%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO058^4 : TPTP v9.2.1. 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 : n005.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 09:11:54 AM UTC 2026 % Result : Theorem 0.31s 0.57s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO058^4 : TPTP v9.2.1. Released v4.0.0. % 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 : n005.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 23:52:48 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.31/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.31/0.57 % SZS status Theorem % 0.31/0.57 % SZS output start Proof % 0.31/0.57 ( % 0.31/0.57 (declare-sort $$unsorted 0) % 0.31/0.57 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.31/0.57 (declare-const tptp.a (-> $$unsorted Bool)) % 0.31/0.57 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.31/0.57 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.31/0.57 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.31/0.57 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.31/0.57 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.31/0.57 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.irel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.31/0.57 (define tptp.iatom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.31/0.57 (define tptp.inot () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 _let_2)) _let_1))))) % 0.31/0.57 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.31/0.57 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.31/0.57 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.31/0.57 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.31/0.57 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.31/0.57 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iand (_ (_ tptp.iimplies _let_2) _let_3)) (_ (_ tptp.iimplies _let_3) _let_2)) _let_1)))))) % 0.31/0.57 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.31/0.57 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.31/0.57 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.31/0.57 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.31/0.57 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.31/0.57 (define @t1 () (@var "X" $$unsorted)) % 0.31/0.57 (define @t2 () (_ tptp.irel @t1)) % 0.31/0.57 (define @t3 () (@var "Z" $$unsorted)) % 0.31/0.57 (define @t4 () (@var "Y" $$unsorted)) % 0.31/0.57 (define @t5 () (_ @t2 @t4)) % 0.31/0.57 (define @t6 () (_ tptp.ivalid (_ tptp.iatom tptp.a))) % 0.31/0.57 (define @t7 () (not @t6)) % 0.31/0.57 (define @t8 () (@var "U" $$unsorted)) % 0.31/0.57 (define @t9 () (@var "X" (-> $$unsorted Bool))) % 0.31/0.57 (define @t10 () (_ @t9 @t8)) % 0.31/0.57 (define @t11 () (lambda (@list @t9 @t8) (not @t10))) % 0.31/0.57 (define @t12 () (@var "Y" (-> $$unsorted Bool))) % 0.31/0.57 (define @t13 () (_ @t12 @t8)) % 0.31/0.57 (define @t14 () (@list @t9 @t12 @t8)) % 0.31/0.57 (define @t15 () (lambda @t14 (or @t10 @t13))) % 0.31/0.57 (define @t16 () (lambda @t14 (and @t10 @t13))) % 0.31/0.57 (define @t17 () (@var "__flatten_var_0" $$unsorted)) % 0.31/0.57 (define @t18 () (@var "V" (-> $$unsorted Bool))) % 0.31/0.57 (define @t19 () (@var "U" (-> $$unsorted Bool))) % 0.31/0.57 (define @t20 () (lambda (@list @t19 @t18 @t17) (_ (_ (_ tptp.mor (_ tptp.mnot @t19)) @t18) @t17))) % 0.31/0.57 (define @t21 () (@var "P" (-> $$unsorted Bool))) % 0.31/0.57 (define @t22 () (lambda (@list @t21 @t1) (forall (@list @t4) (=> @t5 (_ @t21 @t4))))) % 0.31/0.57 (define @t23 () (@list @t21 @t17)) % 0.31/0.57 (define @t24 () (lambda @t23 (_ @t21 @t17))) % 0.31/0.57 (define @t25 () (_ tptp.mbox_s4 @t21)) % 0.31/0.57 (define @t26 () (lambda @t23 (_ (_ tptp.mnot @t25) @t17))) % 0.31/0.57 (define @t27 () (@var "W" $$unsorted)) % 0.31/0.57 (define @t28 () (@list @t27)) % 0.31/0.57 (define @t29 () (lambda @t28 true)) % 0.31/0.57 (define @t30 () (@var "Q" (-> $$unsorted Bool))) % 0.31/0.57 (define @t31 () (@list @t21 @t30 @t17)) % 0.31/0.57 (define @t32 () (lambda @t31 (_ (_ (_ tptp.mand @t21) @t30) @t17))) % 0.31/0.57 (define @t33 () (_ tptp.mbox_s4 @t30)) % 0.31/0.57 (define @t34 () (lambda @t31 (_ (_ (_ tptp.mor @t25) @t33) @t17))) % 0.31/0.57 (define @t35 () (lambda @t31 (_ (_ (_ tptp.mimplies @t25) @t33) @t17))) % 0.31/0.57 (define @t36 () (_ (_ tptp.iimplies @t30) @t21)) % 0.31/0.57 (define @t37 () (lambda @t31 (_ @t36 @t17))) % 0.31/0.57 (define @t38 () (lambda @t31 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t21) @t30)) @t36) @t17))) % 0.31/0.57 (define @t39 () (lambda @t31 (_ (_ tptp.inot (_ (_ tptp.iequiv @t21) @t30)) @t17))) % 0.31/0.57 (define @t40 () (@var "Phi" (-> $$unsorted Bool))) % 0.31/0.57 (define @t41 () (_ @t40 @t27)) % 0.31/0.57 (define @t42 () (forall @t28 @t41)) % 0.31/0.57 (define @t43 () (@list @t40)) % 0.31/0.57 (define @t44 () (lambda @t43 @t42)) % 0.31/0.57 (define @t45 () (lambda @t43 (exists @t28 @t41))) % 0.31/0.57 (define @t46 () (not @t41)) % 0.31/0.57 (define @t47 () (lambda @t43 (exists @t28 @t46))) % 0.31/0.57 (define @t48 () (lambda @t43 (forall @t28 @t46))) % 0.31/0.57 (define @t49 () (tptp.a @t27)) % 0.31/0.57 (define @t50 () (_ tptp.a @t27)) % 0.31/0.57 (define @t51 () (lambda (@list @t17) (_ tptp.a @t17))) % 0.31/0.57 (define @t52 () (_ @t51 @t27)) % 0.31/0.57 (define @t53 () (forall @t28 @t52)) % 0.31/0.57 (define @t54 () (_ @t40 @t27)) % 0.31/0.57 (define @t55 () (lambda @t43 (forall @t28 @t54))) % 0.31/0.57 (define @t56 () (_ @t24 tptp.a)) % 0.31/0.57 (assume @p1 (forall (@list @t1) (_ @t2 @t1))) % 0.31/0.57 (assume @p2 (forall (@list @t1 @t4 @t3) (=> (and @t5 (_ (_ tptp.irel @t4) @t3)) (_ @t2 @t3)))) % 0.31/0.57 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.31/0.57 (assume @p4 @t6) % 0.31/0.57 (assume @p5 @t7) % 0.31/0.57 (assume @p6 true) % 0.31/0.57 (step @p7 (= tptp.mnot @t11) :rule refl :args (@t11)) % 0.31/0.57 (step @p8 (= tptp.mor @t15) :rule refl :args (@t15)) % 0.31/0.57 (step @p9 (= tptp.mand @t16) :rule refl :args (@t16)) % 0.31/0.57 (step @p10 (= tptp.mimplies @t20) :rule refl :args (@t20)) % 0.31/0.57 (step @p11 (= tptp.mbox_s4 @t22) :rule refl :args (@t22)) % 0.31/0.57 (step @p12 (= tptp.iatom @t24) :rule refl :args (@t24)) % 0.31/0.57 (step @p13 (= tptp.inot @t26) :rule refl :args (@t26)) % 0.31/0.57 (step @p14 (= tptp.itrue @t29) :rule refl :args (@t29)) % 0.31/0.57 (step @p15 (= tptp.iand @t32) :rule refl :args (@t32)) % 0.31/0.57 (step @p16 (= tptp.ior @t34) :rule refl :args (@t34)) % 0.31/0.57 (step @p17 (= tptp.iimplies @t35) :rule refl :args (@t35)) % 0.31/0.57 (step @p18 (= tptp.iimplied @t37) :rule refl :args (@t37)) % 0.31/0.57 (step @p19 (= tptp.iequiv @t38) :rule refl :args (@t38)) % 0.31/0.57 (step @p20 (= tptp.ixor @t39) :rule refl :args (@t39)) % 0.31/0.57 (step @p21 (= tptp.ivalid @t44) :rule refl :args (@t44)) % 0.31/0.57 (step @p22 (= tptp.isatisfiable @t45) :rule refl :args (@t45)) % 0.31/0.57 (step @p23 (= tptp.icountersatisfiable @t47) :rule refl :args (@t47)) % 0.34/0.57 (step @p24 (= tptp.iinvalid @t48) :rule refl :args (@t48)) % 0.34/0.57 (step @p25 :rule refl :args (@t49)) % 0.34/0.57 (step @p26 :rule refl :args (@t50)) % 0.34/0.57 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t50 @t49))) % 0.34/0.57 (step @p28 :rule symm :premises (@p27)) % 0.34/0.57 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 0.34/0.57 (step @p30 :rule cong :premises (@p29) :args ((forall @t28 @t50))) % 0.34/0.57 (step @p31 :rule beta-reduce :args ((= @t52 @t50))) % 0.34/0.57 (step @p32 :rule cong :premises (@p31) :args (@t53)) % 0.34/0.57 (step @p33 :rule trans :premises (@p32 @p30)) % 0.34/0.57 (step @p34 :rule beta-reduce :args ((= (_ @t55 @t51) @t53))) % 0.34/0.57 (step @p35 :rule trans :premises (@p34 @p33)) % 0.34/0.57 (step @p36 :rule beta-reduce :args ((= @t56 @t51))) % 0.34/0.57 (step @p37 :rule refl :args (@t55)) % 0.34/0.57 (step @p38 :rule ho_cong :premises (@p37 @p36)) % 0.34/0.57 (step @p39 :rule trans :premises (@p38 @p35)) % 0.34/0.57 (step @p40 :rule cong :premises (@p39) :args ((not (_ @t55 @t56)))) % 0.34/0.57 (step @p41 :rule refl :args (tptp.a)) % 0.34/0.57 (step @p42 :rule ho_cong :premises (@p12 @p41)) % 0.34/0.57 (step @p43 :rule refl :args (@t54)) % 0.34/0.57 (step @p44 :rule refl :args (@t41)) % 0.34/0.57 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t41 @t54))) % 0.34/0.57 (step @p46 :rule symm :premises (@p45)) % 0.34/0.57 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.34/0.57 (step @p48 :rule cong :premises (@p47) :args (@t42)) % 0.34/0.57 (step @p49 :rule cong :premises (@p48) :args (@t44)) % 0.34/0.57 (step @p50 :rule trans :premises (@p21 @p49)) % 0.34/0.57 (step @p51 :rule ho_cong :premises (@p50 @p42)) % 0.34/0.57 (step @p52 :rule cong :premises (@p51) :args (@t7)) % 0.34/0.57 (step @p53 :rule trans :premises (@p52 @p40)) % 0.34/0.57 (step @p54 :rule eq_resolve :premises (@p5 @p53)) % 0.34/0.57 (step @p55 :rule trans :premises (@p51 @p39)) % 0.34/0.57 (step @p56 :rule eq_resolve :premises (@p4 @p55)) % 0.34/0.57 (step @p57 false :rule contra :premises (@p56 @p54)) % 0.34/0.57 ) % 0.34/0.57 % SZS output end Proof % 0.34/0.57 % cvc5 exiting %------------------------------------------------------------------------------