ @t20 @t16 @t31 @t14))) % 121.31/121.98 (step @p94 :rule cong :premises (@p76 @p75 @p74) :args (@t67)) % 121.31/121.98 (step @p95 :rule trans :premises (@p94 @p93)) % 121.31/121.98 (step @p96 :rule refl :args (@t21)) % 121.31/121.98 (step @p97 :rule ho_cong :premises (@p96 @p75)) % 121.31/121.98 (step @p98 :rule ho_cong :premises (@p97 @p74)) % 121.31/121.98 (step @p99 :rule cong :premises (@p98 @p95) :args ((= (_ (_ @t21 @t65) @t14) @t67))) % 121.31/121.98 (step @p100 :rule symm :premises (@p99)) % 121.31/121.98 (step @p101 :rule refl :args (@t33)) % 121.31/121.98 (step @p102 :rule eq_resolve :premises (@p101 @p100)) % 121.31/121.98 (step @p103 :rule ho_cong :premises (@p96 @p89)) % 121.31/121.98 (step @p104 :rule ho_cong :premises (@p103 @p74)) % 121.31/121.98 (step @p105 :rule trans :premises (@p104 @p102)) % 121.31/121.98 (step @p106 :rule nary_cong :premises (@p105 @p92) :args (@t34)) % 121.31/121.98 (step @p107 :rule cong :premises (@p106) :args (@t36)) % 121.31/121.98 (step @p108 :rule cong :premises (@p107) :args (@t38)) % 121.31/121.98 (step @p109 :rule trans :premises (@p108 @p72)) % 121.31/121.98 (step @p110 :rule nary_cong :premises (@p109 @p71) :args (@t39)) % 121.31/121.98 (step @p111 :rule cong :premises (@p110) :args (@t40)) % 121.31/121.98 (step @p112 :rule cong :premises (@p111 @p54) :args (@t41)) % 121.31/121.98 (step @p113 :rule cong :premises (@p112) :args (@t42)) % 121.31/121.98 (step @p114 :rule eq_resolve :premises (@p1 @p113)) % 121.31/121.98 (step @p115 :rule not_implies_elim2 :premises (@p114)) % 121.31/121.98 (step @p116 :rule not_not_elim :premises (@p115)) % 121.31/121.98 (step @p117 :rule beta-reduce :args ((= @t75 @t70))) % 121.31/121.98 (step @p118 :rule cong :premises (@p117) :args (@t76)) % 121.31/121.98 (step @p119 :rule refl :args (@t46)) % 121.31/121.98 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t77)) % 121.31/121.98 (step @p121 :rule cong :premises (@p120) :args (@t78)) % 121.31/121.98 (step @p122 :rule cong :premises (@p121) :args (@t79)) % 121.31/121.98 (step @p123 :rule refl :args (@t50)) % 121.31/121.98 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t50 @t79))) % 121.31/121.98 (assume-push @p154 @t50) % 121.31/121.98 (step @p126 :rule instantiate :premises (@p116) :args ((@list @t74))) % 121.31/121.98 (step-pop @p155 :rule scope :premises (@p126)) % 121.31/121.98 (step @p127 :rule process_scope :premises (@p155) :args (@t79)) % 121.31/121.98 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 121.31/121.98 (step @p130 :rule implies_elim :premises (@p129)) % 121.31/121.98 (step @p131 :rule chain_m_resolution :premises (@p130 @p116) :args ((not @t80) (@list false) (@list @t50))) % 121.31/121.98 (step @p132 :rule skolemize :premises (@p131)) % 121.31/121.98 (step @p133 :rule bool-double-not-elim :args (@t83)) % 121.31/121.98 (step @p134 :rule refl :args (@t86)) % 121.31/121.98 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or @t86 (not @t85)))) % 121.31/121.98 (step @p136 :rule cnf_or_neg :args (@t86 0)) % 121.31/121.98 (step @p137 :rule eq_resolve :premises (@p136 @p135)) % 121.31/121.98 (step @p138 :rule reordering :premises (@p137) :args ((or @t83 @t86))) % 121.31/121.98 (step @p139 :rule chain_m_resolution :premises (@p138 @p132) :args (@t83 @t87 @t88)) % 121.31/121.98 ; WARNING: add trust step for TRUST % 121.31/121.98 ; trust TRUST THEORY_LEMMA % 121.31/121.98 (step @p140 :rule trust :premises () :args ((forall @t73 (or (forall @t90 (not (_ @t71 @t89))) (_ @t71 @t72))))) % 121.31/121.98 (step @p141 :rule instantiate :premises (@p140) :args ((@list @t82))) % 121.31/121.98 (step @p142 :rule cnf_or_neg :args (@t86 1)) % 121.31/121.98 (step @p143 :rule chain_m_resolution :premises (@p142 @p132) :args ((not @t84) @t87 @t88)) % 121.31/121.98 (step @p144 :rule cnf_or_pos :args (@t92)) % 121.31/121.98 (step @p145 :rule reordering :premises (@p144) :args ((or @t84 @t91 (not @t92)))) % 121.31/121.98 (step @p146 :rule chain_m_resolution :premises (@p145 @p143 @p141) :args (@t91 (@list true false) (@list @t84 @t92))) % 121.31/121.98 (assume-push @p156 @t91) % 121.31/121.98 (step @p148 :rule instantiate :premises (@p146) :args ((@list @t81))) % 121.31/121.98 (step-pop @p157 :rule scope :premises (@p148)) % 121.31/121.98 (step @p149 :rule process_scope :premises (@p157) :args (@t85)) % 121.31/121.98 (step @p151 :rule implies_elim :premises (@p149)) % 121.31/121.98 (step @p152 :rule reordering :premises (@p151) :args ((or @t85 (not @t91)))) % 121.31/121.98 (step @p153 false :rule chain_m_resolution :premises (@p152 @p146 @p139) :args (false (@list false false) (@list @t91 @t83))) % 121.31/121.98 ) % 121.31/121.98 % SZS output end Proof % 121.31/121.98 % cvc5 exiting %------------------------------------------------------------------------------