%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL741^5 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n031.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 32.31s 32.67s % Output : Proof 32.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL741^5 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.37 % Computer : n031.cluster.edu % 0.09/0.37 % Model : x86_64 x86_64 % 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.37 % Memory : 8046.5625MB % 0.09/0.37 % OS : Linux 6.8.0-71-generic % 0.09/0.37 % CPULimit : 300 % 0.09/0.37 % WCLimit : 300 % 0.09/0.37 % DateTime : Sat Sep 5 12:14:10 UTC 2026 % 0.09/0.37 % CPUTime : % 0.09/0.44 %----Proving TH0 % 32.31/32.67 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 32.31/32.67 % SZS status Theorem % 32.31/32.67 % SZS output start Proof % 32.31/32.67 ( % 32.31/32.67 (declare-sort tptp.b 0) % 32.31/32.67 (define @t1 () (@var "Xp" (-> tptp.b Bool))) % 32.31/32.67 (define @t2 () (@var "Xj" (-> (-> tptp.b Bool) tptp.b))) % 32.31/32.67 (define @t3 () (_ @t2 @t1)) % 32.31/32.67 (define @t4 () (_ @t1 @t3)) % 32.31/32.67 (define @t5 () (@var "Xz" tptp.b)) % 32.31/32.67 (define @t6 () (_ @t1 @t5)) % 32.31/32.67 (define @t7 () (@list @t5)) % 32.31/32.67 (define @t8 () (exists @t7 @t6)) % 32.31/32.67 (define @t9 () (=> @t8 @t4)) % 32.31/32.67 (define @t10 () (@list @t1)) % 32.31/32.67 (define @t11 () (forall @t10 @t9)) % 32.31/32.67 (define @t12 () (@list @t2)) % 32.31/32.67 (define @t13 () (exists @t12 @t11)) % 32.31/32.67 (define @t14 () (@var "Xw_11" tptp.b)) % 32.31/32.67 (define @t15 () (@var "Xx" (-> tptp.b Bool))) % 32.31/32.67 (define @t16 () (@var "Xf" (-> (-> tptp.b Bool) tptp.b))) % 32.31/32.67 (define @t17 () (_ @t16 @t15)) % 32.31/32.67 (define @t18 () (@var "Xr_28" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 32.31/32.67 (define @t19 () (_ @t18 @t15)) % 32.31/32.67 (define @t20 () (_ (_ @t19 @t17) @t14)) % 32.31/32.67 (define @t21 () (@var "Xr_27" (-> (-> tptp.b Bool) tptp.b tptp.b Bool))) % 32.31/32.67 (define @t22 () (_ @t21 @t15)) % 32.31/32.67 (define @t23 () (_ (_ @t22 @t17) @t14)) % 32.31/32.67 (define @t24 () (or @t23 @t20)) % 32.31/32.67 (define @t25 () (@list @t15 @t14)) % 32.31/32.67 (define @t26 () (forall @t25 @t24)) % 32.31/32.67 (define @t27 () (@list @t16)) % 32.31/32.67 (define @t28 () (exists @t27 @t26)) % 32.31/32.67 (define @t29 () (@var "Xy" tptp.b)) % 32.31/32.67 (define @t30 () (_ (_ @t19 @t29) @t14)) % 32.31/32.67 (define @t31 () (_ (_ @t22 @t29) @t14)) % 32.31/32.67 (define @t32 () (or @t31 @t30)) % 32.31/32.67 (define @t33 () (@list @t14)) % 32.31/32.67 (define @t34 () (forall @t33 @t32)) % 32.31/32.67 (define @t35 () (@list @t29)) % 32.31/32.67 (define @t36 () (exists @t35 @t34)) % 32.31/32.67 (define @t37 () (@list @t15)) % 32.31/32.67 (define @t38 () (forall @t37 @t36)) % 32.31/32.67 (define @t39 () (=> @t38 @t28)) % 32.31/32.67 (define @t40 () (@list (@var "Xr" (-> (-> tptp.b Bool) tptp.b Bool)) @t21 @t18)) % 32.31/32.67 (define @t41 () (forall @t40 @t39)) % 32.31/32.67 (define @t42 () (=> @t41 @t13)) % 32.31/32.67 (define @t43 () (not @t42)) % 32.31/32.67 (define @t44 () (_ @t2 @t1)) % 32.31/32.67 (define @t45 () (_ @t1 @t44)) % 32.31/32.67 (define @t46 () (@var "BOUND_VARIABLE_7505" tptp.b)) % 32.31/32.67 (define @t47 () (not (_ @t1 @t46))) % 32.31/32.67 (define @t48 () (or @t47 @t45)) % 32.31/32.67 (define @t49 () (@list @t1 @t46)) % 32.31/32.67 (define @t50 () (forall @t49 @t48)) % 32.31/32.67 (define @t51 () (forall @t12 (not @t50))) % 32.31/32.67 (define @t52 () (@list @t46)) % 32.31/32.67 (define @t53 () (forall @t52 @t48)) % 32.31/32.67 (define @t54 () (forall @t52 @t47)) % 32.31/32.67 (define @t55 () (or @t54 @t45)) % 32.31/32.67 (define @t56 () (_ @t1 @t5)) % 32.31/32.67 (define @t57 () (forall @t7 (not @t56))) % 32.31/32.67 (define @t58 () (or @t57 @t4)) % 32.31/32.67 (define @t59 () (not @t57)) % 32.31/32.67 (define @t60 () (not @t6)) % 32.31/32.67 (define @t61 () (forall @t7 @t60)) % 32.31/32.67 (define @t62 () (not @t61)) % 32.31/32.67 (define @t63 () (_ @t16 @t15)) % 32.31/32.67 (define @t64 () (_ @t18 @t15 @t63 @t14)) % 32.31/32.67 (define @t65 () (_ @t21 @t15 @t63 @t14)) % 32.31/32.67 (define @t66 () (forall @t25 (or @t65 @t64))) % 32.31/32.67 (define @t67 () (not (forall @t27 (not @t66)))) % 32.31/32.67 (define @t68 () (_ @t18 @t15 @t29 @t14)) % 32.31/32.67 (define @t69 () (_ @t21 @t15 @t29 @t14)) % 32.31/32.67 (define @t70 () (forall @t33 (or @t69 @t68))) % 32.31/32.67 (define @t71 () (not (forall @t35 (not @t70)))) % 32.31/32.67 (define @t72 () (forall @t37 @t71)) % 32.31/32.67 (define @t73 () (or (not @t72) @t67)) % 32.31/32.67 (define @t74 () (@const 0 (-> (-> tptp.b Bool) tptp.b))) % 32.31/32.67 (define @t75 () (_ @t74 @t1)) % 32.31/32.67 (define @t76 () (@var "BOUND_VARIABLE_741484" (-> tptp.b Bool))) % 32.31/32.67 (define @t77 () (_ @t74 @t76)) % 32.31/32.67 (define @t78 () (@list @t76)) % 32.31/32.67 (define @t79 () (lambda @t78 @t77)) % 32.31/32.67 (define @t80 () (_ @t79 @t1)) % 32.31/32.67 (define @t81 () (_ @t1 @t80)) % 32.31/32.67 (define @t82 () (or @t47 @t81)) % 32.31/32.67 (define @t83 () (forall @t49 @t82)) % 32.31/32.67 (define @t84 () (not @t83)) % 32.31/32.67 (define @t85 () (forall @t49 (or @t47 (_ @t1 @t75)))) % 32.31/32.67 (define @t86 () (@quantifiers_skolemize @t85 1)) % 32.31/32.67 (define @t87 () (@quantifiers_skolemize @t85 0)) % 32.31/32.67 (define @t88 () (_ @t87 @t86)) % 32.31/32.67 (define @t89 () (_ @t87 (_ @t74 @t87))) % 32.31/32.67 (define @t90 () (not @t88)) % 32.31/32.67 (define @t91 () (or @t90 @t89)) % 32.31/32.67 (define @t92 () (@list true)) % 32.31/32.67 (define @t93 () (@list @t91)) % 32.31/32.67 (define @t94 () (@var "x" tptp.b)) % 32.31/32.67 (define @t95 () (@list @t94)) % 32.31/32.67 (define @t96 () (forall @t95 (not (_ @t87 @t94)))) % 32.31/32.67 (define @t97 () (or @t96 @t89)) % 32.31/32.67 (assume @p1 @t43) % 32.31/32.67 (assume @p2 true) % 32.31/32.67 (step @p3 :rule exists-elim :args ((= (exists @t12 @t50) (not @t51)))) % 32.31/32.67 (step @p4 :rule quant-merge-prenex :args ((= (forall @t10 @t53) @t50))) % 32.31/32.67 (step @p5 :rule refl :args (@t45)) % 32.31/32.67 (step @p6 :rule alpha_equiv :args (@t54 (@list @t46) (@list @t5))) % 32.31/32.67 (step @p7 :rule nary_cong :premises (@p6 @p5) :args (@t55)) % 32.31/32.67 (step @p8 :rule quant-miniscope-or :args ((= @t53 @t55))) % 32.31/32.67 (step @p9 :rule trans :premises (@p8 @p7)) % 32.31/32.67 (step @p10 :rule symm :premises (@p9)) % 32.31/32.67 (step @p11 :rule cong :premises (@p10) :args ((forall @t10 (or @t57 @t45)))) % 32.31/32.67 (step @p12 :rule trans :premises (@p11 @p4)) % 32.31/32.67 (step @p13 :rule refl :args ((_ @t1 @t3))) % 32.31/32.67 (step @p14 :rule refl :args (@t44)) % 32.31/32.67 (step @p15 :rule cong :premises (@p14) :args (@t45)) % 32.31/32.67 (step @p16 :rule trans :premises (@p15 @p13)) % 32.31/32.67 (step @p17 :rule refl :args (@t1)) % 32.31/32.67 (step @p18 :rule ho_cong :premises (@p17 @p14)) % 32.31/32.67 (step @p19 :rule cong :premises (@p18 @p16) :args ((= (_ @t1 @t44) @t45))) % 32.31/32.67 (step @p20 :rule symm :premises (@p19)) % 32.31/32.67 (step @p21 :rule refl :args (@t4)) % 32.31/32.67 (step @p22 :rule eq_resolve :premises (@p21 @p20)) % 32.31/32.67 (step @p23 :rule refl :args (@t3)) % 32.31/32.67 (step @p24 :rule cong :premises (@p23 @p14) :args ((= @t3 @t44))) % 32.31/32.67 (step @p25 :rule symm :premises (@p24)) % 32.31/32.67 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 32.31/32.67 (step @p27 :rule ho_cong :premises (@p17 @p26)) % 32.31/32.67 (step @p28 :rule trans :premises (@p27 @p22)) % 32.31/32.67 (step @p29 :rule refl :args (@t57)) % 32.31/32.67 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t58)) % 32.31/32.67 (step @p31 :rule cong :premises (@p30) :args ((forall @t10 @t58))) % 32.31/32.67 (step @p32 :rule trans :premises (@p31 @p12)) % 32.31/32.67 (step @p33 :rule bool-double-not-elim :args (@t57)) % 32.31/32.67 (step @p34 :rule nary_cong :premises (@p33 @p21) :args ((or (not @t59) @t4))) % 32.31/32.67 (step @p35 :rule bool-impl-elim :args (@t59 @t4)) % 32.31/32.67 (step @p36 :rule trans :premises (@p35 @p34)) % 32.31/32.67 (step @p37 :rule cong :premises (@p36) :args ((forall @t10 (=> @t59 @t4)))) % 32.31/32.67 (step @p38 :rule trans :premises (@p37 @p32)) % 32.31/32.67 (step @p39 :rule refl :args (@t4)) % 32.31/32.67 (step @p40 :rule refl :args (@t56)) % 32.31/32.67 (step @p41 :rule refl :args (@t6)) % 32.31/32.67 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t6 @t56))) % 32.31/32.67 (step @p43 :rule symm :premises (@p42)) % 32.31/32.67 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 32.31/32.67 (step @p45 :rule cong :premises (@p44) :args (@t60)) % 32.31/32.67 (step @p46 :rule cong :premises (@p45) :args (@t61)) % 32.31/32.67 (step @p47 :rule cong :premises (@p46) :args (@t62)) % 32.31/32.67 (step @p48 :rule exists-elim :args ((= @t8 @t62))) % 32.31/32.67 (step @p49 :rule trans :premises (@p48 @p47)) % 32.31/32.67 (step @p50 :rule cong :premises (@p49 @p39) :args (@t9)) % 32.31/32.67 (step @p51 :rule cong :premises (@p50) :args (@t11)) % 32.31/32.67 (step @p52 :rule trans :premises (@p51 @p38)) % 32.31/32.67 (step @p53 :rule cong :premises (@p52) :args (@t13)) % 32.31/32.67 (step @p54 :rule trans :premises (@p53 @p3)) % 32.31/32.67 (step @p55 :rule quant-unused-vars :args ((= (forall @t40 @t73) (forall (@list @t21 @t18) @t73)))) % 32.31/32.67 (step @p56 :rule bool-impl-elim :args (@t72 @t67)) % 32.31/32.67 (step @p57 :rule cong :premises (@p56) :args ((forall @t40 (=> @t72 @t67)))) % 32.31/32.67 (step @p58 :rule trans :premises (@p57 @p55)) % 32.31/32.67 (step @p59 :rule exists-elim :args ((= (exists @t27 @t66) @t67))) % 32.31/32.67 (step @p60 :rule refl :args ((_ @t18 @t15 @t17 @t14))) % 32.31/32.67 (step @p61 :rule refl :args (@t14)) % 32.31/32.67 (step @p62 :rule refl :args (@t63)) % 32.31/32.67 (step @p63 :rule refl :args (@t15)) % 32.31/32.67 (step @p64 :rule cong :premises (@p63 @p62 @p61) :args (@t64)) % 32.31/32.67 (step @p65 :rule trans :premises (@p64 @p60)) % 32.31/32.67 (step @p66 :rule refl :args (@t19)) % 32.31/32.67 (step @p67 :rule ho_cong :premises (@p66 @p62)) % 32.31/32.67 (step @p68 :rule ho_cong :premises (@p67 @p61)) % 32.31/32.67 (step @p69 :rule cong :premises (@p68 @p65) :args ((= (_ (_ @t19 @t63) @t14) @t64))) % 32.31/32.67 (step @p70 :rule symm :premises (@p69)) % 32.31/32.67 (step @p71 :rule refl :args (@t20)) % 32.31/32.67 (step @p72 :rule eq_resolve :premises (@p71 @p70)) % 32.31/32.67 (step @p73 :rule refl :args (@t17)) % 32.31/32.67 (step @p74 :rule cong :premises (@p73 @p62) :args ((= @t17 @t63))) % 32.31/32.67 (step @p75 :rule symm :premises (@p74)) % 32.31/32.67 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 32.31/32.67 (step @p77 :rule ho_cong :premises (@p66 @p76)) % 32.31/32.67 (step @p78 :rule ho_cong :premises (@p77 @p61)) % 32.31/32.67 (step @p79 :rule trans :premises (@p78 @p72)) % 32.31/32.67 (step @p80 :rule refl :args ((_ @t21 @t15 @t17 @t14))) % 32.31/32.67 (step @p81 :rule cong :premises (@p63 @p62 @p61) :args (@t65)) % 32.31/32.67 (step @p82 :rule trans :premises (@p81 @p80)) % 32.31/32.67 (step @p83 :rule refl :args (@t22)) % 32.31/32.67 (step @p84 :rule ho_cong :premises (@p83 @p62)) % 32.31/32.67 (step @p85 :rule ho_cong :premises (@p84 @p61)) % 32.31/32.67 (step @p86 :rule cong :premises (@p85 @p82) :args ((= (_ (_ @t22 @t63) @t14) @t65))) % 32.31/32.67 (step @p87 :rule symm :premises (@p86)) % 32.31/32.67 (step @p88 :rule refl :args (@t23)) % 32.31/32.67 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 32.31/32.67 (step @p90 :rule ho_cong :premises (@p83 @p76)) % 32.31/32.67 (step @p91 :rule ho_cong :premises (@p90 @p61)) % 32.31/32.67 (step @p92 :rule trans :premises (@p91 @p89)) % 32.31/32.67 (step @p93 :rule nary_cong :premises (@p92 @p79) :args (@t24)) % 32.31/32.67 (step @p94 :rule cong :premises (@p93) :args (@t26)) % 32.31/32.67 (step @p95 :rule cong :premises (@p94) :args (@t28)) % 32.31/32.67 (step @p96 :rule trans :premises (@p95 @p59)) % 32.31/32.67 (step @p97 :rule exists-elim :args ((= (exists @t35 @t70) @t71))) % 32.31/32.67 (step @p98 :rule refl :args (@t68)) % 32.31/32.67 (step @p99 :rule refl :args (@t30)) % 32.31/32.67 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t30 @t68))) % 32.31/32.67 (step @p101 :rule symm :premises (@p100)) % 32.31/32.67 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 32.31/32.67 (step @p103 :rule refl :args (@t69)) % 32.31/32.67 (step @p104 :rule refl :args (@t31)) % 32.31/32.67 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t31 @t69))) % 32.31/32.67 (step @p106 :rule symm :premises (@p105)) % 32.31/32.67 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 32.31/32.67 (step @p108 :rule nary_cong :premises (@p107 @p102) :args (@t32)) % 32.31/32.67 (step @p109 :rule cong :premises (@p108) :args (@t34)) % 32.31/32.67 (step @p110 :rule cong :premises (@p109) :args (@t36)) % 32.31/32.67 (step @p111 :rule trans :premises (@p110 @p97)) % 32.31/32.67 (step @p112 :rule cong :premises (@p111) :args (@t38)) % 32.31/32.67 (step @p113 :rule cong :premises (@p112 @p96) :args (@t39)) % 32.31/32.67 (step @p114 :rule cong :premises (@p113) :args (@t41)) % 32.31/32.67 (step @p115 :rule trans :premises (@p114 @p58)) % 32.31/32.67 (step @p116 :rule cong :premises (@p115 @p54) :args (@t42)) % 32.31/32.67 (step @p117 :rule cong :premises (@p116) :args (@t43)) % 32.31/32.67 (step @p118 :rule eq_resolve :premises (@p1 @p117)) % 32.31/32.67 (step @p119 :rule not_implies_elim2 :premises (@p118)) % 32.31/32.67 (step @p120 :rule not_not_elim :premises (@p119)) % 32.31/32.67 (step @p121 :rule beta-reduce :args ((= @t80 @t75))) % 32.31/32.67 (step @p122 :rule cong :premises (@p121) :args (@t81)) % 32.31/32.67 (step @p123 :rule refl :args (@t47)) % 32.31/32.67 (step @p124 :rule nary_cong :premises (@p123 @p122) :args (@t82)) % 32.31/32.67 (step @p125 :rule cong :premises (@p124) :args (@t83)) % 32.31/32.67 (step @p126 :rule cong :premises (@p125) :args (@t84)) % 32.31/32.67 (step @p127 :rule refl :args (@t51)) % 32.31/32.67 (step @p128 :rule cong :premises (@p127 @p126) :args ((=> @t51 @t84))) % 32.31/32.67 (assume-push @p158 @t51) % 32.31/32.67 (step @p130 :rule instantiate :premises (@p120) :args ((@list @t79))) % 32.31/32.67 (step-pop @p159 :rule scope :premises (@p130)) % 32.31/32.67 (step @p131 :rule process_scope :premises (@p159) :args (@t84)) % 32.31/32.67 (step @p133 :rule eq_resolve :premises (@p131 @p128)) % 32.31/32.67 (step @p134 :rule implies_elim :premises (@p133)) % 32.31/32.67 (step @p135 :rule chain_m_resolution :premises (@p134 @p120) :args ((not @t85) (@list false) (@list @t51))) % 32.31/32.67 (step @p136 :rule skolemize :premises (@p135)) % 32.31/32.67 (step @p137 :rule bool-double-not-elim :args (@t88)) % 32.31/32.67 (step @p138 :rule refl :args (@t91)) % 32.31/32.67 (step @p139 :rule nary_cong :premises (@p138 @p137) :args ((or @t91 (not @t90)))) % 32.31/32.67 (step @p140 :rule cnf_or_neg :args (@t91 0)) % 32.31/32.67 (step @p141 :rule eq_resolve :premises (@p140 @p139)) % 32.31/32.67 (step @p142 :rule reordering :premises (@p141) :args ((or @t88 @t91))) % 32.31/32.67 (step @p143 :rule chain_m_resolution :premises (@p142 @p136) :args (@t88 @t92 @t93)) % 32.31/32.67 ; WARNING: add trust step for TRUST % 32.31/32.67 ; trust TRUST THEORY_LEMMA % 32.31/32.67 (step @p144 :rule trust :premises () :args ((forall @t78 (or (forall @t95 (not (_ @t76 @t94))) (_ @t76 @t77))))) % 32.31/32.67 (step @p145 :rule instantiate :premises (@p144) :args ((@list @t87))) % 32.31/32.67 (step @p146 :rule cnf_or_neg :args (@t91 1)) % 32.31/32.67 (step @p147 :rule chain_m_resolution :premises (@p146 @p136) :args ((not @t89) @t92 @t93)) % 32.31/32.67 (step @p148 :rule cnf_or_pos :args (@t97)) % 32.31/32.67 (step @p149 :rule reordering :premises (@p148) :args ((or @t89 @t96 (not @t97)))) % 32.31/32.67 (step @p150 :rule chain_m_resolution :premises (@p149 @p147 @p145) :args (@t96 (@list true false) (@list @t89 @t97))) % 32.31/32.67 (assume-push @p160 @t96) % 32.31/32.67 (step @p152 :rule instantiate :premises (@p150) :args ((@list @t86))) % 32.31/32.67 (step-pop @p161 :rule scope :premises (@p152)) % 32.31/32.67 (step @p153 :rule process_scope :premises (@p161) :args (@t90)) % 32.31/32.67 (step @p155 :rule implies_elim :premises (@p153)) % 32.31/32.67 (step @p156 :rule reordering :premises (@p155) :args ((or @t90 (not @t96)))) % 32.31/32.67 (step @p157 false :rule chain_m_resolution :premises (@p156 @p150 @p143) :args (false (@list false false) (@list @t96 @t88))) % 32.31/32.68 ) % 32.31/32.68 % SZS output end Proof % 32.31/32.68 % cvc5 exiting %------------------------------------------------------------------------------