%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL609^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n005.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 11:23:09 AM UTC 2026 % Result : Theorem 0.19s 0.50s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL609^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.36 % Computer : n005.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 14:47:21 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.43 %----Proving TH0 % 0.19/0.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.50 % SZS status Theorem % 0.19/0.50 % SZS output start Proof % 0.19/0.50 ( % 0.19/0.50 (declare-sort $$unsorted 0) % 0.19/0.50 (declare-sort tptp.individuals 0) % 0.19/0.50 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.50 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.50 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.50 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.50 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.50 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.19/0.50 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.50 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.50 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.50 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.50 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.50 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.50 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.50 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.50 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.50 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.50 (define @t2 () (@var "X" tptp.individuals)) % 0.19/0.50 (define @t3 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.50 (define @t4 () (_ @t3 @t2)) % 0.19/0.50 (define @t5 () (lambda (@list @t2 @t1) (_ @t4 @t1))) % 0.19/0.50 (define @t6 () (@list @t2)) % 0.19/0.50 (define @t7 () (forall @t6 (_ tptp.mvalid @t4))) % 0.19/0.50 (define @t8 () (=> @t7 (_ tptp.mvalid (_ tptp.mall @t5)))) % 0.19/0.50 (define @t9 () (@list @t3)) % 0.19/0.50 (define @t10 () (forall @t9 @t8)) % 0.19/0.50 (define @t11 () (not @t10)) % 0.19/0.50 (define @t12 () (@var "X" $$unsorted)) % 0.19/0.50 (define @t13 () (@list @t12)) % 0.19/0.50 (define @t14 () (lambda @t13 false)) % 0.19/0.50 (define @t15 () (lambda @t13 true)) % 0.19/0.50 (define @t16 () (@var "U" $$unsorted)) % 0.19/0.50 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.50 (define @t18 () (_ @t17 @t16)) % 0.19/0.50 (define @t19 () (lambda (@list @t17 @t16) (not @t18))) % 0.19/0.50 (define @t20 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.50 (define @t21 () (_ @t20 @t16)) % 0.19/0.50 (define @t22 () (@list @t17 @t20 @t16)) % 0.19/0.50 (define @t23 () (lambda @t22 (or @t18 @t21))) % 0.19/0.50 (define @t24 () (lambda @t22 (and @t18 @t21))) % 0.19/0.50 (define @t25 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.50 (define @t26 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.50 (define @t27 () (@list @t26 @t25 @t1)) % 0.19/0.50 (define @t28 () (lambda @t27 (_ (_ (_ tptp.mor (_ tptp.mnot @t26)) @t25) @t1))) % 0.19/0.50 (define @t29 () (lambda @t27 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t26) @t25)) (_ (_ tptp.mimpl @t25) @t26)) @t1))) % 0.19/0.50 (define @t30 () (@var "Y" $$unsorted)) % 0.19/0.50 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.50 (define @t32 () (_ @t31 @t30)) % 0.19/0.50 (define @t33 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.50 (define @t34 () (_ (_ @t33 @t12) @t30)) % 0.19/0.50 (define @t35 () (@list @t30)) % 0.19/0.50 (define @t36 () (@list @t33 @t31 @t12)) % 0.19/0.50 (define @t37 () (lambda @t36 (forall @t35 (=> @t34 @t32)))) % 0.19/0.50 (define @t38 () (lambda @t36 (exists @t35 (and @t34 @t32)))) % 0.19/0.50 (define @t39 () (@var "W" $$unsorted)) % 0.19/0.50 (define @t40 () (_ @t4 @t39)) % 0.19/0.50 (define @t41 () (forall @t6 @t40)) % 0.19/0.50 (define @t42 () (@list @t3 @t39)) % 0.19/0.50 (define @t43 () (lambda @t42 @t41)) % 0.19/0.50 (define @t44 () (lambda @t42 (exists @t6 @t40))) % 0.19/0.50 (define @t45 () (_ @t31 @t39)) % 0.19/0.50 (define @t46 () (@list @t39)) % 0.19/0.50 (define @t47 () (forall @t46 @t45)) % 0.19/0.50 (define @t48 () (@list @t31)) % 0.19/0.50 (define @t49 () (lambda @t48 @t47)) % 0.19/0.50 (define @t50 () (lambda @t48 (exists @t46 @t45))) % 0.19/0.50 (define @t51 () (not @t45)) % 0.19/0.50 (define @t52 () (lambda @t48 (exists @t46 @t51))) % 0.19/0.50 (define @t53 () (lambda @t48 (forall @t46 @t51))) % 0.19/0.50 (define @t54 () (@var "BOUND_VARIABLE_7792" $$unsorted)) % 0.19/0.50 (define @t55 () (@var "BOUND_VARIABLE_7794" tptp.individuals)) % 0.19/0.50 (define @t56 () (_ @t3 @t55 @t54)) % 0.19/0.50 (define @t57 () (_ @t3 @t2 @t39)) % 0.19/0.50 (define @t58 () (@list @t2 @t39)) % 0.19/0.50 (define @t59 () (forall @t58 @t57)) % 0.19/0.50 (define @t60 () (not @t59)) % 0.19/0.50 (define @t61 () (or @t60 @t56)) % 0.19/0.50 (define @t62 () (forall (@list @t3 @t54 @t55) @t61)) % 0.19/0.50 (define @t63 () (@list @t54 @t55)) % 0.19/0.50 (define @t64 () (forall @t63 @t61)) % 0.19/0.50 (define @t65 () (forall @t63 @t56)) % 0.19/0.50 (define @t66 () (or @t60 @t65)) % 0.19/0.50 (define @t67 () (forall (@list @t39 @t2) @t57)) % 0.19/0.50 (define @t68 () (forall @t6 @t57)) % 0.19/0.50 (define @t69 () (lambda @t46 @t68)) % 0.19/0.50 (define @t70 () (_ @t69 @t39)) % 0.19/0.50 (define @t71 () (forall @t46 @t70)) % 0.19/0.50 (define @t72 () (_ @t31 @t39)) % 0.19/0.50 (define @t73 () (lambda @t48 (forall @t46 @t72))) % 0.19/0.50 (define @t74 () (_ @t5 @t2 @t39)) % 0.19/0.50 (define @t75 () (forall @t6 @t74)) % 0.19/0.50 (define @t76 () (lambda @t46 @t75)) % 0.19/0.50 (define @t77 () (_ (lambda @t42 @t68) @t5)) % 0.19/0.50 (define @t78 () (_ @t4 @t39)) % 0.19/0.50 (define @t79 () (forall @t46 @t78)) % 0.19/0.50 (define @t80 () (_ @t73 @t4)) % 0.19/0.50 (define @t81 () (forall @t6 @t80)) % 0.19/0.50 (define @t82 () (=> @t81 (_ @t73 @t77))) % 0.19/0.50 (define @t83 () (forall @t9 @t82)) % 0.19/0.50 (define @t84 () (@quantifiers_skolemize @t62 0)) % 0.19/0.50 (define @t85 () (forall @t58 (_ @t84 @t2 @t39))) % 0.19/0.50 (define @t86 () (@quantifiers_skolemize @t62 1)) % 0.19/0.50 (define @t87 () (@quantifiers_skolemize @t62 2)) % 0.19/0.50 (define @t88 () (_ @t84 @t87 @t86)) % 0.19/0.50 (define @t89 () (not @t85)) % 0.19/0.50 (define @t90 () (or @t89 @t88)) % 0.19/0.50 (define @t91 () (@list true)) % 0.19/0.50 (define @t92 () (@list @t90)) % 0.19/0.50 (assume @p1 @t11) % 0.19/0.50 (assume @p2 true) % 0.19/0.50 (step @p3 (= tptp.mfalse @t14) :rule refl :args (@t14)) % 0.19/0.50 (step @p4 (= tptp.mtrue @t15) :rule refl :args (@t15)) % 0.19/0.50 (step @p5 (= tptp.mnot @t19) :rule refl :args (@t19)) % 0.19/0.50 (step @p6 (= tptp.mor @t23) :rule refl :args (@t23)) % 0.19/0.50 (step @p7 (= tptp.mand @t24) :rule refl :args (@t24)) % 0.19/0.50 (step @p8 (= tptp.mimpl @t28) :rule refl :args (@t28)) % 0.19/0.50 (step @p9 (= tptp.miff @t29) :rule refl :args (@t29)) % 0.19/0.50 (step @p10 (= tptp.mbox @t37) :rule refl :args (@t37)) % 0.19/0.50 (step @p11 (= tptp.mdia @t38) :rule refl :args (@t38)) % 0.19/0.50 (step @p12 (= tptp.mall @t43) :rule refl :args (@t43)) % 0.19/0.50 (step @p13 (= tptp.mexists @t44) :rule refl :args (@t44)) % 0.19/0.50 (step @p14 (= tptp.mvalid @t49) :rule refl :args (@t49)) % 0.19/0.50 (step @p15 (= tptp.msatisfiable @t50) :rule refl :args (@t50)) % 0.19/0.50 (step @p16 (= tptp.mcountersatisfiable @t52) :rule refl :args (@t52)) % 0.19/0.50 (step @p17 (= tptp.minvalid @t53) :rule refl :args (@t53)) % 0.19/0.50 (step @p18 :rule quant-merge-prenex :args ((= (forall @t9 @t64) @t62))) % 0.19/0.50 (step @p19 :rule alpha_equiv :args (@t65 (@list @t54 @t55) (@list @t39 @t2))) % 0.19/0.50 (step @p20 :rule refl :args (@t60)) % 0.19/0.50 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t66)) % 0.19/0.50 (step @p22 :rule quant-miniscope-or :args ((= @t64 @t66))) % 0.19/0.50 (step @p23 :rule trans :premises (@p22 @p21)) % 0.19/0.50 (step @p24 :rule symm :premises (@p23)) % 0.19/0.50 (step @p25 :rule cong :premises (@p24) :args ((forall @t9 (or @t60 @t67)))) % 0.19/0.50 (step @p26 :rule trans :premises (@p25 @p18)) % 0.19/0.50 (step @p27 :rule bool-impl-elim :args (@t59 @t67)) % 0.19/0.50 (step @p28 :rule cong :premises (@p27) :args ((forall @t9 (=> @t59 @t67)))) % 0.19/0.50 (step @p29 :rule trans :premises (@p28 @p26)) % 0.19/0.50 (step @p30 :rule quant-merge-prenex :args ((= (forall @t46 @t68) @t67))) % 0.19/0.50 (step @p31 :rule beta-reduce :args ((= @t70 @t68))) % 0.19/0.50 (step @p32 :rule cong :premises (@p31) :args (@t71)) % 0.19/0.50 (step @p33 :rule trans :premises (@p32 @p30)) % 0.19/0.50 (step @p34 :rule beta-reduce :args ((= (_ @t73 @t69) @t71))) % 0.19/0.50 (step @p35 :rule trans :premises (@p34 @p33)) % 0.19/0.50 (step @p36 :rule refl :args (@t57)) % 0.19/0.50 (step @p37 :rule refl :args (@t40)) % 0.19/0.50 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t40 @t57))) % 0.19/0.50 (step @p39 :rule symm :premises (@p38)) % 0.19/0.50 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.19/0.50 (step @p41 :rule cong :premises (@p40) :args (@t41)) % 0.19/0.50 (step @p42 :rule beta-reduce :args ((= @t74 @t40))) % 0.19/0.50 (step @p43 :rule cong :premises (@p42) :args (@t75)) % 0.19/0.50 (step @p44 :rule trans :premises (@p43 @p41)) % 0.19/0.50 (step @p45 :rule cong :premises (@p44) :args (@t76)) % 0.19/0.50 (step @p46 :rule beta-reduce :args ((= @t77 @t76))) % 0.19/0.50 (step @p47 :rule trans :premises (@p46 @p45)) % 0.19/0.50 (step @p48 :rule refl :args (@t73)) % 0.19/0.50 (step @p49 :rule ho_cong :premises (@p48 @p47)) % 0.19/0.50 (step @p50 :rule trans :premises (@p49 @p35)) % 0.19/0.50 (step @p51 :rule quant-merge-prenex :args ((= (forall @t6 (forall @t46 @t57)) @t59))) % 0.19/0.50 (step @p52 :rule cong :premises (@p40) :args ((forall @t46 @t40))) % 0.19/0.50 (step @p53 :rule refl :args (@t78)) % 0.19/0.50 (step @p54 :rule cong :premises (@p53) :args (@t79)) % 0.19/0.50 (step @p55 :rule trans :premises (@p54 @p52)) % 0.19/0.50 (step @p56 :rule beta-reduce :args ((= @t80 @t79))) % 0.19/0.50 (step @p57 :rule trans :premises (@p56 @p55)) % 0.19/0.50 (step @p58 :rule cong :premises (@p57) :args (@t81)) % 0.19/0.50 (step @p59 :rule trans :premises (@p58 @p51)) % 0.19/0.50 (step @p60 :rule cong :premises (@p59 @p50) :args (@t82)) % 0.19/0.50 (step @p61 :rule cong :premises (@p60) :args (@t83)) % 0.19/0.50 (step @p62 :rule trans :premises (@p61 @p29)) % 0.19/0.50 (step @p63 :rule cong :premises (@p62) :args ((not @t83))) % 0.19/0.50 (step @p64 :rule refl :args (@t5)) % 0.19/0.50 (step @p65 :rule cong :premises (@p41) :args (@t43)) % 0.19/0.50 (step @p66 :rule trans :premises (@p12 @p65)) % 0.19/0.50 (step @p67 :rule ho_cong :premises (@p66 @p64)) % 0.19/0.50 (step @p68 :rule refl :args (@t72)) % 0.19/0.50 (step @p69 :rule refl :args (@t45)) % 0.19/0.50 (step @p70 :rule cong :premises (@p69 @p68) :args ((= @t45 @t72))) % 0.19/0.50 (step @p71 :rule symm :premises (@p70)) % 0.19/0.50 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.19/0.50 (step @p73 :rule cong :premises (@p72) :args (@t47)) % 0.19/0.50 (step @p74 :rule cong :premises (@p73) :args (@t49)) % 0.19/0.50 (step @p75 :rule trans :premises (@p14 @p74)) % 0.19/0.50 (step @p76 :rule ho_cong :premises (@p75 @p67)) % 0.19/0.50 (step @p77 :rule refl :args (@t4)) % 0.19/0.50 (step @p78 :rule ho_cong :premises (@p75 @p77)) % 0.19/0.50 (step @p79 :rule cong :premises (@p78) :args (@t7)) % 0.19/0.50 (step @p80 :rule cong :premises (@p79 @p76) :args (@t8)) % 0.19/0.50 (step @p81 :rule cong :premises (@p80) :args (@t10)) % 0.19/0.50 (step @p82 :rule cong :premises (@p81) :args (@t11)) % 0.19/0.50 (step @p83 :rule trans :premises (@p82 @p63)) % 0.19/0.50 (step @p84 :rule eq_resolve :premises (@p1 @p83)) % 0.19/0.50 (step @p85 :rule skolemize :premises (@p84)) % 0.19/0.50 (step @p86 :rule bool-double-not-elim :args (@t85)) % 0.19/0.50 (step @p87 :rule refl :args (@t90)) % 0.19/0.50 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or @t90 (not @t89)))) % 0.19/0.50 (step @p89 :rule cnf_or_neg :args (@t90 0)) % 0.19/0.50 (step @p90 :rule eq_resolve :premises (@p89 @p88)) % 0.19/0.50 (step @p91 :rule reordering :premises (@p90) :args ((or @t85 @t90))) % 0.19/0.50 (step @p92 :rule chain_m_resolution :premises (@p91 @p85) :args (@t85 @t91 @t92)) % 0.19/0.50 (step @p93 :rule cnf_or_neg :args (@t90 1)) % 0.19/0.50 (step @p94 :rule chain_m_resolution :premises (@p93 @p85) :args ((not @t88) @t91 @t92)) % 0.19/0.50 (assume-push @p101 @t85) % 0.19/0.50 (step @p96 :rule instantiate :premises (@p92) :args ((@list @t87 @t86))) % 0.19/0.50 (step-pop @p102 :rule scope :premises (@p96)) % 0.19/0.50 (step @p97 :rule process_scope :premises (@p102) :args (@t88)) % 0.19/0.50 (step @p99 :rule implies_elim :premises (@p97)) % 0.19/0.50 (step @p100 false :rule chain_m_resolution :premises (@p99 @p94 @p92) :args (false (@list true false) (@list @t88 @t85))) % 0.19/0.50 ) % 0.19/0.50 % SZS output end Proof % 0.19/0.50 % cvc5 exiting %------------------------------------------------------------------------------